Modification de Elasticity and its application

Based on a course by Federica Sbergami<ref>[https://www.unige.ch/gsem/en/research/faculty/all/federica-sbergami/ Page personnelle de Federica Sbergami sur le site de l'Université de Genève]</ref><ref>[https://www.unine.ch/irene/home/equipe/federica_sbergami.html Page personnelle de Federica Sbergami sur le site de l'Université de Neuchâtel]</ref><ref>[https://www.researchgate.net/scientific-contributions/14836393_Federica_Sbergami Page personnelle de Federica Sbergami sur Research Gate]</ref> 

{{Translations
| fr = Les élasticités et ses applications
| es = La elasticidad y sus aplicaciones
| it = Elasticità e loro applicazioni
| pt = Elasticidades e suas aplicações
| de = Die Elastizitäten und ihre Anwendungen
}}

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|[[Introduction to microeconomics]]
|[[Microeconomics Principles and Concept]] ● [[Supply and demand: How markets work]] ● [[Elasticity and its application]] ● [[Supply and demand: Markets and welfare]] ● [[The economics of the public sector]] ● [[The costs of production]] ● [[Firms in competitive markets]] ● [[Monopoly]] ● [[Oligopoly]] ● [[Monopolisitc competition]]
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}}

Elasticity in economics is a fundamental concept that measures the sensitivity of the quantity demanded or offered of a good or service to changes in its determinants, such as price. It is expressed as a percentage to indicate the responsiveness of demand or supply to changes in price or other factors.

Elasticity can be of different types. For example, the price elasticity of demand measures the percentage change in quantity demanded in response to a percentage change in price. When this elasticity is greater than 1, demand is said to be elastic, i.e. sensitive to price changes. If it is less than 1, demand is inelastic, indicating low sensitivity to price changes. Similarly, the price elasticity of supply focuses on the quantity offered and its responsiveness to price changes. There are also other forms of elasticity, such as the elasticity of demand in relation to income or the prices of substitute and complementary goods.

Understanding elasticity is crucial for businesses and policy-makers. Companies use it to set prices and anticipate sales. For example, the price of a product with inelastic demand may increase without leading to a significant drop in the quantity sold. Governments use elasticity to predict the impact of taxes, subsidies and other policies on markets.

Elasticity is generally measured as the ratio of the percentage change in quantity demanded or offered to the percentage change in price or other factors. On a graph, the slope of the demand or supply curve can provide clues about elasticity. A flat demand curve suggests high elasticity, while a steeper curve indicates inelasticity. Let's take a concrete example: if the price of a good rises by 10% and the quantity demanded falls by 20%, the price elasticity of demand would be -2 (20% / 10%). This high responsiveness of demand to price indicates a high elasticity.

= The need to understand elasticity =

Elasticity meets a fundamental need in economics: to understand and measure how the quantity demanded of a product or service reacts to changes in price. This concept is crucial for both businesses and policy-makers, as it enables consumer behaviour in response to price changes to be analysed and predicted.

As we move along the demand curve, we observe how the quantity demanded changes in response to a variation in price. This observation is essential for determining the price elasticity of demand. The slope of the demand curve plays a key role here. A relatively flat demand curve indicates a high sensitivity of quantity demanded to price variations, thus characterising elastic demand. Conversely, a steep demand curve suggests that the quantity demanded is relatively insensitive to price changes, indicating inelastic demand. This information is vital for companies when determining their pricing strategies. For example, if a company knows that demand for its product is elastic, a small price increase could lead to a significant decrease in the quantity demanded, potentially affecting its revenues. On the other hand, for a product with inelastic demand, the company could raise prices without fearing a significant drop in demand.

For governments and policy-makers, understanding elasticity is just as important. It helps to predict the economic consequences of taxes, subsidies and other policies. For example, imposing a tax on a product with a high elasticity could lead to a considerable drop in demand, whereas the same tax on a product with a low elasticity might not have such a marked impact on the quantity demanded.

Simply knowing the slope of the demand function is not enough to adequately express the sensitivity of the response of demand to price changes. There are two main reasons for this. Firstly, the slope of the demand curve is influenced by the units of measurement used, which can make comparisons between different goods difficult. For example, if demand for coffee increases by 10 cups following a price reduction of 1 franc, this information is specific to that context and those units. Comparing this variation with that of another good measured in metres or hours is complex because the units are not directly comparable. This can lead to erroneous or misleading interpretations. Secondly, the variation in absolute terms (for example, 10 cups or 1 franc) gives no indication of the relative importance of this variation. Without knowing the initial level of the price or quantity requested, it is difficult to judge whether a variation is significant. For example, an increase of 10 cups may be considerable if the initial demand was for 20 cups, but relatively minor if the initial demand was for 1000 cups. Similarly, a change of 1 franc may be significant for a cheap product but insignificant for an expensive one.

This is where elasticity comes into play, as it measures relative rather than absolute variations. Elasticity provides a standardised measure of the responsiveness of demand, which is independent of units of measurement and takes account of the proportionality of variations in relation to initial price and quantity levels. In this way, it provides a better understanding of the sensitivity of demand and enables more meaningful comparisons to be made between different products or services.

Elasticity is an essential tool in economics because it measures the reaction of buyers and sellers to changes in market conditions, while avoiding the problems associated with using absolute measures such as the slope of the demand curve. Here's how elasticity addresses these problems:

* Independence from units of measurement: Elasticity is expressed in relative terms, making it independent of the units of measurement used. For example, the price elasticity of demand calculates the percentage change in quantity demanded relative to the percentage change in price. This approach allows meaningful comparisons to be made between different goods or services, even if they are measured in different units (such as cups, metres or hours). 
* Putting variations into context : Elasticity provides a framework for assessing the relative importance of changes in quantity and price. Rather than focusing on absolute changes (such as an increase of 10 cups of coffee), elasticity allows these changes to be understood in proportion to initial levels. 
* Universal applicability: Elasticity can be used to analyse various types of markets and products, providing a standardised method for studying economic behaviour. Whether we are examining the response of consumers to changes in the price of consumer goods, or the response of businesses to changes in the cost of raw materials, elasticity offers a consistent way of assessing these responses.

In short, elasticity is a valuable tool for economists and decision-makers because it offers a standardised, relative measure of the responsiveness of demand and supply, which takes account of the specific features of each market and product, while avoiding the pitfalls of absolute measures. This makes it possible to better understand how economic players react to changes and to develop more effective and better-informed strategies or policies.

= Analyse des élasticités de la demande =

== Price elasticity of demand ==

Price elasticity of demand is a central measure in economics that quantifies how the quantity demanded of a good or service reacts to a change in its price. The formula for calculating the price elasticity of demand is the ratio between the percentage change in the quantity demanded and the percentage change in the price of the good.

Here is the mathematical formula for the price elasticity of demand (Ep):

<math> Ep = \frac{% \text{ change in quantity demanded}}{% \text{ change in price}} </math>

To calculate the percentage change, we generally use the following formula:

<math>% \text{change} = \frac{\text{Change}}{\text{Initial value}} \times 100 </math>.

In the context of price elasticity of demand, this means: *For quantity demanded: The percentage change in quantity demanded is calculated by dividing the change in quantity demanded by the initial quantity demanded, then multiplying by 100. *For price: Similarly, the percentage change in price is calculated by dividing the change in price by the initial price, then multiplying by 100.

It is important to note that the price elasticity of demand can be positive or negative, but it is generally negative because the quantity demanded tends to fall when the price rises, and vice versa. However, the negative sign is often omitted in practice, as it is generally understood that the elasticity of demand is inversely proportional to price.

Price elasticity of demand allows companies and policy makers to understand consumer sensitivity to price changes, which is crucial for pricing, marketing and economic policy decisions.

For discrete variations:

<math>\epsilon_p^d = \frac{\text{percentage change in quantity requested}}{\text{percentage change in price}}</math> = <math>\frac{\frac{\Delta q^d}{q^d}}{\frac{\Delta p}{p}}</math> = <math>\frac{\Delta q^d}{\Delta p} \times \frac{p}{q^d} = \frac{\frac{(q_1^d - q_0^d)}{q_0^d}}{\frac{p_1 - p_0}{p_0}} < 0</math>.

This formula represents the price elasticity of demand (<math>epsilon_p^d</math>) in terms of discrete variations. It uses the absolute differences in quantities demanded (<math>q_1^d - q_0^d</math>) and prices (<math>p_1 - p_0</math>) to measure relative changes, and then determines the ratio of these relative changes. The sign "< 0" at the end indicates that, generally, the price elasticity of demand is negative, reflecting the inverse relationship between price and quantity demanded.

For infinitesimal variations (or at the margin), the formula for the price elasticity of demand is as follows:

<math>\epsilon_p^d = \frac{\text{percentage change in quantity requested}}{\textrm{percentage change in price}}</math> = <math>\frac{\partial q^d}{\partial p} \times \frac{p}{q^d} < 0</math>.

In this expression, <math>\epsilon_p^d</math> represents the price elasticity of demand. The term <math>\frac{\partial q^d}{\partial p}</math> is the partial derivative of quantity demanded with respect to price, indicating how quantity demanded changes instantaneously with a small change in price. The product of this partial derivative and the ratio <math>\frac{p}{q^d}</math> (price to quantity demanded) gives the price elasticity of demand. The sign "< 0" at the end indicates that this elasticity is generally negative, in accordance with the law of demand, which states that the quantity demanded of a good generally decreases when its price increases.

== Factors influencing the price elasticity of demand ==

=== Impact of the availability of close substitutes === 

When there are close substitutes for a good or service, demand for that good or service tends to be more elastic. This means that consumers are more likely to change their choice in response to changes in price or other factors.

Consider the demand for a heli-skiing holiday in Alaska compared to a skiing holiday in Chamonix. If Chamonix ski holidays are seen as a close substitute for Alaskan heli-ski holidays, then a significant increase in the price of Alaskan heli-ski holidays could lead to a significant fall in demand for them. Consumers, faced with this price increase, might turn to Chamonix ski holidays, which offer a similar experience at a potentially lower cost.

This example demonstrates how the presence of close substitutes makes consumers more flexible in their choices, encouraging them to opt for alternatives if the price or other conditions of the initial good or service become less attractive. As a result, companies and service providers need to be aware of the presence of close substitutes in the market when making decisions about pricing or promoting their products or services.

