2. Suppose TC 5005q2 for each firm in a perfectly competitive industry a. Derive

Question

2. Suppose TC 5005q2 for each firm in a perfectly competitive industry a. Derive MC and ATC b. Derive the typical firm's supply function c. If there are currently 100 firms in the industry, derive the market supply function d. If Qd 1200-5P, solve for the equilibrium P e. Solve for the Eqilibrium market quantity and firm quantity f. Solve for the firm's profits g. In the long, run explain whether entry or exit will occur h. Solve for the long run firm quantity i. Solve for the long run price j. Solve for the long run market quantity k. Solve for the number of firms that will exist in the market in the long run

Explanation / Answer

i - in long run the firm produced at the lowest of the long run average cost

AC = TC/Q = 500/Q+5Q

TAKE DERIVATIVE AND PUT EQUAL TO ZERO

SO 5-500/Q^2 = 0

SO Q = 10

j -------

now the firm produced AT Q = 10

ALSO P = MC IN PERFECT COMPETITION

SO P = 10Q

AT Q = 10, SO P = 100

NOW PUT P = 100 IN The demand equation, we get Q = 700 Thus long run quantity is 700

K ----- NOW WE GET THE MARKET DEMAND FROM THE PROCEDURE DEFINED ABOVE,

ALSO WE HAVE THE PER FIRM OUTPUT THAT IS Q = 10

DIVIDE THE MARKET DEMAND BY PER FIRM OUTPUT WE GET NO. OF FIRMS

which here is 700/10 = 70

so no. of firms are 70

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