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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.

  1. How does this tax affect the firm’s fixed, marginal, and average costs?

  2. 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

Expert verified

  1. The firm’s fixed cost and average fixed cost will increase by T and T/Q, respectively. The marginal cost will remain untouched.

  2. The firm’s marginal and average total cost will increase while the fixed cost remains the same.

Step by step solution

01

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

02

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).

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Most popular questions from this chapter

You manage a plant that mass-produces engines by teams of workers using assembly machines. The technology is summarized by the production function q = 5KL where q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r = \(10,000 per week, and each team costs w = \)5000 per week. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design.

  1. What is the cost function for your plant—namely, how much would it cost to produce q engines? What are average and marginal costs for producing q engines? How do average costs vary with output?

  2. How many teams are required to produce 250 engines? What is the average cost per engine?

  3. You are asked to make recommendations for the design of a new production facility. What capital/ labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing at any level of output q?

Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path.

A firm has a fixed production cost of \(5000 and a constant marginal cost of production of \)500 per unit produced.

  1. What is the firm’s total cost function? Average cost?

  2. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.

Suppose that a paving company produces paved parking spaces (q) using a fixed quantity of land (T) and variable quantities of cement (C) and labor (L). The firm is currently paving 1000 parking spaces. The firm’s cost of cement is \(4,000 per acre covered, and its cost of labor is \)12/hour. For the quantities of C and L that the firm has chosen, MPC = 50 and MPL = 4.

  1. Is this firm minimizing its cost of producing parking spaces? How do you know?

  2. If the firm is not cost-minimizing, how must it alter its choices of C and L in order to decrease cost?

A computer company’s cost function, which relates its average cost of production AC to its cumulative output in thousands of computers Q and its plant size in terms of thousands of computers produced per year q (within the production range of 10,000 to 50,000 computers), is given by AC = 10 - 0.1Q + 0.3q

  1. Is there a learning-curve effect?

  2. Are there economies or diseconomies of scale?

  3. During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease? Explain.
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