=== Contrast between essential goods and luxury goods === 

An important distinction in economics is the difference between essential goods and luxury goods in terms of elasticity of demand.

Basic necessities, such as food, electricity, medicine and basic clothing, generally have inelastic demand. This means that even if the prices of these goods rise or fall significantly, the quantity demanded does not change much. Consumers continue to buy these products because they are essential to everyday life. For example, demand for food remains relatively constant despite price fluctuations, because people need to eat whatever the economic situation.

In contrast, luxury goods such as Champions League tickets have an elastic demand. These goods are not essential, and their purchase is often influenced by consumers' disposable income. If the price of tickets to a prestigious sporting event rises considerably, many people will choose not to buy them because there are many other entertainment options available. The quantity demanded for these goods is therefore very sensitive to price variations.

It is important to note that the categorisation of a good as a necessity or luxury can depend on consumer preferences and income levels. What is considered a luxury for one person may be a necessity for another. This distinction is therefore not always clearly defined and can vary according to individual circumstances and the economic context.

=== Influence of market size on demand === 

Market size is an important factor influencing the elasticity of demand. In general, the larger the market, the more inelastic demand tends to be. This is partly due to the diversity and availability of alternatives in large markets, as well as the variety of consumer needs and preferences.

For example, consider the difference between the elasticity of demand for meat in general and for chicken meat specifically. Meat, as a general category, encompasses various types of product such as chicken, beef, pork, etc. In a large market where these different types of meat are available, demand for the overall meat category can be relatively inelastic. This means that price changes in one type of meat may lead consumers to switch to other types, but they will probably continue to consume a certain amount of meat.

On the other hand, demand for a specific type of meat, such as chicken, can be more elastic, especially in smaller or local markets. In a small market or in a region where preferences for chicken are strong and substitutes less available, an increase in the price of chicken could lead to a significant drop in demand, as consumers may not find suitable alternatives.

Market size and definition therefore play a crucial role in determining the elasticity of demand. Local markets, with more limited options and more specific preferences, are likely to have a higher elasticity of demand than larger, more diversified markets.

=== Temporal dynamics of demand responses === 

Short-term demand functions are more elastic than long-term ones:
* Short-Term Demand Functions: In the short term, consumers and businesses often have less flexibility to adjust their behaviour and choices in response to price changes. As a result, demand is generally more inelastic in the short term. The options for substituting a product or changing consumption are limited by habits, contracts, the costs of change, or the absence of immediate alternatives. 
* Long-Term Demand Functions: In the long term, consumers and businesses have more time to adapt to price changes. They can find substitutes, change their consumption habits, or invest in new technologies. As a result, demand becomes more elastic in the long term, as people have more opportunities and means to react to price changes.

The example of energy demand for oil is a good illustration of this concept. In the short term, say over the next month, consumers and industries have limited options for doing without oil or finding energy alternatives. They will probably continue to consume similar quantities of oil even if prices rise, making demand inelastic. On the other hand, over a 10-year timescale, consumers and industry can make significant adaptations. They may invest in more fuel-efficient vehicles, develop and adopt alternative energy sources, or change their energy consumption habits. These adjustments make the demand for oil energy more elastic in the long term, as price variations will lead to greater changes in the quantity demanded.

When a good accounts for a large proportion of a consumer's budget, demand for that good is generally more sensitive to price changes, resulting in higher elasticity. This is because changes in the price of these goods have a significant impact on consumers' overall finances, forcing them to adjust their purchasing behaviour.

Let's take the example of rent versus matches. Rent generally makes up a substantial proportion of a household's monthly budget. Consequently, a significant increase in rent can force households to reconsider their housing situation, look for cheaper alternatives, or make adjustments in other areas of expenditure. This means that demand for housing is relatively elastic: changes in price tend to lead to significant changes in the amount of housing demanded. On the other hand, matches represent a very small proportion of the total budget. Even if the price of matches doubles or triples, the impact on a household's overall budget is minimal. As a result, consumers are less likely to change their purchasing behaviour in response to such price variations. Demand for products such as matches is therefore inelastic: price changes do not lead to large variations in the quantity demanded.

In short, the greater the share of a good in the budget, the more consumers will pay attention to its price and the more they will be prepared to look for alternatives or modify their consumption in response to price changes. This reflects the greater sensitivity of demand for these goods in relation to their weight in consumers' budgets.

== Illustration of price elasticity of demand ==

Which of these two individuals has a more elastic demand?

{| class="wikitable"
!Price 
!Quantity requested by Individual A 
!Quantity requested by Individual B
|-
|1
|20
|100
|-
|2
|15
|80
|-
|4
|10
|60
|-
|8
|5
|50
|} 


To determine which of the two individuals has a more elastic demand, we need to examine the price elasticity of demand of each. The price elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Let's look at the following data: 
*For Individual A: When the price increases from 1 to 8 (an increase of 700%), the quantity demanded decreases from 20 to 5 (a decrease of 75%). Price elasticity of demand for Individual A = (75% / 700%) = approximately 0.
* For Individual B: When the price rises from 1 to 8 (an increase of 700%), the quantity demanded falls from 100 to 50 (a decrease of 50%). Price elasticity of demand for Individual B = (50% / 700%) = approximately 0.071.

In this example, Individual A shows a greater percentage decrease in the quantity demanded, compared with Individual B, for the same price increase. This means that Individual A's demand is more elastic than Individual B's. It is important to note that even though in absolute terms Individual B reduces his consumption by greater quantities, it is the percentage change in relation to initial consumption and in response to the price variation that determines elasticity. Thus, even with smaller absolute reductions, Individual A has a proportionally stronger reaction to price changes, indicating a greater elasticity of demand.

To calculate the price elasticity of demand for the ice cream in the example, we will use the following formula. Here is the detailed calculation: 
#Price change: The price increases from CHF 2 to CHF 2.20. This represents an increase of CHF 0.20, which in percentage terms is <math>\frac{0.20}{2} = 0.10</math> or 10%. #Change in quantity demanded: The quantity demanded decreases from 10 to 8 cones. This represents a decrease of 2 cones, which in percentage terms is <math>\frac{2}{10} = 0.20</math> or 20%. 
#Calculation of the price elasticity of demand:
<math>\epsilon_p^d = \frac{\text{percentage change in quantity requested}}{\text{percentage change in price}} = \frac{-0.20}{0.10} = -2</math>

The price elasticity of demand for ice cream in this example is -2. This means that for every 1% increase in price, the quantity demanded falls by 2%. An elasticity of -2 indicates relatively elastic demand, where the quantity demanded is fairly sensitive to changes in price.

Elasticity calculated at the mean point is often preferred to avoid the problem of asymmetry, where elasticity calculated from two points differs depending on whether we are measuring the effect of a price increase or decrease. Here is the formula:

<math>\epsilon_p^d = \frac{\frac{\Delta q^d}{\bar{q^d}}}{\frac{\Delta p}{\bar{p}}} = \frac{\frac{q_1^d - q_0^d}{\frac{q_1^d + q_0^d}{2}}}{\frac{p_1 - p_0}{\frac{p_1 + p_0}{2}}}</math>

In this formula, <math>epsilon_p^d</math> is the price elasticity of demand. <math>\Delta q^d</math> is the change in quantity demanded, and <math>\Delta p</math> is the change in price. The terms <math>\bar{q^d}</math> and <math>\bar{p}</math> represent the averages of quantities demanded and prices before and after the change, respectively. This method of calculation provides a measure of elasticity that is more representative over the whole interval under consideration.

In the example, the formula for the price elasticity of demand at the average point is used to calculate the elasticity of demand for a specific change in quantity and price. Here is the formula:

<math>\epsilon_p^d = \frac{\frac{8 - 10}{\frac{8 + 10}{2}}}{\frac{2.20 - 2}{\frac{2.20 + 2}{2}}} = \frac{\frac{-2}{9}}{\frac{0.2}{2.1}} = -2.3</math>

In this formula, elasticity is calculated by taking the average of quantities and prices before and after the change, which gives a more general measure of the responsiveness of demand to price changes. The result, -2.3, indicates relatively elastic demand, meaning that the quantity demanded is sensitive to price changes.

When the price elasticity of demand (<math>\epsilon_p^d</math>) is known, it can be used to predict the percentage change in quantity demanded (<math>\frac{\Delta q^d}{q_d}</math>) as a function of a percentage change in price (<math>\frac{\Delta p}{p}</math>). Here's the formula:

<math>\frac{\Delta q^d}{q_d} = \epsilon_p^d \cdot \frac{\Delta p}{p}</math>

In this formula, <math>\Delta q^d</math> represents the change in quantity demanded, <math>q_d</math> is the initial quantity demanded, <math>\Delta p</math> is the change in price, and <math>p</math> is the initial price. Multiplying the price elasticity of demand by the percentage change in price gives the expected percentage change in quantity demanded. This relationship is fundamental in economics for understanding how price changes affect the quantities demanded on the market.

In the example, the price elasticity of demand used to calculate the percentage change in quantity demanded following a price increase of 20% is 20%. With a price elasticity of demand of -1.5, here is the calculation:

If the price increases by 20% and <math>\epsilon_p^d = -1.5</math>, the percentage change in quantity demanded is calculated as follows:

<math>\frac{\Delta q^d}{q_d} = -1.5 \cdot 0.2 = -0.3</math>

This means that the quantity demanded falls by 30% in response to a 20% increase in price. This substantial fall reflects relatively elastic demand, where changes in price lead to significant variations in quantity demanded.

== Meaning of absolute price elasticity ==

The price elasticity of demand is often expressed as an absolute value, because although this elasticity is generally negative (following the law of demand which states that the quantity demanded decreases when the price increases), it is common practice in economics to refer to elasticity in terms of its absolute value to make it easier to understand and compare. Here is the formula:

<math>\left| \epsilon_p^d \right| = \frac{\frac{\Delta Q^d}{Q^d}}{\frac{\Delta P}{P}} \geq 0</math>

In this expression, <math>\left| \epsilon_p^d \right|</math> is the absolute value of the price elasticity of demand. <math>\Delta Q^d</math> is the change in quantity demanded, <math>Q^d</math> is the initial quantity demanded, <math>\Delta P</math> is the change in price, and <math>P</math> is the initial price. This notation emphasises the magnitude of the response of quantity demanded to changes in price, irrespective of the direction (increase or decrease) of that response.

