CHAPTER 6 Firms and Production CHAPTER OUTLINE 6.1 The Ownership and Management of Firms Ownership of Firms The Management of Firms What Owners Want 6.2 Production Production Functions Time and the Variability of Inputs 6.3 Short-Run Production: One Variable and One Fixed Input Total Product Marginal Product of Labor Average Product of Labor Graphing the Product Curves Law of Diminishing Marginal Returns 6.4 Long-Run Production: Two Variable Inputs Isoquants Substituting Inputs 6.5 Returns to Scale Constant, Increasing, and Decreasing Returns to Scale Varying Returns to Scale 6.6 Productivity and Technical Change Relative Productivity Innovations TEACHING TIPS Before beginning the material in Chapter 6, you might remind students that the course is broken roughly into thirds, and that this material begins the second portion of the course, in which activity inside the firm is discussed in detail. Throughout Chapters 6 and 7, it is helpful to students if you emphasize the conceptual parallels between the mechanics of cost minimization, isoquants, and isocost lines to those of utility maximization, indifference curves, and budget lines. Because students take for granted that firms exist, you may want to begin with a discussion of why firms do exist. If you begin by asking the class to define the purpose of a firm, “to make money” will likely be the most frequently offered response, although some may also offer answers related to tax advantages or limitation of liability. In an effort to get students to think about firms as a mechanism for reducing transaction costs, you might ask the class to consider the following example. Suppose I want to make money in the landscaping industry. But instead of starting a firm, each morning I rent a U-haul truck, rent several lawn mowers, trimmers, and rakes, and drive up and down the street yelling: “Who wants to cut lawns today?” Once I have enough workers, I ring doorbells to get customers, collect the money, pay the workers, pay for the rented capital, and put the residual in my pocket. Thus, I am making money, but there is no firm. At this point, students may not remember the term transaction costs from Chapter 1, but they should be able to suggest lots of ways that the residual (profits) could be increased by doing things such as purchasing some or all of the capital, hiring permanent employees, and contracting with customers. You might want to conclude this with counterexamples of instances where it is better to use the market rather than internalize all transactions related to a final product. Suppose, for example, that a firm that manufactures engines needs castings. If the quality of the castings drops off, the firm can seek other suppliers, which is

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36 ❈ Part One\Teaching Aids the foundry owner’s problem. If the firm owns the foundry, problems at the foundry are internal to the firm and must be solved by management, rather than through the use of the market. This discussion can lead you into the material on ownership and management that begins the chapter, or to a discussion of outsourcing and mergers that are covered later in the text. Another point you may want to make regarding terminology is the reference to firms as having wants and needs. Firms are operated by owners and managers who want and need things, but a firm is simply a legal entity that, of course, cannot want or need anything. It is a misuse of terms to say that “a firm wants…” but it is a convenience that economists use. As you work through Chapters 6 and 7, you may need to remind students at times that this material is not about prices and profits. As the text notes, efficient production is necessary, but not sufficient for profit maximization. I also remind the class occasionally that capital, labor, and output are measured in physical units rather than dollars in Chapter 6. When covering the short-run product definitions (total, average, and marginal), it is important to note that while quantities of labor and output information must be given or come from a production function that is given, all of the remaining concepts are derived from the relationship between these two variables. Students sometimes get confused about what information must be given, and what can be derived from information that is already known. It is also important to explain how each curve is related to the others, as students tend to think of each as a stand-alone object. This strategy is also effective in Chapter 7, where you should note that all of the cost and product curves are different ways to look at the same information. When discussing long-run production, you may want to begin by asking the class about the similarities between isoquants and indifference curves. This is helpful when introducing the concept of substitutability and the MRTS. The text has a nice, straightforward explanation of technical change. Since most of the technical change that is discussed in the popular press is not neutral, but has some effect on employment, it is well worth covering and supplementing with current examples to go with the applications already in the chapter. As a contrast, you may want to discuss the inability to adopt technical change in some production processes, as in the piano industry described below in the additional application. ADDITIONAL APPLICATION Technical Changes in Piano Making It takes one year and over 200 production workers to build a Steinway Model D grand piano, which has 12,000 parts. The factory produces 150 of these pianos per year. Steinway’s technology virtually stopped evolving about 1900. The number of pianos produced per year and the number of workers in the factory has remained constant. They can’t use machinery to replace workers, but they can use machinery to aid the workers. Steinway still uses some equipment that was built in the Victorian era, such as a veneer-edge cutter from 1871. Modern equipment is used to refine the tools they use, improve the tolerances of action parts, and make parts that don’t need custom fitting. A computer-aided router cuts the final shape of the top lid. A “sounder” machine breaks the pianos in by pounding every key 8,000 times within 45 minutes. An engineer uses CAD/CAM software on a computer to design an action part. Similarly, new materials are used, partly of necessity. Since the ban on the trade of ivory in 1989, keys are now made of a mock-ivory polymer. Cloth bushings that line certain metal pins that serve as hinges in the action are now made of TeflonTM-impregnated wool. Yamaha, using a more mechanized approach, makes 250,000 pianos per year, compared to the 523,000 pianos Steinway has produced in 140 years. Yamaha makes fine instruments, but they are not in the class of the Steinway grand piano.

