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## 8.3 Review and Practice

### Summary

In this chapter we have concentrated on the production and cost relationships facing firms in the short run and in the long run.

In the short run, a firm has at least one factor of production that it cannot vary. This fixed factor limits the firm’s range of factor choices. As a firm uses more and more of a variable factor (with fixed quantities of other factors of production), it is likely to experience at first increasing, then diminishing, then negative marginal returns. Thus, the short-run total cost curve has a positive value at a zero level of output (the firm’s total fixed cost), then slopes upward at a decreasing rate (the range of increasing marginal returns), and then slopes upward at an increasing rate (the range of diminishing marginal returns).

In addition to short-run total product and total cost curves, we derived a firm’s marginal product, average product, average total cost, average variable cost, average fixed cost, and marginal cost curves.

If the firm is to maximize profit in the long run, it must select the cost-minimizing combination of factors for its chosen level of output. Thus, the firm must try to use factors of production in accordance with the marginal decision rule. That is, it will use factors so that the ratio of marginal product to factor price is equal for all factors of production.

A firm’s long-run average cost (LRAC) curve includes a range of economies of scale, over which the curve slopes downward, and a range of diseconomies of scale, over which the curve slopes upward. There may be an intervening range of output over which the firm experiences constant returns to scale; its LRAC curve will be horizontal over this range. The size of operations necessary to reach the lowest point on the LRAC curve has a great deal to do with determining the relative sizes of firms in an industry.

This chapter has focused on the nature of production processes and the costs associated with them. These ideas will prove useful in understanding the behavior of firms and the decisions they make concerning supply of goods and services.

### Concept Problems

1. Which of the following would be considered long-run choices? Which are short-run choices?

1. A dentist hires a new part-time dental hygienist.
2. The local oil refinery plans a complete restructuring of its production processes, including relocating the plant.
3. A farmer increases the quantity of water applied to his or her fields.
4. A law partnership signs a 3-year lease for an office complex.
5. The university hires a new football coach on a 3-year contract.
2. “There are no fixed costs in the long run.” Explain.
3. Business is booming at the local McDonald’s restaurant. It is contemplating adding a new grill and french-fry machine, but the day supervisor suggests simply hiring more workers. How should the manager decide which alternative to pursue?
4. Suppose that the average age of students in your economics class is 23.7 years. If a new 19-year-old student enrolls in the class, will the average age in the class rise or fall? Explain how this relates to the relationship between average and marginal values.
5. Barry Bond’s career home run average in his first 15 years in major league baseball (through 1997) was 33 home runs per season. In 2001, he hit 73 home runs. What happened to his career home run average? What effect did his performance in 2001 have on his career home run average? Explain how this relates to the relationship between average and marginal values.
6. Suppose a firm is operating at the minimum point of its short-run average total cost curve, so that marginal cost equals average total cost. Under what circumstances would it choose to alter the size of its plant? Explain.
7. What happens to the difference between average total cost and average variable cost as a firm’s output expands? Explain.
8. How would each of the following affect average total cost, average variable cost, and marginal cost?

1. An increase in the cost of the lease of the firm’s building
2. A reduction in the price of electricity
3. A reduction in wages
4. A change in the salary of the president of the company
9. Consider the following types of firms. For each one, the long-run average cost curve eventually exhibits diseconomies of scale. For which firms would you expect diseconomies of scale to set in at relatively low levels of output? Why?

1. A copy shop
2. A hardware store
3. A dairy
4. A newspaper
5. An automobile manufacturer
6. A restaurant
10. As car manufacturers incorporate more sophisticated computer technology in their vehicles, auto-repair shops require more computerized testing equipment, which is quite expensive, in order to repair newer cars. How is this likely to affect the shape of these firms’ long-run average total cost curves? How is it likely to affect the number of auto-repair firms in any market?

### Numerical Problems

1. The table below shows how the number of university classrooms cleaned in an evening varies with the number of janitors:

 Janitors per evening 0 1 2 3 4 5 6 7 Classrooms cleaned per evening 0 3 7 12 16 17 17 16
1. What is the marginal product of the second janitor?
2. What is the average product of four janitors?
3. Is the addition of the third janitor associated with increasing, diminishing, or negative marginal returns? Explain.
4. Is the addition of the fourth janitor associated with increasing, diminishing, or negative marginal returns? Explain.
5. Is the addition of the seventh janitor associated with increasing, diminishing, or negative marginal returns? Explain.
6. Draw the total product, average product, and marginal product curves and shade the regions corresponding to increasing marginal returns, decreasing marginal returns, and negative marginal returns.
7. Calculate the slope of the total product curve as each janitor is added.
8. Characterize the nature of marginal returns in the region where