When we talk about the price elasticity of demand, a value of -2 means that demand is more elastic (or sensitive to price changes) than a value of -1.5, even though -2 is mathematically smaller than -1.5. Using absolute values, we can say that the price elasticity of -2 (which becomes 2 in absolute value) is greater than -1.5 (which becomes 1.5 in absolute value). This allows us to communicate more clearly that demand with a price elasticity of -2 is more reactive to price changes than demand with a price elasticity of -1.5.

Using absolute values avoids any confusion linked to the negative sign and makes it easier to understand the elasticity. A higher absolute value elasticity indicates greater sensitivity of quantities demanded to price changes, regardless of the negative sign associated with the price elasticity of demand according to the law of demand.

== Diversity of price elasticity curves for demand ==

[[Fichier:Différentes courbes de l’élasticité-prix de la demande 1.png|400px|vignette|center]]

Each of these graphs illustrates a specific type of reaction of the quantity demanded to a change in price, i.e. different types of elasticity of demand.

(a) Perfectly inelastic demand: The first graph shows a vertical demand curve. This indicates that the quantity demanded remains constant (here at 100 units) regardless of price changes. This could be the case for essential goods for which there are no substitutes, such as certain life-saving drugs.

(b) Perfectly elastic demand: The second graph shows a horizontal demand curve at a price level of €4. This means that consumers are prepared to buy an infinite quantity at this price, but will not demand anything if the price rises above €4. This case can occur in highly competitive markets where consumers can easily find close substitutes if the price rises even slightly.

(c) Inelastic demand: The third graph shows a relatively steep demand curve, indicating that the quantity demanded does not vary much in response to a price change. In this example, a price increase of 22% only leads to a decrease in quantity demanded of 11%. This can happen for necessary goods for which consumers cannot easily reduce their consumption, even if the price increases.

(d) Elastic demand: The last graph shows a demand curve that is relatively flat, indicating that the quantity demanded is very sensitive to changes in price. Here, a 22% increase in price causes a 67% decrease in the quantity demanded. This type of demand often occurs for luxury goods or goods for which there are many substitutes.

Each of these graphs helps to understand how price variations affect quantity demanded and are essential for pricing and economic policy decisions. They also illustrate the importance of elasticity for companies when assessing the potential impact of price changes on their revenues and on the quantity sold.

=== Extreme demand elasticity scenarios ===

==== Case of perfectly inelastic demand ==== 

When we speak of '''perfectly inelastic demand''', this means that the quantity demanded of a good or service does not change, regardless of price variations. In this case, the price elasticity of demand is equal to zero :

<math>\epsilon_p^d = 0</math>

In a situation of perfectly inelastic demand, the demand curve is vertical on a price-quantity graph. This reflects a situation where consumers are willing to buy the same quantity of the good or service, regardless of its price. Typical examples of goods with perfectly inelastic demand include essential medicines for which there are no substitutes, or other absolutely necessary goods and services for which consumers have no alternative.

==== Case of perfectly elastic demand ==== 

In the case of '''perfectly elastic demand''', the slightest change in price leads to an extreme variation in the quantity demanded, which can range from zero to infinity. This is represented by a price elasticity of demand equal to minus infinity :

<math>\epsilon_p^d = -\infty</math>

In this situation, the demand curve is horizontal on a price-quantity graph. This means that consumers are willing to buy an infinite quantity of the good or service at a given price, but the slightest increase in price will cause demand to fall to zero. Situations of perfectly elastic demand are rare in reality, but they can occur in certain highly competitive markets where goods are considered to be perfectly substitutable and consumers are extremely sensitive to price variations.

=== Intermediate elasticity of demand scenarios ===

==== Characterisation of inelastic demand ====

In the case of '''inelastic demand''', demand is not very responsive to changes in price. This means that the quantity demanded varies less than proportionally to the variation in price. In mathematical terms, and using the absolute value to express the price elasticity of demand, this translates into an elasticity of less than 1 :

<math>\left| \epsilon_p^d \right| < 1</math>

Inelastic demand is characteristic of goods and services that are considered necessary or for which there are few close substitutes. For example, consumers will continue to buy these goods even if their price rises, because they cannot easily replace them with other products. As a result, price changes have a relatively small impact on the quantity demanded.

==== Identifying elastic demand ==== 

An '''elastic demand''' is characterised by a very high responsiveness of quantity demanded to price changes. This means that the quantity demanded varies more than proportionally to the variation in price. Mathematically, and using the absolute value to express the price elasticity of demand, a demand is considered elastic when the elasticity is greater than 1 :

<math>\left| \epsilon_p^d \right| > 1</math>

In the case of elastic demand, consumers are very sensitive to changes in price. If the price rises, they will substantially reduce their consumption of the good or service, and conversely, if the price falls, their consumption will increase substantially. This type of demand is typical for luxury goods and services or for those with many close substitutes.

==== Understanding demand with unit elasticity ==== 
A '''demand with unit elasticity''' occurs when the percentage change in quantity demanded is exactly equal to the percentage change in price. In mathematical terms, this translates into a price elasticity of demand of absolute value equal to 1 :

<math>\left| \epsilon_p^d \right| = 1</math>

In the case of unit elasticity, total changes in income and expenditure remain the same despite changes in price, because any increase or decrease in price is exactly offset by an inverse change in quantity demanded. This is often illustrated by an equilateral hyperbola in a price-quantity graph.

The Cobb-Douglas utility function is an example where the elasticity of demand is often unitary. This type of utility function, widely used in economics, implies that consumers allocate their spending between different goods in such a way that the share of each good in the total budget remains constant, resulting in a price elasticity of demand of absolute value equal to 1.

== Overview of elasticity concepts ==

[[Fichier:Élasticités en résumé 1.png|400px|vignette|centré]]

The table illustrates the nuances of demand responsiveness to price changes, focusing on the effect of a 1% price increase on the quantity demanded. When demand for a good or service is perfectly inelastic, such an increase does not lead to any change in the quantity purchased. This is generally the case for essential goods that consumers cannot do without, such as certain medicines.

If demand is inelastic, which translates into an elasticity of between 0 and 1, the quantity demanded decreases only slightly when there is a price increase - less than the increase itself. For these types of goods, consumers are likely to continue buying almost the same quantity despite a price increase, because there are no readily available substitutes or because they are considered necessary.

When demand has unit elasticity, the quantity demanded varies in exactly the same proportion as the price. If the price rises by 1%, the quantity demanded falls by 1%. Total consumer spending on the good or service remains constant. This means that an increase in price is exactly offset by a decrease in quantity, which could be the case for goods for which consumers have a fixed budget.

Elastic demand occurs when the elasticity is greater than 1. In this scenario, a 1% increase in price leads to a reduction in quantity demanded of more than 1%. Consumers are therefore very sensitive to price variations, significantly reducing their consumption or turning to other alternatives. This is often characteristic of luxury or non-essential goods, where consumers can easily change their purchasing habits.

Finally, perfectly elastic demand, where elasticity is infinite, means that any increase in price, however small, will reduce the quantity demanded to zero. This suggests that at a certain price, consumers will buy as much as they can, but at a higher price, they will buy nothing. Although rare in practice, this can happen in markets with perfectly substitutable products where the slightest change in price can lead consumers to opt for another product.

Understanding these concepts is vital for companies in their pricing strategy and for economists studying market dynamics. It makes it possible to predict how price variations can influence consumption patterns and, consequently, overall demand for a good or service.

== Elasticity in linear demand functions ==

To calculate the price elasticity of demand for a linear demand function, we use the following formula:

<math>epsilon_p^d = \frac{\partial q^d}{\partial p} \times \frac{p}{q^d}</math>

Using the given linear demand function <math>q^d = 10 - 2p</math>, we find that the derivative of quantity demanded with respect to price (<math>\frac{\partial q^d}{\partial p}</math>) is -2. This represents the slope of the demand function.

Then, for a price (<math>p</math>) of 1, the quantity demanded (<math>q^d</math>) is <math>10 - 2 <times 1 = 8</math>.

Inserting these values into the formula, the price elasticity of demand is calculated as follows:

<math>\epsilon_p^d = -2 \times \frac{1}{8}</math>

This gives:

<math>\epsilon_p^d = -0.25</math>

So the price elasticity of demand at a price of 1 for this linear demand function is -0.25. This means that for a 1% increase in price, the quantity demanded would fall by 0.25%. This value of price elasticity indicates inelastic demand at this price level, as the quantity demanded changes less than proportionally to the change in price.

To calculate the price elasticity of demand when the market price is 4, we will use the same linear demand function given by <math> q^d = 10 - 2p </math>. First, we determine the quantity demanded at this price:

<math> q^d = 10 - 2 \times 4 = 10 - 8 = 2 </math>

Now we apply the price elasticity of demand formula with the market price (p) of 4 and the quantity demanded (<math>q^d</math>) of 2 :

<math> \epsilon_p^d = \frac{\partial q^d}{\partial p} \times \frac{p}{q^d} = -2 \times \frac{4}{2} </math>

Performing the calculation:

<math> \epsilon_p^d = -2 \times 2 = -4 </math>

This means that the price elasticity of demand at a market price of 4 is -4. In absolute terms, this indicates highly elastic demand. For every 1% increase in price, the quantity demanded falls by 4%. This high level of elasticity indicates that consumers are very sensitive to price changes at this price level.

Along a linear demand curve, the price elasticity of demand is not constant but varies at different points along the curve. This is because the elasticity depends not only on the slope of the demand curve (which is constant for a linear function), but also on the ratio of price to quantity demanded at each point. The price elasticity of demand is calculated as the product of the slope of the demand curve and the ratio of price to quantity demanded at the specific point. For a linear demand curve, where the slope is constant, the elasticity becomes greater in absolute value as you move up the curve (where the price is higher and the quantity demanded is lower). This means that demand becomes more elastic in absolute terms as the price increases.

