Question

Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output. a. How does this tax affect the firm's fixed, marginal, and average costs? b. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm's fixed, marginal, and average costs?

Short answer

A fixed sum tax increases the firm's fixed and average costs but does not affect the marginal cost. On the other hand, a tax that is proportional to the number of items produced increases the marginal cost and average cost but does not affect the fixed cost.

Step-by-step solution

Impact of Fixed Sum Tax

If a firm must pay a fixed sum tax regardless of its production, then this tax will be considered part of the firm's fixed costs because it does not vary with the level of production. As a result, it increases the firm's fixed costs by the amount of the tax. However, this tax does not affect the firm's marginal cost because it will not increase the cost of producing one more unit. Similarly, it will increase average costs indirectly since average cost is derived from fixed and variable costs (average cost = total fixed costs/quantity + variable cost/quantity).

Impact of Proportional Tax

If the firm is charged a tax that is proportional to the number of units it produces, then this tax does not affect the firm's fixed costs but it does affect its marginal and average costs. This kind of tax increases the marginal cost and the average variable cost by the amount of the tax per unit because it increases the cost of production for each unit. The more a firm produces, the more tax it will have to pay, so the cost per unit (both marginal and average) increase.