5. The wage rate increases in a purely competitive industry. This change will result in a(n):
A. Decrease in average total cost for a firm in the industry
B. Decrease in average variable cost for a firm in the industry
C. Increase in the marginal cost curve for a firm in the industry
D. Increase in short-run supply curve for a firm in the industry

Question

BlackTom AI · Accepted Answer

Wage is a variable input cost, so an increase in the wage raises a firm’s variable costs and therefore its marginal cost (MC) and average variable/total costs. Key concepts: in a competitive firm short-run total cost TC = FC + VC, where VC depends on wage w and labor L; marginal cost is the extra cost of producing one more unit and depends on how much additional labor is required per extra unit produced.

Step-by-step reasoning with a small derivation:
1. Let Q = f(L, K) with K fixed in the short run. Define marginal product of labor MPL = dQ/dL.
2. Variable cost from labor is VC = w · L. Total cost derivative with respect to Q gives marginal cost:
   MC = dTC/dQ = dVC/dQ = (d(w·L)/dL)·(dL/dQ) = w · (dL/dQ).
   But dL/dQ = 1/(dQ/dL) = 1/MPL. Therefore:
   MC = w / MPL.
3. If w increases (holding MPL constant at any given Q), MC rises at every output level (MC shifts upward).

Why this makes answer C correct: an increase in w directly increases MC = w/MPL, so the firm’s marginal cost curve shifts up (an increase in the marginal cost curve).

Why other choices are incorrect:
- A (Decrease in average total cost): incorrect because higher wages raise variable costs and thus increase average total cost (ATC = TC/Q), not decrease it.
- B (Decrease in average variable cost): incorrect for the same reason—AVC = VC/Q rises when w rises.
- D (Increase in short-run supply curve): incorrect because the firm’s short-run supply (the MC curve above AVC) shifts upward/leftward (less quantity at each price), implying a decrease in supply, not an increase.

Conclusion: the correct choice is C, which matches the provided answer.

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