Final answer:
A lump-sum profits tax does not affect the profit-maximizing quantity of output because it does not change the marginal cost or marginal revenue, which are crucial for determining the optimal output level. The overall profit of the firm, however, is reduced by the amount of the tax.
Step-by-step explanation:
Would a lump-sum profits tax affect the profit-maximizing quantity of output? A lump-sum profits tax is a tax that is a fixed amount, regardless of the quantity of output produced. In general, this type of tax does not affect the decision of a firm regarding the quantity of output at which it maximizes its profits. This is because the lump-sum tax doesn't change the marginal cost (MC) or marginal revenue (MR) of producing additional units, which are the factors that influence the profit-maximizing level of output.
Profit maximization typically occurs when MR = MC. Assuming the market conditions are such that the firm is producing in a range where MR > MC, it continues to expand production until MR = MC. If a lump-sum tax is imposed, it does not alter the MR or the MC directly. Hence, the profit-maximizing quantity of output, where MR = MC, remains unchanged. In other words, the tax has no impact on the decision-making process regarding output levels, because it does not affect the variable costs of production.
However, while the quantity of output that maximizes profits stays the same, the overall profitability of the firm will be reduced by the amount of the lump-sum tax. This may have implications for other financial decisions but does not change the profit-maximizing output level.