Intermediate Microeconomics

PERFECT COMPETITIONBEN VAN KAMMEN, PHDPURDUE UNIVERSITY

Price takingPrice Taker: A firm or individual whose decisions regarding buying or selling have no effect on the prevailing market price of a good.In a perfectly competitive market, sellers (firms) are price takers because there other firms that would immediately be willing to undercut anyone attempting to charge more than the market price.◦ Any firm that tried to charge more would not sell anything at all.

The result of price taking is that a single firm can sell as many units of output as it wishes, provided it does so at the market price.

MR = P*If the market equilibrium price in a competitive market is denoted P*, the marginal revenue to a firm in that market equals P*.◦ Remember MR is the additional revenue from selling an extra unit of

output.

Since the individual firm is a price taker in this market, P* does not change when the firm alters its quantity of output.◦ P*, and consequently MR, is constant for all values of q in perfect

competition.

MR (graphically)

Total revenueSince the firm gets the same price for all units it sells (P*), its total revenue is given simply by:

𝑇𝑇𝑇𝑇 = 𝑞𝑞𝑃𝑃∗.◦ This is a linear function of q that has slope (𝑃𝑃∗).

Now if we just bring a cost function into the mix, we can construct the firm’s profit function.

Profit maximization in the SRIn the Short Run, the Total Cost function is always upward-sloping and exhibits increasing marginal cost. E.g.,

𝑇𝑇𝑇𝑇 = 7.5 + 0.1𝑞𝑞3 and 𝑀𝑀𝑇𝑇 = 0.3𝑞𝑞2.

Combining the TR and TC into a profit function:

Π = 9𝑞𝑞 − 7.5 + 0.1𝑞𝑞2 .Marginal profit is: 9 − 0.3𝑞𝑞2.Set equal to zero for maximization, and solve for q*:

𝑞𝑞∗ =9

0.3

12≈ 5.477 units.

TC, TR, Π (graphically)

q*

Distance between TR and TC maximized

MC intersects MR at q*

The unfortunate thing for firms in perfect competitionAny time competitive firms make profits, the profit is always fleeting.

Perfectly competitive markets have a property called “free entry”.◦ This means that if existing firms are making positive economic profits, new

firms will enter the market and “compete” the profits away.◦ That is what would happen in this case, since q* results in positive

economic profits.Π(𝑞𝑞∗) = 9 5.477 − 7.5 + 0.1 5.477 3 ≈ $25.36.

The erosion of profits only occurs in the long run, though, so competitive firms can earn temporary economic profits.

Long run zero profit conditionThe erosion of economic profits in a perfectly competitive market takes the form of entry by new firms.◦ This causes the market supply curve to shift outward—depressing

the market price to the minimum at which firms can break even.◦ In the long run the price in a competitive market will be the

minimum average total cost of production when all inputs are variable: 𝑃𝑃𝐿𝐿𝐿𝐿∗ = min 𝐴𝐴𝑇𝑇 .

In the specific case of constant returns to scale in the production function, marginal cost is constant, so 𝐴𝐴𝑇𝑇 =𝑀𝑀𝑇𝑇 for all levels of output, and this is the long-run price of the output:

𝑀𝑀𝑇𝑇 = 𝐴𝐴𝑇𝑇 = 𝑀𝑀𝑇𝑇 = 𝑃𝑃𝐿𝐿𝐿𝐿∗ .

Losses in the short runThe reverse case of profits in the short run occurs when the market price is less than the short run average cost of production.◦ Even when the firm does its best, it makes losses under these

conditions.This will be ameliorated in the long run by having some firms exit the market.◦ Thus pulling up the market price with an inward shift of market

supply.

MR as the firm’s demand curveIn a perfectly competitive market, the demand for a specific firm’s output is perfectly elastic.

You can think of the horizontal MR curve as the firm’s demand curve.◦ When a demand curve is perfectly flat, its price elasticity is infinite,

i.e., perfectly elastic.

The shut down ruleFor the sake of considering all the firm’s possible options, it is worth noting that the firm always has the option of producing nothing in the short run and incurring only its fixed costs.

It would do this when the market price of output is less than the average variable cost of producing its profit maximizing q*.◦ Shut Down if 𝑃𝑃∗ < 𝐴𝐴𝐴𝐴𝑇𝑇.

ExampleThe firm’s capital stock in the short run is 𝐾𝐾𝑆𝑆𝐿𝐿 = 8.

Its production function is 𝑞𝑞 = 𝐾𝐾23𝐿𝐿

13.

◦ But with capital fixed, it is 𝑞𝑞 = 4𝐿𝐿13.

Assume that the rental rate is $2.50, so the firm incurs $12 of sunk costs regardless of how much it produces.

Total costs are given by 𝑇𝑇𝑇𝑇 = 12 + 𝑤𝑤𝑞𝑞3

64.

◦ If the wage rate is $12 as in the costs lesson, the total cost function is: 𝑇𝑇𝑇𝑇 = 12 + 3

16𝑞𝑞3.

◦ $12 is the fixed cost; 316

𝑞𝑞3 is the variable cost.

Average variable costAVC is defined as Variable Costs divided by q:

𝐴𝐴𝐴𝐴𝑇𝑇 =3

16𝑞𝑞2.

In cases where the production always has the same returns to scale, AVC will lie below the Marginal Cost curve, but where there are increasing returns over some range of output the shut down rule will come into relevance.

Relevant cost curves

Shut down rule doesn’t come into play here.

Shut down rule

If the price is less than the starred point, the firm should shut down.

ReasoningThe shut down rule applies because the firm cannot be made to incur more losses by producing output.◦ If the price wasn’t even sufficient to cover the variable costs of

production, the firm would have smaller losses if it produced nothing.

Significance of the MC curveIf you arbitrarily vary the market price of a firm’s output, it will respond by producing a quantity determined by the MC curve—where 𝑀𝑀𝑇𝑇 = 𝑃𝑃∗.When P* changes, the new optimal quantity is found by plugging the new P* into the MC curve again.

So MC gives the firms quantity supplied when you plug in the market price.

Consequently the MC curve is the firm’s supply curve.

SummaryFirms in perfectly competitive markets are price takers in the sense that they cannot affect the market price through their own actions.

The marginal revenue for a competitive firm is the market price, P*.

Competitive firms can earn either profits or losses in the short run.

The maximize profits in the short run by producing a quantity such that MC = MR = P*.

SummaryIn the long run, free entry and exit drives the price to the minimum average cost.◦ The result of this is zero economic profit for firms in a competitive

market.

MR is the demand curve for the individual firm’s output.

MC is the individual firm’s supply curve.

Firms have the option of shutting down in the short run if they would incur larger losses by producing output.

ConclusionWe have examined the revenue for a firm that has a very specific shape for its demand curve (perfectly elastic).

In general this is a restrictive condition. It is more common that a firm faces a downward-sloping demand curve.◦ This violates the condition, 𝑀𝑀𝑇𝑇 = 𝑃𝑃∗.

Next we will look at scenarios in which the firm must decrease the price in order to sell additional units . . . and in which MR < P.