Question

A3-10. Imagine a firm with the short run cost structure: Total Cost (TC) = 9 + q 2  Marginal Cost (MC) = 2q.

(a) Write out expressions for total fixed cost (FC), total variable cost (VC), average variable cost (AVC), and average total cost (ATC). Be sure to show your work.

(b) At what quantity is AVC at its minimum (at what AVC level)? At what quantity is ATC at its minimum (at what ATC level)?

(c) Given your results above, sketch MC and AVC from q = 0 to q = 9. Calculate ATC for q = 1, 3, 6, and 9. Use this information to add ATC to your diagram (from q = 1 to q = 9).

(d) Assuming that the firm is a price-taker operating in a competitive market, derive an expression for the firm’s supply curve, (ie. the profit maximizing output for the firm as a function of the market price). What is the shut-down price for this firm (ie. at what price would this firm choose to produce zero)?

(e) Suppose the competitive market is composed of firms (and potential firms) identical to the one described above. Is it possible that a market price of $8 is a short run equilibrium price? Is it possible that a market price of $4 is a short run equilibrium price? Explain.

(f) Assuming that the minimum point of the short run ATC curve for all firms is also the minimum point of the long run average cost curve (LRAC) is it possible that either of the prices identified in part (e) is a long run equilibrium price? Explain.

(g) Under the assumptions of parts (e) and (f), what is the long run equilibrium price in this market? If, at that price, the quantity demanded in the market is 882 units, what is long run equilibrium number of firms in this market?

Answer 1

In the last part, since both MC and ATC lie to the left of AVC (which is actually the P=q line), P<q will never occur at any price.