MICROECONOMICS by Robert S. Pindyck Daniel Rubinfeld Ninth Edition Copyright © 2016, 2012, 2009 Pearson Education, Inc. All Rights Reserved

Chapter 6 Production In this chapter and the next we discuss the theory of the firm, which describes how a firm makes cost-minimizing production decisions and how the firm’s resulting cost varies with its output. CHAPTER OUTLINE 6.1 Firms and Their Production Decisions 6.2 Production with One Variable Input (Labor) 6.3 Production with Two Variable Inputs 6.4 Returns to Scale LIST OF EXAMPLES 6.1 The Authors Debate a Production Function for Health Care 197 6.2 Malthus and the Food Crisis 6.3 Labor Productivity and the Standard of Living 6.4 A Production Function for Wheat 6.5 Returns to Scale in the Carpet Industry

The Production Decisions of a Firm The production decisions of firms can be understood in three steps: Production Technology: How inputs (such as labor, capital, and raw materials) can be transformed into outputs. Cost Constraints: How inputs (such as labor, capital, and raw materials) can be transformed into outputs. Input Choices: Just as a consumer is constrained by a limited budget, the firm is concerned about the cost of production and the prices of labor, capital, and other inputs. theory of the firm Explanation of how a firm makes cost-minimizing production decisions and how its cost varies with its output.

6.1 Firms and Their Production Decisions (1 of 3) Why Do Firms Exist? Firms offer a means of coordination that is extremely important and would be sorely missing if workers operated independently. Firms eliminate the need for every worker to negotiate every task that he or she will perform, and bargain over the fees that will be paid for those tasks. Firms can avoid this kind of bargaining by having managers that direct the production of salaried workers—they tell workers what to do and when to do it, and the workers (as well as the managers themselves) are simply paid a weekly or monthly salary.

6.1 Firms and Their Production Decisions (2 of 3) The Technology of Production factors of production Inputs into the production process (e.g., labor, capital, and materials). We can divide inputs into the broad categories of labor, materials and capital, each of which might include more narrow subdivisions. Labor inputs include skilled workers (carpenters, engineers) and unskilled workers (agricultural workers), as well as the entrepreneurial efforts of the firm’s managers. Materials include steel, plastics, electricity, water, and any other goods that the firm buys and transforms into final products. Capital includes land, buildings, machinery and other equipment, as well as inventories.

6.1 Firms and Their Production Decisions (3 of 3) The Production Function production function Function showing the highest output that a firm can produce for every specified combination of inputs. (6.1) Production functions describe what is technically feasible when the firm operates efficiently—that is, when the firm uses each combination of inputs as effectively as possible. The Short Run versus the Long Run short run Period of time in which quantities of one or more production factors cannot be changed. fixed input Production factor that cannot be varied. long run Amount of time needed to make all production inputs variable In this chapter and those that follow, we will use the variable q for the output of the firm, and Q for the output of the industry. It is important to keep in mind that inputs and outputs are flows. Unless otherwise indicated, however, we mean the amount of labor and capital used each year and the amount of output produced each year. Note that equation (6.1) applies to a given technology. There is no specific time period, such as one year, that separates the short run from the long run.

6.2 Production with One Variable Input (Labor) (1 of 7) Average and Marginal Products average product Output per unit of a particular input. marginal product Additional output produced as an input is increased by one unit. Remember that the marginal product of labor depends on the amount of capital used. If the capital input increased from 10 to 20, the marginal product of labor most likely would increase. Average product of labor = Output/labor input = q/L Marginal product of labor = Change in output/change in labor input = ∆q/ ∆ L The contribution that labor makes to the production process can be described on both an average and a marginal (i.e., incremental) basis.

