Question

Consider a firm with the following total cost function: TC = 50 + 6Q + 4Q2 . The marginal cost associated with the given cost function is MC = 6 + 8Q. Assume the firm is operating in the short-run.

A) What are the firm’s fixed costs? What are the firm’s variable costs?

B) Calculate average fixed costs, average variable costs, and average total costs.

C) Suppose the firm is in a competitive market and is a price taker. Suppose the equilibrium price is P = 86. Will the firm participate in the market or shutdown? Determine whether the firm is able to recover its fixed costs when P = 86.

Answer 1

A) Fixed costs are incurred when no output is produced i.e. Q=0. By putting this in TC equation, we get TC = 50 which is the firm's fixed cost. Variable Cost is Total Cost - Fixed Cost = 6Q + 4Q2.

B) Average Fixed Cost = Fixed Cost/ Q

= 50 / Q.

Average total Cost= TC / Q

= 50/Q + 6 + 4Q

Average variable cost = Variable Cost/ Q

= 6 + 4Q.

C) If P < AVC then the firm will shut down its operations

Now, if the firm is price taker then P= MC

=> 86 = 6 + 8Q

=> Q = 10.

At this value of Q, AVC = 6 + 4(10)

= 46

Hence the firm continues to operate in the market.