Chapter 6\Firms and Production ❈

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1. Given the information provided, what do you predict about the shape of isoquants for Steinway? 2. The story about production at Steinway is very similar to that of the C. F. Martin Company, makers of some of the world’s finest acoustic guitars. The production of Martin guitars is also characterized by the use of highly skilled labor, limited substitutability between capital and labor, and use of very old machines to perform certain tasks. Why do you suppose that this limited substitutability occurs in the musical instrument industry, when other industries, such as the automobile industry, are characterized by a much greater degree of input substitutability? DISCUSSION QUESTIONS 1. For what type of firms is the long run likely to be only a matter of hours or days? For what type of firms is it likely to be measured in years? 2. What do you think are the main causes of inefficiency in most firms? 3. Why do both the marginal product of labor and average product of labor curves usually rise first and then fall as labor is increased? 4. Can you describe a production process that first has constant returns, then increasing returns to scale? 5. Does the long run occur sooner if there is a rental market for capital (machines)? 6. Are inventions and organizational innovations more likely to be labor or capital saving? 7. Under what circumstance would society not want a firm to produce efficiently? ADDITIONAL QUESTIONS AND MATH PROBLEMS 1. Write the equation for the marginal product of capital for each of the following production functions. a) Q = K + L b) Q = 4K.5L c) Q = 5L.5K – L 2. Using the production function from part (c) above, assume that capital is fixed at two units. At what point does MPL reach zero? 3. Suppose inputs are only substitutable at two units of labor for every one unit of capital. What would be the equation for the production function? What is the average and marginal product of labor in this case? 4. Draw a graph showing a set of isoquants that depict capital and labor to be perfect complements (not substitutable at all) in a production function that exhibits constant returns to scale. Be sure to label the input and output levels on the isoquants. 5. The original production function is Q = 10K.4L.5. A technological change occurs that alters the production function to Q = 15K.4L.7. Is this an example of neutral technological change? Why or why not? 6. True or false, explain your answer. “Marginal products in the Cobb-Douglas function cannot be negative.” 7. In some firms, managers are given sales volume-based bonuses. Explain why this might not be an efficient compensation strategy. 8. Suppose that as long as neither input exceeds four times the other, capital and labor are perfect substitutes at a one-to-one ratio. However, once the input ratio reaches four to one in favor of either input, no further substitution is possible. Draw the isoquants.

38 ❈ Part One\Teaching Aids ANSWERS TO ADDITIONAL QUESTIONS AND MATH PROBLEMS 1. In each case, the derivative ∂Q/∂K gives the marginal product of capital MPK. a) MPK = 1 b) MPK = 2K-.5L c) MPK = 5L.5 – L 2. For the production function Q = 5L.5K – L, when K = 2, Q = 10L.5 - L. MPL = 5L-.5 – 1. Thus, MPL = 0 when L = 25. 3. The production function is Q = 2K + L. APL = 2K/L + 1. MPL = 1. 4. The isoquants are “L” shaped, indicating perfect complementarity, and for every doubling of inputs, output also doubles. See Figure 6.1. Figure 6.1

4

Q = 40

2

Q = 20

1

Q = 10

1

2

4

L

5. This is not a neutral technical change because the marginal productivity of the inputs, and thus the input ratio is affected by the change in the output elasticity of labor from .4 to .7 (the productivity of labor increases). If the only difference had been the increase in the technology constant from 10 to 15, it would have been a neutral change. 6. In the Cobb-Douglas production function Q = AKαLβ, as long as the output elasticities are positive, the marginal products cannot be negative. For example, increases in labor will always have the marginal effect βQ/L. 7. When managers have the incentive to maximize revenue, they may cause the firm to overproduce. Especially when capital is fixed, there are limits to how much a firm can efficiently produce. In an attempt to achieve greater bonus levels, managers may sell product that the firm is not capable of producing profitably or even at all in the short run. Not only does this error cost the firm in the current period, but it also may damage customer relations, reducing revenues in future periods due to customer loss.

Chapter 6\Firms and Production ❈

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8. See Figure 6.2. As long as the input ratio stays with the 4 to 1 limits, the isoquants have a slope of –1. Outside these limits, they are either vertical or horizontal, indicating that no further substitution is possible.

Figure 6.2

K, Units of capital 8 7 6 5 4 Q3

3 Q1

2 Q0

1 1

2

3

4

5 6 7 8 L, Units of labor