It is important not to confuse elasticity with slope, although they are related. Slope is a measure of the absolute change in quantity relative to the absolute change in price (ΔQ/ΔP), while elasticity measures the relative change in quantity relative to the relative change in price (percentage change in Q relative to percentage change in P). In simple terms, slope is a linear measure while elasticity is a relative measure. This distinction is crucial in economics, as it affects how companies set their prices and how consumers react to price changes. For example, even if two products have the same slope of demand, their elasticities can be very different because of differences in price levels and quantities demanded. This can have significant implications for pricing strategy and economic policy decision-making.

== Relation entre élasticité-prix de la demande et les dépenses totales ==
The link between the price elasticity of demand and total expenditure (or total revenue) is a fundamental aspect of economic theory. Consumers' total expenditure on a good is the product of the price and the quantity purchased (<math>p \times q</math>). The price elasticity of demand helps us to understand how changes in price affect this total expenditure.

When prices fall, there are two opposing effects:
* Price effect: Total expenditure decreases because the price is lower 
* Quantity effect: Total expenditure increases because more units are sold, provided that consumers react to lower prices by increasing their quantity demanded.

The overall effect on total expenditure depends on the price elasticity of demand:
* If demand is elastic (<math>\left| \epsilon_p^d \right| > 1</math>), a fall in price leads to a proportionately greater increase in the quantity demanded, which increases total spending. Conversely, a price increase would lead to a decrease in total expenditure. 
* If demand is inelastic (<math>\left| \epsilon_p^d \right| < 1</math>), a price decrease leads to only a small increase in quantity demanded, and total expenditure decreases. If demand has unit elasticity (<math>\left| \epsilon_p^d \right| = 1</math>), total expenditure remains the same when the price changes, because the increase or decrease in quantity demanded is exactly proportional to the decrease or increase in price.

Thus, understanding the price elasticity of demand is essential for companies when considering price changes. If they increase the price of a good with an elastic demand, they can expect a reduction in total expenditure, whereas they could see total expenditure increase if the good has an inelastic demand. This is why companies need to carefully assess the elasticity of demand for their products before making pricing decisions.

The link between the price elasticity of demand and the price level is an inverse relationship: when prices are high, even a small relative decrease in price can lead to a significant increase in the quantity demanded, revealing elastic demand. This is because, in relative terms, the price reduction represents a small portion of the higher price, while the quantity response is proportionately greater.

Conversely, when prices are low, a price reduction, even if proportionately large, may not result in a substantial increase in quantity demanded, indicating inelastic demand. At these lower price levels, consumers can already satisfy their need for the good in question, so their responsiveness to a further price cut is less.

To illustrate this with a linear demand curve, where the slope remains constant, price elasticity varies along the curve:
* At higher price levels (and therefore lower quantities demanded), demand is more elastic because a change in price results in a large percentage change in quantity demanded 
* At lower price levels (and higher quantities demanded), demand becomes inelastic because a change in price has a smaller percentage effect on quantity demanded.

This concept is crucial to pricing management and revenue strategy. Companies can adjust prices according to the expected sensitivity of consumers. For example, a company may be more inclined to reduce prices if it operates in a range where demand is elastic, as the expected increase in quantity demanded could compensate for lower prices and increase total revenues. Conversely, if demand is inelastic, the company could raise prices in the knowledge that the quantity sold will not fall substantially, which could also increase total revenues.

[[Fichier:Elasticité-prix de la demande et dépense totale 1.png|400px|vignette|centré]]
The image shown is a graph illustrating how the price elasticity of demand affects total consumer spending, also known as total revenue for sellers. The graph shows a classic demand curve, decreasing from top left to bottom right, divided into three segments that indicate different levels of elasticity.

# Elastic Demand Segment: In the left-hand segment of the graph, demand is elastic, meaning that the price elasticity of demand is greater than 1 (<math>| \epsilon_p^d | > 1</math>). In this area, a fall in price (p ↓) leads to a proportionately greater increase in quantity demanded (q ↑), which increases total expenditure (p × q). This is illustrated by the area of the rectangle getting larger as you move to the right along the demand curve. 
# Demand Segment with Unit Elasticity: At the centre of the graph, where the demand curve crosses the total expenditure axis, the price elasticity of demand is unitary (<math>| \epsilon_p^d | = 1</math>). This is the point at which total revenue is maximised. At this level, the percentage change in quantity demanded is equal to the percentage change in price, so total expenditure remains the same despite price changes. 
# Inelastic Demand Segment: On the right-hand segment of the graph, demand is inelastic, meaning that the price elasticity of demand is less than 1 (<math>| \epsilon_p^d | < 1</math>). In this zone, a decrease in price (p ↓) leads to a less than proportional increase in quantity demanded (q ↑), resulting in a decrease in total expenditure (p × q). Similarly, an increase in price would lead to an increase in total expenditure because the decrease in quantity demanded would not compensate for the increase in price.

The graph clearly illustrates the inverse relationship between price and quantity demanded, but also the direct relationship between elasticity and total expenditure. In terms of elasticity, a decrease in price leads to an increase in total expenditure when demand is elastic, whereas it leads to a decrease in total expenditure when demand is inelastic. This relationship is fundamental to understanding how companies should approach the pricing of their products according to consumers' sensitivity to price.

[[Fichier:Elasticité-prix de la demande et dépense totale 2.png|400px|vignette|centré|Demande inélastique.]]

These two graphs illustrate how the price elasticity of demand affects total revenue at different price levels for a given product. In the graph on the left, we can see that when the price of a product increases from €1 to €3, the total revenue, initially €100 (suggesting that 100 units are demanded at €1 per unit), changes as a result of this increase.

The graph on the right shows the result of this price increase: total revenue rises to €240. This indicates that, despite the price tripling, the quantity demanded only fell to 80 units, suggesting a less than proportional reaction of the quantity demanded to the price increase. This low sensitivity of demand, illustrated by an increase in total revenue despite the significant increase in price, is characteristic of inelastic demand. In other words, consumers continue to buy almost as much of this product even though its price has risen considerably, which could indicate that the product is perceived as necessary or that there is a lack of close substitutes.

This analysis of price elasticity is vital for economic decision-makers, particularly when it comes to pricing strategy. It shows that if consumers are not very reactive to a price increase, the company could raise prices without fearing a significant drop in the quantity sold, which could in turn increase the company's revenues and profits. That said, a thorough understanding of price elasticity is essential, as it determines a company's ability to generate additional revenue through price changes. A poor estimate could lead to decisions that reduce rather than maximise profits.

[[Fichier:Elasticité-prix de la demande et dépense totale 3.png|400px|vignette|centré|Demande élastique.]]

These two graphs show the effects of a price increase on demand and total revenue for a product.

In the first graph, a price increase from €4 to €5 is shown. Before the price increase, the total revenue was €200, which suggests that 50 units of the product were in demand (because €4 multiplied by 50 units equals €200). The graph shows a demand curve descending from left to right, indicating that as the price increases, fewer consumers buy the product.

The second graph shows the effect of the price increase on total revenue. After the price reaches €5, total revenue falls to €100, implying that only 20 units are sold at this price (€5 multiplied by 20 units equals €100). This shows that demand is highly responsive to price changes, i.e. that demand is elastic. In this case, the price increase has led to a proportionally greater fall in the quantity demanded, which has reduced total revenue.

This situation illustrates a scenario where demand is sufficiently elastic for a price increase to lead to a decrease in total revenue. This can happen for non-essential products or products for which consumers have numerous substitutes. For businesses, this means that price increases are not always beneficial and can sometimes reduce revenues if demand is elastic. This highlights the importance of understanding the price elasticity of demand before making price adjustments. To maximise revenues, a company needs to assess whether its products fall within an elastic or inelastic zone of the demand curve. This knowledge would enable the company to set prices that would not significantly reduce the quantity demanded, or on the contrary, to identify a price that would maximise total revenue without losing too many customers. An effective pricing strategy therefore depends on a company's ability to understand and respond correctly to the elasticity of demand for its products.

== Detailed income elasticity of demand ==

The income elasticity of demand measures the responsiveness of the quantity demanded of a good or service to a change in consumer income. It is expressed as the ratio between the percentage change in quantity demanded and the percentage change in income.

The income elasticity of demand is formulated as follows:

<math>\epsilon_y^d = \frac {\text{percentage change in quantity requested}} {\text{percentage change in income}}</math> = <math>\frac{\frac{\Delta q^d}{q^d}}{\frac{\Delta y}{y}} = \frac{\Delta q^d}{\Delta y} \times \frac{y}{q^d} = \frac{\partial q^d}{\partial y} \times \frac{y}{q^d}</math>.

In this equation: 
*<math>\Delta q^d</math> represents the change in quantity demanded, 
*<math>q^d</math> is the initial quantity demanded, 
*<math>\Delta y</math> is the change in revenue, 
*<math>y</math> is the initial revenue.

The income elasticity of demand is positive for normal goods, meaning that consumption of these goods increases as income rises. For inferior goods, on the other hand, this elasticity is negative, because an increase in income leads consumers to buy fewer of these goods, turning instead to higher-quality goods or more expensive substitutes. This measure is important for businesses and economists as it helps to understand changes in consumption patterns in response to overall economic variations or changes in household income.

The income elasticity of demand varies according to whether the good is normal or inferior, and this is reflected in the sign of the elasticity:

For normal goods, where the quantity demanded increases as consumer income increases, the income elasticity of demand is positive. This is indicated by :

<math>\epsilon_y^d > 0</math>.

This means that normal goods are those that consumers buy in greater quantities as their purchasing power increases. Normal goods can be of two types: necessities, where the income elasticity of demand is positive but less than 1, and luxuries, where this elasticity is greater than 1.

For inferior goods, where the quantity demanded falls when consumer income rises, the income elasticity of demand is negative. This is represented by :

<math>\epsilon_y^d < 0</math>.

Inferior goods are typically products that consumers abandon or replace with better alternatives as their income increases. This is the case for certain basic food products or goods and services considered less desirable or of inferior quality.

Knowledge of the income elasticity of demand is essential for understanding how demand for different goods and services evolves with economic change, and is a valuable tool for policy analysis and strategic business planning.

Income elasticity of demand plays a key role in classifying goods according to how their consumption changes with increases in consumer income.

For essential goods, the income elasticity of demand is positive but relatively low, typically between 0 and 1. This means that although consumption of these goods increases when consumer income rises, it does not grow as quickly as income itself. In practical terms, consumers spend a smaller proportion of their extra income on these goods as their income grows. Basic necessities include items such as basic food, clothing and housing.

