# Firms in competitive markets

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Firms in competitive markets
Cours Introduction to microeconomics

Lectures

# What is a competitive Market? The meaning of competition

A competitive market, sometimes called a perfectly competitive market has two characteristics:

1. There are many buyers and many sellers in the market
2. The goods offered by the various sellers are largely the same

As a result of these conditions, the actions of any single buyer or seller in the market have a negligible impact on the market price. Each buyer and seller takes the market price as given, meaning, he must accept the price the market determines and therefore, buyers and sellers are said to be price takers.

## The revenue of a competitive firm

A firm in a competitive market tries to maximize profit, which equals total revenue minus total cost.

The average revenue is total revenue divided by the quantity sold (amount of output). Average revenue tells us how much revenue a firm for the typical unit sold. (total revenue is ${\displaystyle P\times Q}$, price times quantity).

The marginal revenue is the change in total revenue from the sale of each additional unit of output. Total revenue is ${\displaystyle P\times Q}$ and ${\displaystyle P}$ is fixed for a competitive firm. Therefore, when ${\displaystyle Q}$ rises by 1 unit, total revenue rises by ${\displaystyle P}$ euros. For competitive firms, marginal revenue equals the price ${\displaystyle f}$ the good (attention: ONLY FOR COMPETITIVE MARKETS).

## Profit maximization and the competitive firm’s supply curve

A simple example of profit maximization

If marginal revenue is greater than marginal cost the firm should increase the production. If marginal revenue is less than marginal cost, the firm should decrease production. If the firms thinks at the margin and make incremental adjustments to the level of production, they are naturally led to produce the profit maximizing quantity.

## The marginal cost curve and the firm’s supply decision

In general we use the rule that at the profit-maximizing level of output, marginal revenue and marginal cost are exactly equal. Because a competitive firm is a price taker, its marginal revenue equals the market price. For any given price, the competitive firm’s profit-maximizing quantity of output is found by looking at the intersection of the price with the marginal cost curve. (Schnittpunkt Preis und MC ergibt profit maximizing quantity. Da Preis gleich bleibt Punkt auf MC-Kurve die dem Preis entspricht). When the price rises, the firm finds that marginal revenue is now higher than marginal cost that the previous level of output, so that the firm increases production.

Because the firm’s marginal-cost curve determines the quantity of the good the firm is willing to supply at any price, it is the competitive firm’s supply curve.

## The firm’s short-run decision to shut down

In some circumstances the firm will decide to shut down and not produce anything at all. Here we should distinguish between a temporary shutdown of a firm and the permanent exit from the market. A shutdown refers to a short-run decision. Exit refers to a long-run decision. These decisions differ because most firms cannot avoid their fixed costs in the short run but can do so in the long run.

If the firm shuts down, it loses all revenue from the sale of its product. At the same time, it saves the variable cost of making its product. Thus the firm shuts down if the revenue that it would get from producing is less than its variable cost of production. Mathematics:

• Shut down if ${\displaystyle TR
• Shut down if ${\displaystyle {\frac {TR}{Q}}<{\frac {VC}{Q}}}$
• Shut down if ${\displaystyle P
${\displaystyle TR=totalrevenue}$
${\displaystyle VC=variablecost}$
${\displaystyle Q=Quantity}$
${\displaystyle AVC=averagevariablecost(={\frac {VC}{Q}})}$

If the price doesn’t cover the average variable cost, the firm is better off stopping producing altogether. (Logisch oder?) The firm might reopen it the conditions change. If the firm produces anything, it produces the quantity at which marginal cost equals the price of the good. Yet it the price is less than average variable cost at the quantity, the firm is better off shutting down.

## Spilt milk and other sunk costs

Economists say that a cost is a sunk cost when it has already been committed and cannot be recovered. Sunk costs cannot be avoided regardless of the choices you make. (If you cannot erase the cost; if something has already been invested like in infrastructure or if I want to go to the cinema, buy a ticket and lose it). Because nothing can be done about sunk cost, you can ignore them when making decisions.