6.2 Production with One Variable Input (Labor) (2 of 7) TABLE 6.1: PRODUCTION WITH ONE VARIABLE INPUT AMOUNT OF LABOR (L) AMOUNT OF CAPITAL (K) TOTAL OUTPUT (q) AVERAGE PRODUCT (q/L) MARGINAL PRODUCT (∆q/∆L) 10 — 1 15 2 40 20 25 3 69 23 29 4 96 24 27 5 120 6 138 18 7 147 21 9 8 152 19 153 17 150 -3 11 143 13 -7 12 133 11.08 -10

6.2 Production with One Variable Input (Labor) (3 of 7) The Slopes of the Product Curve FIGURE 6.1 (1 OF 2) PRODUCTION WITH ONE VARIABLE INPUT The total output curve in (a) shows the output produced for different amounts of labor input. The average and marginal products in (b) can be obtained (using the data in Table 6.1) from the total product curve. At point A in (a), with 3 units of labor, the marginal product is 29 because the tangent to the total product curve has a slope of 29. The average product of labor, however, is 23, which is the slope of the line from the origin to point A. Also, the marginal product of labor reaches its maximum at this point. At point B, with 5 units of labor, the marginal product of labor has dropped to 24 and is equal to the average product of labor.

6.2 Production with One Variable Input (Labor) (4 of 7) The Slopes of the Product Curve FIGURE 6.1 (2 OF 2) PRODUCTION WITH ONE VARIABLE INPUT Thus, in (b), the average and marginal product curves intersect (at point D). Note that when the marginal product curve is above the average product, the average product is increasing. When the labor input is greater than 5 units, the marginal product is below the average product, so the average product is falling. Once the labor input exceeds 9 units, the marginal product becomes negative, so that total output falls as more labor is added. At C, when total output is maximized, the slope of the tangent to the total product curve is 0, as is the marginal product. Beyond that point, the marginal product becomes negative. When the marginal product is greater than the average product, the average product is increasing. Similarly, when the marginal product is less than the average product, the average product is decreasing.

6.2 Production with One Variable Input (Labor) (5 of 7) The Average Product of Labor Curve In general, the average product of labor is given by the slope of the line drawn from the origin to the corresponding point on the total product curve. The Marginal Product of Labor Curve In general, the marginal product of labor at a point is given by the slope of the total product at that point. THE RELATIONSHIP BETWEEN THE AVERAGE AND MARGINAL PRODUCTS In Figure 6.1, the average product is the slope of the line from the origin, 0B, and the marginal product is the tangent to the total product curve at B (note the equality of the average and marginal products at point D). The slope of the tangent to the total product curve at any point between B and C is lower than the slope of the line from the origin. We can see in Figure 6.1 (b) that the marginal product of labor increases initially, peaks at an input of 3, and then declines as we move up the total product curve to B and C. At C, when total output is maximized, the slope of the tangent to the total product curve is 0, as is the marginal product. Beyond that point, the marginal product becomes negative.

6.2 Production with One Variable Input (Labor) (6 of 7) The Law of Diminishing Marginal Returns law of diminishing marginal returns Principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease. FIGURE 6.2 THE EFFECT OF TECHNOLOGICAL IMPROVEMENT Labor productivity (output per unit of labor) can increase if there are improvements in technology, even though any given production process exhibits diminishing returns to labor. As we move from point A on curve O1 to B on curve O2 to C on curve O3 over time, labor productivity increases.

Example 6.1 The Authors Debate a Production Function for Health Care Expenditures on health care have increased rapidly in many countries. Do these increased expenditures reflect increases in output or do they reflect inefficiencies in the production process? Bob argues that the primary explanation is the fact that the production function for health care exhibits diminishing returns. Dan argues that the production of health care in the United States is inefficient. FIGURE 6.3 A PRODUCTION FUNCTION FOR HEALTH CARE Additional expenditures on health care (inputs) increase life expectancy (output) along the production frontier. Points A, B, and C represent points at which inputs are efficiently utilized, although there are diminishing returns when moving from B to C. Point D is a point of input inefficiency. As you can see from the graph, a move from B to C, an additional $20,000 of health expenditures increases life expectancy by only 1 year. Why is this? The reason for diminishing returns is that given medical technologies, additional expenditures on medical procedures and/or the use of newer drugs has only a minimal effect on life expectancy. As a result, the marginal productivity of dollars expended on health has become less and less effective over time as expenditures have increased.” The system is inefficient because higher medical outputs could be achieved with the same or similar input expenditures if those expenditures were more effectively utilized.