For luxury goods, the income elasticity of demand is higher, exceeding 1. This indicates that demand for these goods is increasing faster than the increase in income. In other words, consumers allocate a greater proportion of their extra income to these goods as their income increases. Luxury goods include items such as top-of-the-range cars, expensive travel and cutting-edge technological products.

Understanding these nuances is vital for businesses so that they can align their production and marketing with economic trends and income levels. Changes in the income structure of the population can affect demand for different types of goods, and businesses need to adapt accordingly to respond effectively to these market changes.

== Practical example of income elasticity of demand ==

In the context of income elasticity of demand, the analysis of discrete variations means that we observe specific, isolated changes in consumers' income and in the quantity of goods they demand, rather than continuous or infinitesimally small changes.

If the average income of ice cream consumers rises from CHF 3,000 to CHF 3,150, and the quantity demanded increases from 10 to 12 cones, the income elasticity of this demand is :

<math>\epsilon_y^d = \frac{\frac{\Delta q^d}{q^d}}{\frac{\Delta y}{y}}  = \frac{\frac{(q_i^1 - q_0^d)}{q_0^d}}{\frac{R_1 - R_0}{R_0}} = \frac{\frac{(12 - 10)}{10}}{\frac{3150 - 3000}{3000}} = \frac{+0.2}{+0.05} = +4</math>

Here is a detailed explanation of the calculation: 
* Calculation of the percentage change in the quantity requested: The quantity requested increases from 10 to 12 cones, which represents an increase of 2 cones. In percentage terms, this gives <math>\frac{2}{10} = 0.2</math>, i.e. an increase of 20%. 
* Calculation of the percentage change in income: The average income increases from CHF 3000 to CHF 3150, which represents an increase of CHF 150. In percentage terms, this gives <math>\frac{150}{3000} = 0.05</math>, an increase of 5%. 
* Calculating the income elasticity of demand: Using the income elasticity of demand formula, we divide the percentage change in quantity demanded by the percentage change in income to obtain the income elasticity of demand. This gives <math>frac{0.2}{0.05} = 4</math>.

Therefore, the income elasticity of demand for ice cream cones in this example is +4. This means that for every 1% increase in the average income of consumers, the quantity demanded of ice cream cones increases by 4%. An income elasticity of demand of +4 suggests that ice cream cones are considered a luxury good for these consumers, as the quantity demanded increases significantly more than the increase in income.

== Cross-price elasticity of demand and its implications ==

The cross-price elasticity of demand, often noted <math>\epsilon_{p\neq i}^d</math>, measures the sensitivity of the quantity demanded for one good A (say apples) to the change in price of another good B (say oranges). If A and B are substitutes, such as coffee and tea, an increase in the price of B will generally lead to an increase in the quantity demanded of A, giving a positive cross-price elasticity. Conversely, if A and B are complements, such as cars and petrol, an increase in the price of B will lead to a decrease in the quantity demanded of A, giving a negative cross-price elasticity.

The formula for the cross-price elasticity of demand is therefore :

<math>\epsilon_{p\neq i}^d = \frac{\text{percentage change in quantity demanded of good A}} {\text{percentage change in the price of good B}}</math>

In calculation terms, this is as follows:

<math>\epsilon_{p\neq i}^d = \frac{\Delta q^d / q^d}{\Delta p_{\neq i} / p_{\neq i}} = \frac{\Delta q^d}{\Delta p_{\neq i}} \times \frac{p_{\neq i}}{q^d} = \frac{\partial q^d}{\partial p_{\neq i}} \times \frac{p_{\neq i}}{q^d}</math>

Here, <math>\Delta q^d</math> is the change in quantity demanded of A, <math>\Delta p_{\neq i}</math> is the change in price of B, <math>q^d</math> is the initial quantity demanded of A, and <math>p_{\neq i}</math> is the initial price of B.

The cross-price elasticity of demand, often noted as <math>\epsilon_{p\neq i}^d</math>, measures the sensitivity of the quantity demanded for one good A (say apples) to the change in price of another good B (say oranges). If A and B are substitutes, such as coffee and tea, an increase in the price of B will generally lead to an increase in the quantity demanded of A, giving a positive cross-price elasticity. Conversely, if A and B are complements, such as cars and petrol, an increase in the price of B will lead to a decrease in the quantity demanded of A, giving a negative cross-price elasticity.

The formula for the cross-price elasticity of demand is therefore :

<math>\epsilon_{p\neq i}^d = \frac{\text{percentage change in quantity demanded of good A}} {\text{percentage change in the price of good B}}</math>

In calculation terms, this is as follows:

<math>\epsilon_{p\neq i}^d = \frac{\Delta q^d / q^d}{\Delta p_{\neq i} / p_{\neq i}} = \frac{\Delta q^d}{\Delta p_{\neq i}} \times \frac{p_{\neq i}}{q^d} = \frac{\partial q^d}{\partial p_{\neq i}} \times \frac{p_{\neq i}}{q^d}</math>

Here, <math>\Delta q^d</math> is the change in quantity demanded of A, <math>\Delta p_{\neq i}</math> is the change in price of B, <math>q^d</math> is the initial quantity demanded of A, and <math>p_{\neq i}</math> is the initial price of B.

When the price of a good <math>i</math> increases and, simultaneously, the price of goods substitutable for that good <math>i</math> also increases, it is possible for the quantity demanded of the good <math>i</math> in equilibrium to increase or to remain relatively stable. This depends on the relative sensitivity of consumers to price changes (elasticity) for these goods.

The reasoning behind this is that, in the case of substitutable goods, consumers look for alternatives when the price of a good increases. If the substitutes for that good also see their prices rise, consumers may not find a cheaper alternative and could therefore continue to buy the original <math>i</math> good, even at a higher price. This could result in a smaller decrease, or even an increase, in the quantity demanded of the <math>i</math> good.

The signs of the cross-price elasticity equation for substitutable goods are important in understanding this relationship. A positive cross-price elasticity (<math>\epsilon_{p\neq i}^d > 0</math>) between two goods indicates that they are substitutable. If the price of one increases, and the price of the other also increases, consumers may choose not to switch away from the original good, depending on the relative magnitude of these price increases and the availability of other alternatives.

This analysis is particularly relevant for companies when defining their pricing strategy in a competitive market. Understanding how competitors' prices affect demand for their own product is essential to maximising revenues and market share.

= Understanding the price elasticity of supply =

== Price elasticity of supply ==

The price elasticity of supply measures the responsiveness of the quantity offered of a good or service to a change in its price. It is an important indicator for understanding how producers or suppliers react to changes in the market.

The formula for the price elasticity of supply is as follows:

<math>\epsilon_p^s = \frac{\text{percentage change in quantity offered}}{\text{percentage change in price}}</math>

En formule mathématique, cela se traduit par :

<math>\epsilon_p^s = \frac{\frac{\Delta q^s}{q^s}}{\frac{\Delta p}{p}} = \frac{\Delta q^s}{\Delta p} \times \frac{p}{q^s} = \frac{\partial q^s}{\partial p} \times \frac{p}{q^s}</math>

Where:

*<math>\Delta q^s</math> is the change in quantity offered, 
*<math>q^s</math> is the initial quantity offered, 
*<math>\Delta p</math> is the change in price, 
*<math>p</math> is the initial price.

This formula is used to determine whether the supply of a product is elastic or inelastic. Elastic supply means that producers are able to change the quantity offered in response to a change in price. Conversely, inelastic supply means that the quantity offered does not change much even if the price changes.

To calculate the price elasticity of the ice cream offer, we use the formula for the price elasticity of the offer mentioned above. Here is the detailed calculation: 
#Price change: The price increases from CHF 2 to CHF 2.20, an increase of CHF 0.20. The percentage change in price is therefore <math>\frac{0.20}{2} = 0.10</math> or 10%. 
#Change in quantity offered: The quantity offered increases from 5 to 6 cones, i.e. an increase of 1 cone. The percentage change in the quantity offered is therefore <math>\frac{1}{5} = 0.20</math> or 20%. 
#Calculation of the price elasticity of the offer:
<math>\epsilon_p^s = \frac{\text{percentage change in quantity offered}}{\text{percentage change in price}} = \frac{0.20}{0.10} = 2</math>

The price elasticity of supply for ice cream in this example is 2. This means that for every 1% increase in price, the quantity offered increases by 2%. A supply elasticity of 2 indicates a relatively elastic supply, where producers are fairly reactive to price changes.

== Determinants of the price elasticity of supply ==

=== The role of inputs in the elasticity of supply === 

The elasticity of supply of a product is strongly influenced by the availability and accessibility of the inputs needed to produce it. When the raw materials, components or labour needed to manufacture a product are readily available and accessible, producers can respond more quickly and effectively to price fluctuations on the market. This ability to obtain additional inputs quickly or to increase the workforce allows companies to increase their production in response to a rise in demand or prices, making their supply more elastic.

In addition, the use of intermediate manufactured goods in production plays a crucial role in determining the elasticity of supply. As intermediate goods are already partly processed or assembled, they offer greater flexibility in the production process. This means that companies can adjust their production more easily and quickly in response to price variations. This is particularly true in industries where production methods are flexible and can adapt quickly to meet changes in demand.

The storage capacity and durability of inputs are also important factors. If inputs can be stored for a long time without deteriorating, this gives companies greater flexibility to adjust their production in response to price fluctuations. Companies can store inputs when their costs are low and use them to increase production when demand and prices rise.

The flexibility of the production chain is another essential element. A company that can easily adjust its production lines to increase or decrease output of a product in response to price variations will have a more elastic supply. This flexibility allows companies to react quickly to market changes, which is crucial in sectors where market conditions are volatile or highly competitive.

The elasticity of a product's supply is therefore highly dependent on the ability of companies to adapt to changes in demand and prices. Factors such as ease of access to inputs, production flexibility, input storage capacity, and the use of intermediate manufactured goods are key to this adaptability. A good understanding and management of these factors is essential for companies wishing to optimise their production and maximise their profits in the face of market fluctuations.

=== Vendors' ability to adjust production ===
The ability of sellers to adapt their level of production of goods has a direct impact on the elasticity of supply of these products. Let's take two examples to illustrate this principle: the seafront and computer production.

