Suppose the short run total cost functions for all existing and potential firms

Question

Suppose the short run total cost functions for all existing and potential firms in a competitive industry are given by: TC = 100 + 10q + q 2 , where q is the output level of the firm in a given period. This means that MC = 10 + 2q. (a) Derive expressions for total fixed cost (FC), total variable cost (VC), average fixed cost (AFC), average variable cost (AVC), and average total cost (ATC). [4] (b) What is ATC when output equals 5? What is ATC when output equals 20? At what level of output is ATC at its minimum, and what is the minimum ATC level? Using this information and the expressions from part (a), sketch MC, AVC, and ATC up to the output level of 20. [6] (c) What does the MC curve tell us about the marginal product (MP) of the firm’s variable factor of production (presumably labour)? [4] (d) What is the firm’s profit maximizing output at the following prices: 5, 20, 30, and 40? What is the level of profits at each of the prices? [8] (e) Now assume that all existing and potential firms have the same cost function and that the minimum point on the short-run ATC is also the minimum point on long-run average cost (LRAC). Briefly explain why only one of the prices identified in part (d) is a long-run equilibrium price. [4]

Explanation / Answer

a) Total fixed cost is the cost which is constant and does not depend on quantity. TFC = 100

Total variable cost is the cost which depends on quantity. TVC = 10q + q2

AFC = TFC/q = 100/q

AVC =TVC/q = 10 + q

ATC = TC/q = (100 + 10q + q2)/q = 100/q + 10 + q

b) ATC when q is 5 = 100/5 + 10 + 5 = 20 + 15 = 35

ATC when q is 20 = 100/20 + 10 + 20 = 35

dATC/dq = - 100/q2 + 1 = 0

q2 = 100

q = 10 units

d2ATC/dq2 = 200/q3 > 0 i.e. minimum

So, ATC is minimum at q = 10 units

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