Example 6.2 Malthus and The Food Crisis (1 of 2) The law of diminishing marginal returns was central to the thinking of political economist Thomas Malthus (1766–1834). Malthus predicted that as both the marginal and average productivity of labor fell and there were more mouths to feed, mass hunger and starvation would result. Malthus was wrong (although he was right about the diminishing marginal returns to labor). Over the past century, technological improvements have dramatically altered food production in most countries (including developing countries, such as India). As a result, the average product of labor and total food output have increased. Hunger remains a severe problem in some areas, in part because of the low productivity of labor there. TABLE 6.2 INDEX OF WORLD FOOD PRODUCTION PER CAPITA YEAR INDEX 1961–64 100 1965 101 1970 105 1975 106 1980 109 1985 115 1990 117 1995 119 2000 127 2005 135 2010 146 2013 151

Example 6.2 Malthus and The Food Crisis (2 of 2) FIGURE 6.4 CEREAL YIELDS AND THE WORLD PRICE OF FOOD Cereal yields have increased. The average world price of food increased temporarily in the early 1970s but has declined since.

6.2 Production with One Variable Input (Labor) (7 of 7) Labor Productivity labor productivity Average product of labor for an entire industry or for the economy as a whole. PRODUCTIVITY AND THE STANDARD OF LIVING Consumers in the aggregate can increase their rate of consumption in the long run only by increasing the total amount they produce. Understanding the causes of productivity growth is an important area of research in economics. We do know that one of the most important sources of growth in labor productivity is growth in the stock of capital stock of capital Total amount of capital available for use in production. technological change Development of new technologies allowing factors of production to be used more effectively. Because the average product measures output per unit of labor input, it is relatively easy to measure (total labor input and total output are the only pieces of information you need). Labor productivity can provide useful comparisons across industries and for one industry over a long period. But labor productivity is especially important because it determines the real standard of living that a country can achieve for its citizens.

Example 6.3 Labor Productivity and The Standard of Living Will the standard of living in the United States, Europe, and Japan continue to improve, or will these economies barely keep future generations from being worse off than they are today? Because the real incomes of consumers in these countries increase only as fast as productivity does, the answer depends on the labor productivity of workers. TABLE 6.3: LABOR PRODUCTIVITY IN DEVELOPED COUNTRIES Blank Cell UNITED STATES JAPAN FRANCE GERMANY UNITED KINGDOM GDP PER HOUR WORKED (IN 2010 U.S. DOLLARS) $62.41 $39.39 $60.28 $58.92 $47.39 YEARS ANNUAL RATE OF GROWTH OF LABOR PRODUCTIVITY (%) 1970-1979 1.7 4.5 4.3 4.1 3.2 1980-1989 1.4 3.8 2.9 2.1 2.2 1990-1999 2.4 2.0 2.3 2000-2009 1.3 1.2 1.1 1.5 2010-2014 0.7 0.9 0.5 Until the 1990s, productivity in the United States grew on average less rapidly than productivity in most other developed nations. Productivity growth during 1980–2014 was much lower in all developed countries than it had been in the past. The greatest capital growth during the postwar period was in Japan, France, and Germany. Productivity growth in the United States accelerated in the 1990s and 2000s. Some economists believe that information and communication technology (ICT) has been the key impetus for this growth.

6.3 Production with Two Variable Inputs (1 of 8) Isoquants Isoquants Curve showing all possible combinations of inputs that yield the same output. TABLE 6.4: PRODUCTION WITH TWO VARIABLE INPUTS LABOR INPUT CAPITAL INPUT 1 2 3 4 5 20 40 55 65 75 60 85 90 100 105 110 115 120 ISOQUANT MAPS isoquant map Graph combining a number of isoquants, used to describe a production function.