On the one hand, the supply of waterfront properties is considered to be inelastic. The main reason for this inelasticity is the geographical limitation and scarcity of the property. There is a fixed amount of land available on the seafront, and this cannot be increased, regardless of demand or price increases. Consequently, even a significant increase in seaside property prices will not lead to an increase in supply, as it is impossible to increase the amount of land available by the sea.

On the other hand, computer production is generally considered to be rather elastic. This is because computer manufacturers can relatively easily increase or decrease production in response to price changes. Computer production is not dependent on geographically limited resources in the same way as seaside real estate. What's more, the technology industry benefits from scalable manufacturing processes and flexible supply chains, allowing computer producers to quickly adjust production to meet market demand.

These two examples illustrate how the nature and characteristics of goods influence the elasticity of supply. Goods that are physically limited or scarce tend to have an inelastic supply, while those that can be produced in large quantities and quickly adjusted to meet market needs have a more elastic supply. Understanding these differences is crucial for decision-makers and companies when planning their production and pricing strategies.

=== Temporal variations in supply responsiveness === 
The elasticity of a product's supply varies considerably depending on the time horizon considered. In the short term, the elasticity of supply is generally rigid or inelastic, because companies are faced with production capacities and infrastructures that are fixed and cannot be changed quickly. This short-term rigidity is due to immediate constraints such as the limits of existing production capacity, fixed costs, and the slowness of production readjustment processes. For example, in the oil industry, increasing oil supply in the short term is a major challenge. This requires significant investment in exploration and the development of new oilfields, as well as the expansion of existing infrastructures, which takes time and requires significant financial investment.

In the long term, however, companies have the capacity to make their supply more elastic. Over time, they can invest in new technologies, expand production capacity, and adjust other aspects of their operations in response to changes in demand and prices. In the long term, oil companies, for example, can develop new oil fields, improve their methods of extracting and processing oil, and adjust their overall strategy in response to changes in the market. This potential for long-term adjustment allows greater flexibility and a more dynamic response to price changes.

These differences in supply elasticity between the short and long term have important implications for understanding markets and making strategic decisions. In sectors where market conditions are volatile or subject to rapid fluctuations, companies' ability to adapt quickly may be limited in the short term. However, in the long term, these same companies can plan and implement strategies to increase their flexibility and responsiveness. This distinction is also crucial for political and economic decision-makers, who need to understand these dynamics in order to develop effective policies and support industrial and economic development.

== Various cases of price elasticity of supply ==

[[Fichier:Elasticité-prix de l’offre cas divers 1.png|400px|vignette|center]]

This image shows four different graphs illustrating the concepts of price elasticity of supply for different scenarios.

Perfectly inelastic supply (Graph a): This graph shows a vertical line, indicating that the quantity supplied remains unchanged whatever the price increase. This is typical of goods for which it is not possible to increase production no matter how much the price rises, often because of physical constraints or limited resources. The price elasticity of supply for such a good is zero, as price changes have no effect on the quantity supplied.

Perfectly elastic supply (Graph b): This graph shows a horizontal line at a specific price. This means that producers are prepared to offer any quantity at the fixed price, but no quantity at a lower price. The price elasticity of supply is infinite at this price, because the slightest variation in price above this threshold would lead to an infinite increase in the quantity offered, while a fall below this threshold would immediately reduce supply to zero.

Inelastic supply (Graph c): In this scenario, an increase in price leads to a relatively small increase in the quantity offered, indicating inelastic supply. The price elasticity of supply is less than 1, as illustrated by a moderate upward slope. This can occur in cases where there are delays in producers' ability to respond or fixed costs that make it difficult or costly to increase production.

Elastic supply (Graph d): Here, an increase in price leads to a proportionally greater increase in the quantity offered, indicating an elastic supply. The price elasticity of supply is greater than 1, as shown by the relatively steep upward slope. This is characteristic of markets where producers can quickly increase output in response to a price rise, for example, when there are few constraints on resources or labour.

Each of these graphs illustrates different situations that producers may encounter in the market, showing how supply may react to changes in the price of their products. Understanding these concepts is essential for producers, economists and policy-makers when analysing markets and predicting producers' reactions to price changes.

=== Extreme cases of supply elasticity ===

==== Analysis of a perfectly inelastic supply ==== 

A '''perfectly inelastic supply''' represents a situation where the quantity offered of a good or service remains constant, regardless of any variation in its price. In this case, the price elasticity of supply is equal to zero, which means that price variations have no impact on the quantity offered.

The formula is expressed as follows:

<math>\epsilon_p^s = 0</math>

This situation is rare in economic reality but can occur in certain cases. For example, the supply of certain heritage or historical goods, such as rare works of art or antiques, can be perfectly inelastic because their quantity is fixed and cannot be increased, whatever the price. Similarly, the availability of limited natural resources, such as specific land or rare minerals, can also be perfectly inelastic.

In these cases, suppliers cannot respond to an increase in demand with an increase in supply, which can lead to situations where prices rise considerably without this being reflected in an increase in the quantity available on the market.

==== Study of a perfectly elastic supply ====

A '''perfectly elastic supply''' describes a situation in which the quantity offered can vary unlimitedly in response to the slightest variation in price. In this case, the price elasticity of supply is considered to be infinite, which means that any change, however small, in the price will lead either to a total absence of supply (if the price falls below a certain level) or to unlimited supply (if the price rises even slightly).

This situation is expressed by the following formula:

<math>\epsilon_p^s = \infty</math>

This perfectly elastic supply condition is theoretical and rarely encountered in practice. However, it can be used to describe situations where suppliers are willing to sell any quantity of a product at a given price, but at no lower price. An example might be a product that is extremely easy and inexpensive to produce, such as certain digital products or online services, where production capacity can be virtually unlimited in response to growing demand, as long as the price remains above the break-even point.

=== Intermediate supply elasticity scenarios === 

An '''inelastic supply''' is characterised by a low responsiveness of the quantity offered to price variations. In this case, the quantity offered varies less than proportionally to the variation in price. This means that even large variations in price lead to relatively small changes in the quantity offered. The price elasticity of supply is therefore less than 1 in absolute terms.

This situation is expressed by the following formula:

<math>\left| \epsilon_p^s \right| < 1</math>

This low elasticity may be due to various factors, such as limited production capacity, the unavailability of additional raw materials, long production lead times, or high fixed costs that make it difficult to adjust the quantity produced quickly in response to price changes.

Goods with inelastic supply often include those that require heavy infrastructure or significant investment, such as the extractive industries (e.g. oil and minerals) or certain types of agricultural production. In these cases, the ability to increase production in response to a price rise is limited by physical or technical constraints.

==== Characteristics of an elastic supply ==== 

An '''elastic supply''' characterises a situation where the quantity offered of a good or service is highly reactive to price variations. In this case, the quantity offered varies more than proportionally to the variation in price. This means that small variations in price lead to significant changes in the quantity offered. The price elasticity of supply is therefore greater than 1 in absolute terms.

This situation is expressed by the following formula:

<math>\left| \epsilon_p^s \right| > 1</math>

Elastic supply is often seen in industries where it is relatively easy to adjust output in response to price changes. This may be due to factors such as the availability of flexible technologies, the ability to ramp up production quickly without significant additional costs, or the presence of readily available raw materials.

A typical example of elastic supply can be found in manufacturing industries where production adjustments can be made quickly in response to market signals. This allows companies to capitalise on market opportunities by increasing production when prices rise and reducing it when prices fall.

==== Supply with unit elasticity explained ==== 

A '''supply with unit elasticity''' occurs when the quantity offered of a good or service changes in exactly the same proportion as the price. In other words, the percentage change in the quantity offered is equal to the percentage change in the price. In this case, the price elasticity of supply is equal to 1 in absolute value.

This situation is expressed by the following formula:

<math>\left| \epsilon_p^s \right| = 1</math>

Supply with unit elasticity indicates a balance between the sensitivity of supply to price variations and the quantity produced. This means that for every 1% increase in price, the quantity offered also increases by 1%, and vice versa. This type of elasticity is important in economic contexts where suppliers need to adjust their production proportionally to price changes in order to remain competitive or to maximise their revenues.

In practice, it is rare to find situations where supply has exactly unit elasticity, but this notion is useful for understanding economic theory and for modelling market behaviour. It provides a useful reference point for analysing how price variations affect the quantity offered and for assessing producers' responsiveness to market changes.

= Applications pratiques des élasticités =

== Interactions entre élasticités et équilibre du marché ==

=== Effets inattendus : l'exemple du blé hybride === 

Le graphique suivant décrit une situation où l'introduction d'un blé hybride, qui a un meilleur rendement que les variétés existantes, impacte le marché du blé.

[[Fichier:Découverte du blé hybride élasticité.png|400px|vignette|centré]]Voici une analyse basée sur les phénomènes économiques habituels dans de telles circonstances :

# Augmentation de l'Offre : La découverte d'un hybride de blé plus productif augmente l'offre de blé sur le marché. Cela est représenté par un déplacement de la courbe d'offre vers la droite, de S1 à S2, indiquant qu'à chaque prix, une plus grande quantité de blé est disponible.
# Chute des Prix : Si la demande reste inélastique (c'est-à-dire que la quantité demandée ne change pas beaucoup en réponse à une variation de prix), l'augmentation de l'offre entraînera une baisse des prix. Cela est dû au fait que, pour vendre toute la quantité supplémentaire de blé, les producteurs doivent baisser le prix pour attirer les consommateurs.
# Réduction du Revenu Total des Producteurs : Une chute significative du prix, avec seulement une légère augmentation de la quantité vendue en raison de l'inélasticité de la demande, peut réduire le revenu total des producteurs. Dans l'exemple donné, le revenu total diminue de CHF 300 à CHF 220, malgré la vente d'une plus grande quantité de blé.

Ce phénomène est parfois appelé "paradoxe de l'abondance" ou "malédiction de la bonne récolte" dans le contexte agricole : une offre accrue due à une meilleure productivité peut paradoxalement nuire aux producteurs si la baisse des prix due à l'excès d'offre l'emporte sur l'augmentation de la quantité vendue. Les producteurs peuvent finir par être pires financièrement, même s'ils ont une récolte plus abondante, en raison de la pression à la baisse sur les prix et de la faible élasticité de la demande pour le bien en question.