## The firm’s long run decision to exit or enter a market

If the firm exits a market, it will lose all revenue from the sale of its product, but now it saves both fixed and variable costs of production. Thus, the firm exits the market if the revenue it would get from producing is less than its total costs. Mathematics:

• Exit if ${\displaystyle TR
• Exit if ${\displaystyle {\frac {TR}{Q}}<{\frac {TC}{Q}}}$
• Exit if ${\displaystyle P
${\displaystyle TC}$ = total cost
${\displaystyle TR}$ = total revenue
${\displaystyle Q}$ = Quantity
${\displaystyle {\frac {TC}{Q}}}$ = average total cost = ATC

The firm will enter the market if such an action would be profitable, which occurs if the price of the good exceeds the average total cost of production. The entry criterion is:

Enter if ${\displaystyle P>ATC}$

## Measuring profit in our graph for the competitive firm

The profit equals total revenue (${\displaystyle TR}$) minus total cost (${\displaystyle TC}$):

${\displaystyle Profit=TR-TC}$
${\displaystyle Profit=({\frac {TR}{Q}}-{\frac {TC}{Q}})\times Q}$
${\displaystyle Q=Quantity}$
${\displaystyle Profit=(P-ATC)\times Q}$
${\displaystyle {\frac {TC}{Q}}=average\ total\ cost=ATC}$
${\displaystyle P={\frac {TR}{Q}}=price}$

# The supply curve in a competitive market

Over short periods of time it is often difficult for firms to enter an exit, so the assumption of a fixed number of firms is appropriate. But over long periods of time, the number of firms can adjust to changing market conditions.

## The short run: market supply with a fixed number of firms

For any given price each firm supplies a quantity of output so that its marginal cost equals the price. That is, as long as price is above average variable costs, each firm’s marginal cost curve is its supply curve. The quantity supplied to the market ist the quantity supplied by each firm times the number of firms.

## The long run: market supply with entry and exit

Now consider what happens if the firms are able to enter or exit the market. Let’s suppose that everyone has access to the same technology for producing the good and access to the same markets to buy the inputs into production. Therefore, all firms and all potential firms have the same cost curves.

If firms already in the market are profitable, then new firms will have an incentive to enter the market. This entry will expand the number of firms, increase the quantity of the good supplied, and drive down prices and profits. Conversely, if firms in the market are making losses, then some existing firms will exit the market. Their exit will reduce the number of firms, decrease the quantity of the good supplied and drive up prices and profits. At the end of this process firms that remain in the market must be making zero economic profit (${\displaystyle Profit=(P-ATC)\times Q}$) An operating firm has zero profit if and only if the price of the good equals the average total cost of producing that good.

The long-run equilibrium of a competitive market with free entry an exit must have firms operating at their efficient scale. (price = marginal cost in competitive markets M free entry and exit forces price to equal average total cost; price equal marginal and average total cost; marginal and average total cost equals each other = efficient scale).

## Why do competitive firms stay in business if they make zero profit?

To answer this question we must keep in mind that profit equals total revenue minus total cost, and that total cost includes all the opportunity costs of the firm. In particular, total cost includes the opportunity cost of the rime an money that firm owners devote to the business.

## A shift in demand in the short run and long run

Because firms can enter an exit a market in the long run but not in the short run, the response of a market to a change in demand depends on the rime horizon.

Suppose the market for a good begins in log-run equilibrium. Firms are earning zero profit, so price equals the minimum of average total cost. Now suppose scientists discover that the good has miraculous health benefits. As a result the demand curve for the good shifts outward, the short run equilibrium moves, the quantity rises and the price rises. All of the existing firms respond by raising the amount produced. Because each firm’s supply curve reflects its marginal cost curve, how much they each increase production is determined by the marginal cost curve. In the new short- run equilibrium, the price of the good exceeds average total cost, so the firms are making positive profit. Over time the profit in this market encourages new firms to enter. As the number of firms grows, the short-run supply curve shifts to the right and this shift causes the price of milk to fall. The price is driven back down to the minimum of average total cost, profits are zero and firms stop entering. Thus the market reaches a new long-run equilibrium. The price has returned, but the quantity produced has risen.

## Why the long-run supply curve might slope upward

There are a large number of potential entrants, each of which faces the same costs. As a result, the long-run market supply curve is horizontal at the minimum of average total cost. When the demand for the good increases, the long-run result is an increase in the number of firms and in the total quantity supplied, without any change in the price.

There are, however, two reasons that the long-run market supply curve might slope upward. The first is that some resource used in production may be available only in limited quantities. A second reason for an upward sloping supply curve is that firms may have different costs.

Notice that if firms have different costs, some firms earns profit even in the long run. In this case, the price in the market reflects the average total cost of the marginal firm – that firm that would exit the market if the price were any lower. This firm earns zero profit, but firms with lower costs earn positive profit.