1. The slope of the total product curve is positive and increasing.
2. The slope of the total product curve is positive and decreasing.
3. The slope of the total product curve is negative.
2. Suppose a firm is producing 1,000 units of output. Its average fixed costs are \$100. Its average variable costs are \$50. What is the total cost of producing 1,000 units of output?
3. The director of a nonprofit foundation that sponsors 8-week summer institutes for graduate students analyzed the costs and expected revenues for the next summer institute and recommended that the session be canceled. In her analysis she included a share of the foundation’s overhead—the salaries of the director and staff and costs of maintaining the office—to the program. She estimated costs and revenues as follows:

 Projected revenues (from tuition and fees) \$300,000 Projected costs Overhead \$ 50,000 Room and board for students \$100,000 Costs for faculty and miscellaneous \$175,000 Total costs \$325,000

What was the error in the director’s recommendation?

4. The table below shows the total cost of cleaning classrooms:

 Classrooms cleaned per evening 0 3 7 12 16 17 Total cost \$100 \$200 \$300 \$400 \$500 \$600
1. What is the average fixed cost of cleaning three classrooms?
2. What is the average variable cost of cleaning three classrooms?
3. What is the average fixed cost of cleaning seven classrooms?
4. What is the average variable cost of cleaning seven classrooms?
5. What is the marginal cost of cleaning the seventeenth classroom?
6. What is the average total cost of cleaning twelve classrooms?
5. The average total cost for printing 10,000 copies of an issue of a magazine is \$0.45 per copy. For 20,000 copies, the average total cost is \$0.35 apiece; for 30,000, the average total cost is \$0.30 per copy. The average total cost continues to decline slightly over every level of output that the publishers of the magazine have considered. Sketch the approximate shapes of the average and marginal cost curves. What are some variable costs of publishing magazines? Some fixed costs?
6. The information in the table explains the production of socks. Assume that the price per unit of the variable factor of production (L) is \$20 and the price per unit of the fixed factor of production (K) is \$5.

Units of Fixed Factor (K) Units of Variable Factor (L) Total Product (Q)
10 0 0
10 1 2
10 2 5
10 3 12
10 4 15
10 5 16
1. Add columns to the table and calculate the values for : Marginal Product of Labor (MPL), Total Variable Cost (TVC), Total Fixed Cost (TFC), Total Cost (TC), Average Variable Cost (AVC), Average Fixed Cost (AFC), Average Total Cost (ATC), and Marginal Cost (MC).
2. On two sets of axes, graph the Total Product and Marginal Product curves. Be sure to label curves and axes and remember to plot marginal product using the midpoint convention. Indicate the point on each graph at which diminishing marginal returns appears to begin.
3. Graph Total Variable Cost, Total Fixed Cost, and Total Cost on another set of axes. Indicate the point on the graph at which diminishing marginal returns appears to begin.
4. Graph the Average Fixed Cost, Average Variable Cost, Average Total Cost, and Marginal Cost curves on another set of axes. Indicate the point at which diminishing marginal returns appears to begin.
7. The table below shows the long-run average cost of producing knives:

 Knives per hour 1,000 2,000 3,000 4,000 5,000 6,000 Cost per knife \$2 \$1.50 \$1.00 \$1.00 \$1.20 \$1.30
1. Draw the long-run average cost curve for knives.
2. Shade the regions corresponding to economies of scale, constant returns to scale, and diseconomies of scale.
3. In the region of the long-run average cost curve that corresponds to economies of scale, what is happening to the cost per knife?
4. In the region of the long-run average cost curve that corresponds to constant returns to scale, what is happening to the cost per knife?
5. In the region of the long-run average cost curve that corresponds to diseconomies of scale, what is happening to the cost per knife?
8. Suppose a firm finds that the marginal product of capital is 60 and the marginal product of labor is 20. If the price of capital is \$6 and the price of labor is \$2.50, how should the firm adjust its mix of capital and labor? What will be the result?
9. A firm minimizes its costs by using inputs such that the marginal product of labor is 10 and the marginal product of capital is 20. The price of capital is \$10 per unit. What must the price of labor be?
10. Suppose that the price of labor is \$10 per unit and the price of capital is \$20 per unit.

1. Assuming the firm is minimizing its cost, if the marginal product of labor is 50, what must the marginal product of capital be?
2. Suppose the price of capital increases to \$25 per unit, while the price of labor stays the same. To minimize the cost of producing the same level of output, would the firm become more capital-intensive or labor-intensive? Explain.