Question

Consider a market for tables. Assume that all current and potential firms have the same total cost function, ?? = 3 + 3? ଶ . In the short run, a firm in the market still has to pay 3 even if ? = 0. In the long run, if a firm chooses to exit, it pays nothing. The market demand curve for this table is given by ?d = 600 − 50P. a. (3 points) Find each firm’s average total cost, average variable cost, and marginal cost functions. b. (2 points) Give the equations for each firm’s supply curve in the short run and in the long run. c. (3 points) Currently, there are 420 firms in the market. Give the equation for the market supply curve for the short run. What is the equilibrium price and quantity for this market in the short run? d. (3 points) In the long run with free entry and exit, what is the equilibrium price and quantity in this market? In the long-run equilibrium, how much does each firm produce? e. (1 point) In this long-run equilibrium from c, how many firms are in the market?

Answer 1

a. Each firm's average total cost, average variable cost, and marginal cost functions are:

b. Each firm equates its marginal cost with the market price to compute its supply function:

c. The market supply is the summation of the individual supply functions:

In the short run, equilibrium market price has to be equal to 3. If it is greater than 3, all firms will supply infinite quantity and supply will never be equal to demand. Similarly, if price is less than 3, no firm will supply any quantity.

d. In the long run too, price has to be equal to 3 for the same reason as above. Therefore, equilibrium price is 3 and equilibrium quantity is 450. However, in the long run, each firm will produce at least 2 units to cover its fixed cost. If any firm produces more than 2 units, it earns a positive profit. Since no firm can earn positive profit in the long run in a competitive setting, each firm produces exactly 2 units. Therefore, number of firms in the long run is 450/2 =225.