Pour atténuer ce problème, les producteurs peuvent rechercher des marchés alternatifs, développer de nouveaux produits à valeur ajoutée à partir du blé ou travailler ensemble pour ajuster l'offre globale et stabiliser les prix. Par ailleurs, l'intervention des gouvernements peut parfois être nécessaire pour soutenir les prix et garantir un revenu stable aux agriculteurs.

=== Durabilité de l'augmentation du prix du pétrole post-choc pétrolier ===
L'augmentation du prix du pétrole après le premier choc pétrolier de 1973 n'a pas duré principalement en raison de la dynamique des élasticités de l'offre et de la demande à long terme. 

Voici une explication détaillée des mécanismes en jeu :

# Élasticité de l'offre à long terme : Dans le court terme, l'offre de pétrole est relativement inélastique en raison des délais nécessaires pour développer de nouveaux champs pétrolifères ou pour améliorer la technologie d'extraction. Cependant, avec le temps, l'incitation à investir dans le développement pétrolier augmente lorsque les prix sont élevés. De nouvelles explorations sont lancées, des technologies existantes sont améliorées et de nouvelles techniques sont développées, ce qui augmente l'offre de pétrole. À moyen et long terme, la quantité de pétrole offerte à un prix donné augmente, contribuant à la stabilisation ou à la baisse des prix.
# Élasticité de la demande à long terme : La demande de pétrole, bien qu'inélastique à court terme (les gens et les entreprises ne peuvent pas changer immédiatement leur consommation de pétrole en réponse à des changements de prix), devient plus élastique à long terme. Lorsque les prix du pétrole augmentent et restent élevés pendant un certain temps, cela crée une incitation pour les consommateurs et les industries à rechercher des substituts ou à adopter des technologies plus économes en énergie. L'efficacité énergétique s'améliore, la consommation de carburant diminue et les alternatives au pétrole, telles que les énergies renouvelables, gagnent du terrain. Cela réduit la demande de pétrole, exerçant une pression à la baisse sur les prix.
# Ajustements du marché : La combinaison d'une offre plus élastique et d'une demande également plus élastique à long terme signifie que les chocs de prix comme ceux causés par le premier choc pétrolier ont tendance à être tempérés avec le temps. Les marchés s'ajustent : l'offre augmente grâce à de nouveaux investissements et à l'innovation, tandis que la demande diminue en réponse à la recherche d'efficacité et à l'adoption de substituts.

En conséquence, l'effet net est qu'une diminution de l'offre ou une augmentation initiale du prix du pétrole entraîne seulement une petite augmentation des prix à long terme par rapport à l'effet beaucoup plus grand observé à court terme. Cela explique pourquoi l'augmentation des prix du pétrole après le premier choc pétrolier n'a pas été durable et pourquoi les prix ont finalement commencé à se stabiliser, voire à baisser, dans les années qui ont suivi.

=== Stratégies de lutte contre la consommation de drogues et criminalité associée ===
La lutte contre la consommation de drogues et son impact sur la criminalité peut être abordée par diverses politiques publiques, chacune ayant des conséquences différentes sur le marché des drogues et sur les comportements criminels associés.

# Politiques de réduction de l'offre : Les politiques qui visent à réduire l'offre de drogues, telles que l'augmentation des contrôles policiers et la répression des vendeurs, peuvent réduire la quantité de drogues disponibles sur le marché. Cependant, si la demande de drogues reste inélastique, c'est-à-dire que les consommateurs continuent à consommer des quantités similaires malgré l'augmentation des prix, ces politiques peuvent involontairement augmenter le prix des drogues sur le marché noir. L'effet pervers potentiel est que, malgré une réduction de la quantité disponible, le revenu total des dealers peut augmenter en raison des prix plus élevés. Cela pourrait renforcer l'attrait financier du trafic de drogues et aggraver les problèmes de criminalité associés, car les bénéfices accrus pourraient encourager plus d'individus à entrer dans le commerce illégal des drogues.
# Politiques de réduction de la demande : À l'opposé, les politiques qui s'attaquent à la demande de drogues, par exemple à travers des programmes d'éducation et d'information, visent à réduire la consommation en sensibilisant aux dangers de la drogue et en offrant des alternatives et des soutiens pour le sevrage. Ces politiques peuvent être plus efficaces à long terme car elles cherchent à réduire la demande directement. Si elles réussissent, la quantité de drogues consommée diminuera, entraînant une baisse des prix sur le marché. Avec une demande moins inélastique et des prix plus bas, le revenu total des dealers diminuerait, ce qui pourrait réduire les incitations financières à la criminalité liée aux drogues. En outre, en s'attaquant aux causes sous-jacentes de la consommation de drogues, ces politiques peuvent également réduire les dommages sociaux et sanitaires associés.

En résumé, les politiques de réduction de la demande pourraient s'avérer plus efficaces pour diminuer à la fois la consommation de drogues et la criminalité liée aux drogues à long terme. Elles visent non seulement à réduire l'attrait économique du trafic de drogues mais aussi à résoudre les problèmes de santé publique et d'addiction qui alimentent la demande. Ces politiques peuvent également être renforcées par des mesures de soutien telles que les traitements de substitution, les thérapies et le soutien à la réinsertion sociale des anciens consommateurs.

== Élasticités et équilibre du marché : vue d'ensemble ==

L'élasticité de la demande joue un rôle central dans la manière dont les chocs de l'offre affectent les marchés. L'élasticité de la demande mesure la sensibilité de la quantité demandée à une variation de prix. Si la demande est élastique, une petite augmentation de prix entraîne une grande diminution de la quantité demandée, et inversement.

# Demande Élastique : Avec une demande élastique, un choc sur l'offre (par exemple, une diminution de la quantité offerte due à une catastrophe naturelle ou à une hausse des coûts de production) entraîne une variation plus importante de la quantité vendue et une variation plus faible du prix. Cela est dû au fait que les consommateurs réduisent significativement leur consommation en réponse à une hausse des prix. Les producteurs ne peuvent donc pas augmenter les prix librement sans risquer une chute substantielle de la quantité vendue.
# Demande Inélastique : À l'inverse, lorsque la demande est inélastique, les consommateurs ne réduisent pas beaucoup leur consommation en réponse à une augmentation de prix. Dans ce cas, un choc sur l'offre se traduit par une augmentation relativement plus importante du prix et une variation plus contenue de la quantité vendue. Cela signifie que les producteurs peuvent répercuter plus facilement une augmentation des coûts de production sur les consommateurs sans craindre une réduction significative des ventes.

L'implication est que, pour les biens à demande inélastique, les producteurs ont une plus grande capacité à transférer les coûts supplémentaires aux consommateurs sous forme de prix plus élevés. C'est souvent observé avec des produits de première nécessité ou des médicaments pour lesquels il y a peu ou pas de substituts directs, et les consommateurs continuent d'acheter même si les prix augmentent.

Les graphiques économiques représentant ces scénarios montrent généralement une courbe de demande plus plate pour les biens à demande élastique et une courbe de demande plus raide pour les biens à demande inélastique. Dans les marchés où la demande est inélastique, les stratégies de prix sont un outil puissant pour les entreprises, tandis que dans les marchés à demande élastique, la compétitivité dépend davantage de la capacité à gérer les coûts et à maintenir des volumes de vente élevés.

Dans le très court terme, la fonction d'offre est souvent rigide ou inélastique parce que les producteurs n'ont pas le temps ou la capacité de changer rapidement leur niveau de production en réponse à des changements de prix. Les installations de production, la main-d'œuvre, les contrats d'approvisionnement, et d'autres facteurs ne peuvent pas être ajustés instantanément. Cela signifie que, face à un choc de demande, les quantités offertes ne peuvent pas augmenter pour satisfaire la demande supplémentaire immédiatement, ce qui entraîne des augmentations de prix.

À court terme, les prix jouent donc un rôle de rationnement de la demande. Quand la demande pour un bien augmente soudainement et que l'offre ne peut pas suivre immédiatement, les prix montent pour rééquilibrer le marché. Les consommateurs qui sont disposés et capables de payer le prix plus élevé obtiennent le produit, tandis que ceux qui ne le sont pas doivent s'en passer ou chercher des substituts.

Dans le moyen et long terme, la fonction d'offre devient plus élastique. Les producteurs ont le temps de répondre à des changements de prix en augmentant la production. Ils peuvent investir dans de nouvelles capacités de production, embaucher plus de travailleurs, ou améliorer l'efficacité pour produire plus. Ainsi, face à un choc de demande durable, l'offre peut augmenter, ce qui peut stabiliser ou même réduire les prix par rapport au pic initial.

Les graphiques économiques qui illustrent ces phénomènes montrent habituellement une courbe d'offre très raide ou verticale dans le très court terme, indiquant une faible réactivité à une variation de prix. À mesure que l'horizon temporel s'étend, la courbe d'offre devient plus inclinée, indiquant une plus grande élasticité. Les implications pour les décideurs économiques sont importantes : dans le court terme, la gestion de la volatilité des prix peut nécessiter des interventions, telles que des réserves stratégiques ou des réglementations des prix, tandis que dans le long terme, les investissements dans la capacité de production et l'innovation sont essentiels pour répondre à la demande croissante.
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== Influence de l'élasticité de la demande sur l'équilibre du marché ==

=== Conséquences d'une demande inélastique ===
Ce graphique illustre un marché où la demande est inélastique, ce qui signifie que la quantité demandée ne varie pas beaucoup en réponse à une variation des prix. Sur ce graphique, nous voyons deux courbes d'offre, S1 et S2, et une courbe de demande relativement raide, indiquant l'inélasticité.[[Fichier:Elasticités de la demande et équilibre 1.png|400px|vignette|centré|Demande inélastique (faible variation de la quantité et grande variation du prix).]]

