If the price of a firm’s variable input increases, which of the following will occur?

Question

BlackTom AI · Accepted Answer

An increase in the price of a variable input raises the firm’s marginal cost, so the firm will decrease its level of production.

1) Relevant concepts
- Total cost (TC) = Fixed cost (FC) + Variable cost (VC). Variable cost depends on input prices.  
- Marginal cost (MC) = ΔTC / ΔQ (or dTC/dQ). Because FC does not change with output, MC comes from changes in VC.  
- Profit-maximizing output in perfect competition (or profit-oriented firms) satisfies P = MC (or produces where MR = MC). An upward shift in MC reduces the profit-maximizing quantity.

2) Step-by-step reasoning
- Let VC = w·L(Q) where w is the variable input price and L(Q) the labor required for output Q. If w increases → VC increases for any given Q.  
- TC(Q) = FC + VC(Q). Therefore TC increases at all Q; MC(Q) = dTC/dQ = dVC/dQ increases because dVC/dQ includes w (higher w → larger marginal cost).  
- Graphically, the MC curve shifts upward. For a given market price P, the intersection P = MC occurs at a lower Q. Thus the firm reduces output.

3) Simple intermediate algebraic steps
- VC = w·L(Q) → ∂VC/∂Q = w·∂L/∂Q. If w rises to w′ = w + Δw (Δw > 0), then MC′ = (w + Δw)·∂L/∂Q = MC + Δw·∂L/∂Q > MC.  
- With P fixed, new Q* satisfies P = MC′(Q*), and since MC′ > MC at each Q, Q* must fall.

4) Why the correct answer is correct
Because rising variable input prices increase marginal and average variable costs, the firm’s profit-maximizing output falls (unless price changes), so it decreases production.

5) Why other options are incorrect
- “The price of the good will decrease in the short run.” Incorrect: higher firm costs typically reduce supply, which tends to raise, not lower, market price (if the market is affected). Short-run price is not guaranteed to fall.  
- “The firm’s marginal costs will decrease at every level of output.” Opposite is true: MC increases.  
- “The firm’s average fixed cost will decrease.” AFC = FC/Q depends only on FC and Q; changing variable input price does not change FC (though Q may fall, raising AFC).  
- “More firms will enter the industry in the long run.” Higher input prices reduce profitability, so entry is less likely.

6) Conclusion
These steps confirm the provided correct answer: The firm will decrease its level of production.

If the price of a firm’s variable input increases, which of the following will occur?单项选择题

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