Q4. Suppose a firm must pay an annua... [FREE SOLUTION]

Chapter 7: Q4. (page 280)

Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output.
How does this tax affect the firm鈥檚 fixed, marginal, and average costs?
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鈥檚 fixed, marginal, and average costs?

Short Answer

Expert verified

The firm鈥檚 fixed cost and average fixed cost will increase by T and T/Q, respectively. The marginal cost will remain untouched.
The firm鈥檚 marginal and average total cost will increase while the fixed cost remains the same.

Step by step solution

Change in the fixed, marginal, and average total cost by a fixed tax

The firm has fixed costs, invested in capital goods like machinery, plant, transportation, etc. It does not vary with the quantity.Since the tax imposed is also a fixed sum irrespective of the output, the fixed cost will increase by the tax (T).

TFC = FC + T

The marginal cost is the variable cost per unit.It will remain unaffected by the tax because tax is not related to quantity. The average total cost will increase by T/Q because the average cost is the combined result of total fixed and total variable costs.

ATC = (FC + T)/Q + AVC

Change in fixed, marginal, and average total cost by a change in the variable tax

The marginal cost varies per unit. Since the tax is proportional to the output produced, the marginal cost will increase by the tax per unit (T/Q). The fixed cost will not alter at all because the tax depends on the number of units. If the firm does not produce any output, the tax will be zero, but the fixed cost will remain the same.

The average total cost will also increase by (T/Q) as the tax will increase the total variable cost by tax (T).