The W Company is a member of the beef industry, which is perfectly competitive.

Question

The W Company is a member of the beef industry, which is perfectly competitive. The price of a beef is $60. The firm’s total cost function is TC = 100 + 10Q + 5Q2 where TC is total cost (in dollars) and Q is hourly output.

a. What output maximizes profit? (3 points).

b. What is the firm’s economic profit at this output? (3 points).

c. What is the firm’s average cost at this output? (3 points).

d. If other firms in the beef industry have the same cost function as this firm, is the industry in equilibrium? Why or why not? (3 points).

Explanation / Answer

(a) profit maximizing is output is one where MR=MC

TR= PQ= 60Q, then MR= 60

As TC= 100 + 10Q + 5Q2, MC=10+10Q

equating MR with MC, 10+10Q= 60

Q=5 is the profit maximizing level of output

(b) Economic profit is given by Total Revenue minus Total cost

hence, 60Q -(100-10Q-5Q2)

Economic profir =300-100-50-125= $25

(c) Average cost : AC=100/Q+5Q+10

AC at profit maximizing output= 100/5+52+ 10= $55

(d) If other firms in the industry have same cost function as this firm, then the total cost and marginal is the same for all firms. Given that Price =AR=MR under perfect competition, all firms will have the same equlibrium profit ($25) and output(5). Hence the indusrty is in equlibrium

or,

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