# Point d'Équilibre Initial : Le point d'équilibre initial, indiqué par le point 1, se situe à l'intersection de la courbe de demande avec la courbe d'offre S1. Ce point montre le prix et la quantité d'équilibre avant tout changement dans les conditions du marché.
# Nouveau Point d'Équilibre après un Choc de l'Offre : Le point 2 représente un nouveau point d'équilibre après un choc positif de l'offre, où la courbe d'offre se déplace vers la droite de S1 à S2. Ce déplacement pourrait être dû à une amélioration technologique, à une réduction des coûts de production, ou à une augmentation de la quantité de producteurs sur le marché.
# Conséquences sur le Prix et la Quantité : En raison de la demande inélastique, le nouveau point d'équilibre montre une réduction considérable du prix, mais seulement une faible augmentation de la quantité vendue. Cela est cohérent avec la nature de la demande inélastique, où les consommateurs ne réagissent pas fortement aux variations de prix.

Ce graphique illustre bien les implications d'une demande inélastique sur le marché. Même si l'offre augmente, ne provoquant qu'une légère augmentation de la quantité vendue, le prix peut considérablement baisser. Cela peut être préoccupant pour les producteurs, car une baisse significative des prix peut réduire leurs revenus, surtout si la quantité vendue n'augmente pas de manière significative. Cela montre également l'importance de comprendre l'élasticité de la demande lors de la mise en œuvre de politiques ou de la prise de décisions d'affaires, car les réactions du marché aux changements d'offre dépendent fortement de cette élasticité.

=== Impacts d'une demande élastique ===
Le graphique illustre un marché où la demande est élastique. Sur ce graphique, deux courbes d'offre (S1 et S2) sont représentées, ainsi qu'une courbe de demande qui a une pente prononcée, indiquant une grande sensibilité de la quantité demandée aux variations de prix.[[Fichier:Elasticités de la demande et équilibre 2.png|400px|vignette|centré|Demande élastique (grande variation de la quantité et faible variation du prix).]]

# Point d'Équilibre Initial (Point 1) : Ce point se trouve à l'intersection de la courbe de demande et de la courbe d'offre initiale S1. Il représente le prix et la quantité d'équilibre sur le marché avant tout changement.
# Nouveau Point d'Équilibre après un Choc de l'Offre (Point 2) : Le point 2 est le nouveau point d'équilibre résultant d'un choc positif de l'offre, où la courbe d'offre s'est déplacée vers la droite de S1 à S2. Ce déplacement de la courbe d'offre pourrait être le résultat d'une amélioration de la technologie, d'une réduction des coûts de production, ou d'une augmentation du nombre de fournisseurs.
# Impact sur le Prix et la Quantité : Avec une demande élastique, une augmentation de l'offre entraîne une augmentation substantielle de la quantité vendue mais une modification relativement faible du prix. Cela est dû à la haute sensibilité de la quantité demandée aux changements de prix dans un marché à demande élastique. Les consommateurs sont prêts à acheter beaucoup plus à un prix légèrement inférieur.

Dans ce scénario, les producteurs peuvent bénéficier d'une augmentation de la quantité vendue, mais ils ne verront pas une hausse significative des prix, ce qui pourrait limiter l'augmentation de leur revenu total. Cette illustration montre l'importance de l'élasticité de la demande dans la détermination des effets des variations de l'offre sur le prix et la quantité d'équilibre. Dans les marchés à demande élastique, les variations de l'offre ont tendance à se traduire davantage par des changements de quantité que de prix.

== Impact de l'élasticité de l'offre sur l'équilibre du marché ==

=== Effets d'une offre inélastique ===
Sur ce graphique est illustré un marché où l'offre est inélastique. L'inélasticité de l'offre est indiquée par la courbe d'offre relativement raide. Le graphique montre également deux courbes de demande, D1 et D2, indiquant deux différents niveaux de demande.[[Fichier:Elasticités de l'offre et équilibre 1.png|400px|vignette|centré|Offre inélastique (faible variation de la quantité et grande variation du prix).]]

# Point d'Équilibre Initial (Point 1) : À l'origine, le marché est à l'équilibre au point 1, où la courbe d'offre inélastique rencontre la courbe de demande initiale D1. Ce point représente le prix et la quantité d'équilibre avant tout changement dans les conditions de marché.
# Nouveau Point d'Équilibre après un Choc de Demande (Point 2) : Le point 2 représente un nouveau point d'équilibre après un choc négatif de la demande, où la courbe de demande se déplace vers la gauche de D1 à D2. Ce déplacement pourrait être dû à une diminution de la demande globale pour le bien en question, peut-être à cause de changements dans les préférences des consommateurs, une augmentation du prix d'un bien complémentaire, ou l'introduction d'un substitut moins cher.
# Impact sur le Prix et la Quantité : Étant donné que l'offre est inélastique, la réduction de la demande entraîne une baisse substantielle du prix mais seulement une faible diminution de la quantité offerte. Cela est cohérent avec la nature de l'offre inélastique, où les producteurs ne peuvent pas ou ne veulent pas réduire significativement la quantité offerte en réponse à une baisse des prix.

Dans ce scénario, les producteurs peuvent subir une baisse notable de leurs revenus due à la baisse des prix, tandis que la quantité vendue diminue légèrement. Cette illustration met en évidence l'importance de l'élasticité de l'offre dans la détermination des effets des variations de la demande sur le prix et la quantité d'équilibre. Dans les marchés à offre inélastique, les variations de la demande ont tendance à se traduire davantage par des changements de prix que de quantité.

=== Conséquences d'une offre élastique ===
Le graphique ci-dessous représente un marché avec une offre élastique, indiquée par une courbe d'offre avec une pente relativement plate. Sur ce graphique, nous voyons un déplacement de la courbe de demande de D1 à D2, suggérant un changement dans les conditions de marché qui affecte la demande.[[Fichier:Elasticités de l'offre et équilibre 2.png|400px|vignette|centré|Offre élastique (grande variation de la quantité et faible variation du prix).]]

# Point d'Équilibre Initial (Point 1) : Le point d'équilibre initial est situé à l'intersection de la courbe d'offre élastique et de la courbe de demande D1. Ce point reflète le prix et la quantité d'équilibre avant le changement de la demande.
# Nouveau Point d'Équilibre après un Choc de Demande (Point 2) : Le point 2 montre le nouvel équilibre après que la courbe de demande se soit déplacée vers la droite, de D1 à D2, indiquant une augmentation de la demande pour le bien ou service. Cette augmentation pourrait résulter d'une baisse du prix d'un bien complémentaire, d'une hausse du prix d'un substitut, d'une augmentation du revenu des consommateurs, ou d'un changement dans les goûts et les préférences en faveur du bien.
# Impact sur le Prix et la Quantité : En raison de l'élasticité de l'offre, l'augmentation de la demande entraîne une augmentation significative de la quantité offerte mais seulement une légère augmentation du prix. Cela montre que les producteurs sont capables de répondre à la hausse de la demande en augmentant la production sans avoir à augmenter considérablement les prix.

Dans ce scénario, les producteurs bénéficient d'une augmentation de la quantité vendue, ce qui peut entraîner une augmentation de leur revenu total, même si la hausse des prix est modeste. Cela illustre l'importance de l'élasticité de l'offre pour absorber les chocs de la demande : dans les marchés où l'offre est élastique, les fournisseurs peuvent ajuster leur production pour répondre aux variations de la demande sans causer de grandes fluctuations de prix. Cela contribue à la stabilité du marché et peut prévenir les fluctuations de prix extrêmes qui pourraient être préjudiciables à la fois aux consommateurs et aux producteurs.

= Synthèse des élasticités et de leur portée =
Les élasticités sont des mesures essentielles en économie qui permettent d'évaluer la réactivité des quantités demandées ou offertes face à des changements de prix ou d'autres facteurs influençant la demande ou l'offre. Elles sont déterminées par le ratio des variations en pourcentage et offrent un aperçu précis de la dynamique de marché.

Lorsque la demande d'un bien est inélastique, cela signifie que les consommateurs ne réduisent pas significativement leur consommation même si le prix augmente. Dans ce cas, toute augmentation du prix tend à entraîner une hausse du revenu total pour les vendeurs. Cela est dû au fait que la quantité demandée diminue peu, donc l'augmentation du prix l'emporte sur la réduction de la quantité dans le calcul du revenu total.

Inversement, si la demande est élastique, c'est-à-dire que les consommateurs réagissent fortement à une augmentation des prix par une baisse de leur consommation, alors le revenu total des vendeurs tend à diminuer lorsque les prix augmentent. Dans ce scénario, l'augmentation des prix conduit à une baisse de la quantité demandée plus importante, ce qui réduit le revenu total généré par les ventes.

L'élasticité-revenu nous informe sur la relation entre le revenu des consommateurs et la quantité demandée d'un bien. Les biens pour lesquels la demande augmente avec l'augmentation des revenus sont considérés comme des biens normaux et ont une élasticité-revenu positive. À l'inverse, les biens dont la demande diminue quand le revenu des consommateurs augmente sont qualifiés de biens inférieurs et ont une élasticité-revenu négative.

L'élasticité-prix croisée entre deux biens nous indique si ces biens sont complémentaires ou substituts. Une valeur négative indique que les biens sont complémentaires, ce qui signifie que l'augmentation du prix de l'un entraîne une baisse de la demande de l'autre. À l'inverse, une valeur positive indique que les biens sont substituts, signifiant que l'augmentation du prix de l'un entraîne une hausse de la demande pour l'autre.

La différence entre les élasticités à court et à long terme est également significative. À court terme, les réponses des consommateurs et des producteurs aux changements de prix sont généralement limitées en raison de contraintes telles que des contrats, des habitudes ou des capacités de production fixes. Par conséquent, les élasticités sont plus faibles. À long terme, cependant, les consommateurs et les producteurs disposent de plus de temps pour ajuster leur comportement, ce qui se traduit par des élasticités plus élevées.

La compréhension des élasticités est cruciale pour anticiper l'impact des chocs de la demande et de l'offre sur l'équilibre du marché. Ces mesures influencent la façon dont les prix et les quantités s'ajustent en réponse aux chocs, affectant ainsi l'équilibre global du marché. Ainsi, les élasticités jouent un rôle fondamental dans la prévision des conséquences des politiques économiques, des changements du marché, et des tendances externes sur les prix et les quantités, ce qui est vital pour les décisions stratégiques dans les secteurs public et privé.

= Annexes =

= References =
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[[Catégorie:Économie]]
[[Catégorie:Microéconomie]]
[[Catégorie:Federica Sbergami]]
[[Catégorie:Giovanni Ferro-Luzzi]]