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Home , Competition, Perfect competition

Intermediate

PERFECT BEN VAN KAMMEN, PHD PURDUE UNIVERSITY taking Price Taker: A firm or individual whose decisions regarding buying or selling have no effect on the prevailing 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 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 . MR (graphically) Total revenue Since the firm gets the same price for all units it sells (P*), its total revenue is given simply by: = . ◦ This is a linear function of q that has∗ slope ( ). 𝑇𝑇𝑇𝑇 𝑞𝑞𝑃𝑃 ∗ Now if we just bring a cost function into𝑃𝑃 the mix, we can construct the firm’s function. in the SR In the Short Run, the Total Cost function is always upward- sloping and exhibits increasing . E.g., = 7.5 + 0.1 and = 0.3 . 3 2 Combining the𝑇𝑇𝑇𝑇 TR and TC into𝑞𝑞 a profit𝑀𝑀𝑀𝑀 function:𝑞𝑞 = 7.5 + 0.1 . 9 0.32 . MarginalΠ 9𝑞𝑞 profit− is: 𝑞𝑞 Set equal to zero for maximization,2 and solve for q*: − 𝑞𝑞 9 = 1 5.477 units. 0.3 2 ∗ 𝑞𝑞 ≈ TC, TR, Π (graphically)

Distance between TR and TC maximized

q* MC intersects MR at q* The unfortunate thing for firms in perfect competition Any time competitive firms make profits, the profit is always fleeting. Perfectly competitive markets have a property called “”. ◦ 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. ( ) = 9 5.477 7.5 + 0.1 5.477 $25.36. ∗ 3 The erosionΠ 𝑞𝑞 of profits only− occurs in the long≈ run, though, so competitive firms can earn temporary economic profits. Long run zero profit condition The erosion of economic profits in a perfectly competitive market takes the form of entry by new firms. ◦ This causes the market 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: = min . ∗ In the specific𝑃𝑃𝐿𝐿𝐿𝐿 case of𝐴𝐴 𝐴𝐴constant in the production function, marginal cost is constant, so = for all levels of output, and this is the long-run price of the output: 𝐴𝐴𝐴𝐴 𝑀𝑀𝑀𝑀 = = = . ∗ 𝑀𝑀𝑀𝑀 𝐴𝐴𝐴𝐴 𝑀𝑀𝑀𝑀 𝑃𝑃𝐿𝐿𝐿𝐿 Losses in the short run The reverse case of profits in the short run occurs when the market price is less than the short run 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 curve In 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 . ◦ When a demand curve is perfectly flat, its price is infinite, i.e., perfectly elastic. The shut down rule For 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 𝐴𝐴𝐴𝐴𝐴𝐴 Example The firm’s capital stock in the short run is = 8. = . 𝑆𝑆𝑆𝑆 Its production function is 2 1 𝐾𝐾 = 4 . 3 3 ◦ But with capital fixed, it is 1 𝑞𝑞 𝐾𝐾3 𝐿𝐿 Assume that the rental rate𝑞𝑞 is𝐿𝐿 $2.50, so the firm incurs $12 of sunk costs regardless of how much it produces.

Total costs are given by = 12 + . 3 ◦ If the rate is $12 as in the costs lesson,𝑤𝑤𝑞𝑞 the total cost function is: = 12 + . 𝑇𝑇𝑇𝑇 64 3 3 ◦ $12𝑇𝑇𝑇𝑇 is the fixed cost;16 𝑞𝑞 is the variable cost. 3 3 16 𝑞𝑞 Average variable cost

AVC is defined as Variable Costs divided by q: 3 = . 16 2 In cases where the production𝐴𝐴𝐴𝐴𝐴𝐴 always𝑞𝑞 has the same returns to scale, AVC will lie below the Marginal , but where there are increasing returns over some range of output the shut down rule will come into relevance. curves

Shut down rule doesn’t come into here. Shut down rule

If the price is less than the starred point, the firm should shut down. Reasoning The 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 curve If you arbitrarily vary the market price of a firm’s output, it will respond by producing a quantity determined by the MC curve—where = . ∗ When P* changes,𝑀𝑀𝑀𝑀 the𝑃𝑃 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. Summary Firms 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*. Summary In 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. Conclusion We 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, = . ∗ Next we will look at scenarios𝑀𝑀𝑀𝑀 in𝑃𝑃 which the firm must decrease the price in order to sell additional units . . . and in which MR < P.