Question

In a perfect competition model, the change in which of the following costs/ imposition of taxes does not affect the equilibrium position of the firm in the short run.
(A). Increase in fixed cost
(B). Imposition of lump-sum tax
(C). Imposition of profit tax
(D). Imposition of specific sales tax (Per unit of output)
Choose the correct answer from the options given below:

• A. (A), (B) and (C) only.
• B. (A), (B) and (D) only.
• C. (A), (B), (C) and (D).
• D. (B), (C) and (D) only.

Hint:

Lump-sum taxes, fixed costs, and profit taxes do not affect Marginal Cost.
If Marginal Cost is unaffected, the firm's profit-maximizing output level remains unchanged in the short run.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In the short run, a perfectly competitive firm maximizes profit at the output level where Marginal Revenue ($MR$) equals Marginal Cost ($MC$).
Because the firm is a price taker, $P = MR$. Therefore, the equilibrium output is determined by the condition:
\[ P = MC \] Any tax or cost change that does not alter the $MC$ curve will not change the short-run equilibrium output.

Step 2: Detailed Explanation:
Let us analyze how each option affects the costs of a firm:
- (A). Increase in fixed cost:
Total Cost ($TC$) is the sum of Total Fixed Cost ($TFC$) and Total Variable Cost ($TVC$).
Marginal Cost ($MC$) is the derivative of Total Cost with respect to output:
\[ MC = \frac{d(TC)}{dQ} = \frac{d(TVC)}{dQ} \] An increase in fixed costs does not change variable costs or the derivative of variable costs.
Since $MC$ remains unchanged, the firm's profit-maximizing output is unaffected.
- (B). Imposition of lump-sum tax:
A lump-sum tax is a fixed fee imposed regardless of the level of output.
It is treated as a fixed cost. Because it does not vary with output, it does not alter the $MC$ curve.
Thus, the short-run equilibrium position is unchanged.
- (C). Imposition of profit tax:
A tax on economic profit is proportional to net earnings.
The post-tax profit function is:
\[ \Pi_{\text{post-tax}} = (1 - t) \times \Pi_{\text{pre-tax}} \] To maximize post-tax profits, we differentiate with respect to output:
\[ \frac{d\Pi_{\text{post-tax}}}{dQ} = (1 - t) \frac{d\Pi_{\text{pre-tax}}}{dQ} = 0 \implies \frac{d\Pi_{\text{pre-tax}}}{dQ} = 0 \] The output level that maximizes pre-tax profits also maximizes post-tax profits.
Hence, a profit tax does not alter the equilibrium output.
- (D). Imposition of a specific sales tax (per unit of output):
A specific sales tax of $t$ per unit is a variable cost.
It shifts the marginal cost curve upward by the amount of the tax ($MC_{\text{new}} = MC_{\text{old}} + t$).
This changes the intersection point of $MR$ and $MC$, altering the firm's equilibrium position by reducing output.
Thus, only (A), (B), and (C) do not affect the equilibrium position in the short run.

Step 3: Final Answer:
Therefore, the correct option is (A).