6.3 Production with Two Variable Inputs (2 of 8) FIGURE 6.5 PRODUCTION WITH TWO VARIABLE INPUTS FIGURE 6.2 A set of isoquants, or isoquant map, describes the firm’s production function. Output increases as we move from isoquant q1 (at which 55 units per year are produced at points such as A and D), to isoquant q2 (75 units per year at points such as B), and to isoquant q3 (90 units per year at points such as C and E). By drawing a horizontal line at a particular level of capital—say 3, we can observe diminishing marginal returns. Reading the levels of output from each isoquant as labor is increased, we note that each additional unit of labor generates less and less additional output.

6.3 Production with Two Variable Inputs (3 of 8) Input Flexibility Isoquants show the flexibility that firms have when making production decisions: They can usually obtain a particular output by substituting one input for another. It is important for managers to understand the nature of this flexibility. Diminishing Marginal Returns Even though both labor and capital are variable in the long run, it is useful for a firm that is choosing the optimal mix of inputs to ask what happens to output as each input is increased, with the other input held fixed. Because adding one factor while holding the other factor constant eventually leads to lower and lower incremental output, the isoquant must become steeper as more capital is added in place of labor and flatter when labor is added in place of capital. There are also diminishing marginal returns to capital. With labor fixed, the marginal product of capital decreases as capital is increased.

6.3 Production with Two Variable Inputs (4 of 8) Substitution Among Inputs marginal rate of technical substitution (MRTS) Amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant. MRTS = −Change in capital input/change in labor input = − ∆𝐾 ∆𝐿 (for a fixed level of q) DIMINISHING MRTS Additional output from increased use of labor = ( MP 𝐿 )(∆𝐿) Reduction in output from decreased use of capital = ( MP 𝐾 )(∆𝐾) Now, by rearranging terms we see that (6.2)

6.3 Production with Two Variable Inputs (5 of 8) FIGURE 6.6 MARGINAL RATE OF TECHNICAL SUBSTITUTION FIGURE 6.2 Like indifference curves, isoquants are downward sloping and convex. The slope of the isoquant at any point measures the marginal rate of technical substitution—the ability of the firm to replace capital with labor while maintaining the same level of output. On isoquant q2, the MRTS falls from 2 to 1 to 2/3 to 1/3.

6.3 Production with Two Variable Inputs (6 of 8) Production Functions—Two Special Cases Two extreme cases of production functions show the possible range of input substitution in the production process: the case of perfect substitutes and the fixed proportions production function, sometimes called a Leonitief production function. fixed-proportions production function Production function with L-shaped isoquants, so that only one combination of labor and capital can be used to produce each level of output. The fixed-proportions production function describes situations in which methods of production are limited.

6.3 Production with Two Variable Inputs (7 of 8) FIGURE 6.7 ISOQUANTS WHEN INPUTS ARE PERFECT SUBSTITUTES When the isoquants are straight lines, the MRTS is constant. Thus the rate at which capital and labor can be substituted for each other is the same no matter what level of inputs is being used. Points A, B, and C represent three different capital-labor combinations that generate the same output q3.

6.3 Production with Two Variable Inputs (8 of 8) FIGURE 6.8 FIXED-PROPORTIONS PRODUCTION FUNCTION When the isoquants are L-shaped, only one combination of labor and capital can be used to produce a given output (as at point A on isoquant q1, point B on isoquant q2, and point C on isoquant q3). Adding more labor alone does not increase output, nor does adding more capital alone. The fixed-proportions production function describes situations in which methods of production are limited.

Example 6.4 A Production Function for Wheat (1 of 2) Food grown on large farms in the United States is usually produced with a capital-intensive technology. However, food can also be produced using very little capital (a hoe) and a lot of labor (several people with the patience and stamina to work the soil). Most farms in the United States and Canada, where labor is relatively expensive, operate in the range of production in which the MRTS is relatively high (with a high capital-to-labor ratio), whereas farms in developing countries, in which labor is cheap, operate with a lower MRTS (and a lower capital-to- labor ratio). The exact labor/capital combination to use depends on input prices, a subject that we discuss in Chapter 7.

Example 6.4 A Production Function for Wheat (2 of 2) FIGURE 6.9 ISOQUANT DESCRIBING THE PRODUCTION OF WHEAT A wheat output of 13,800 bushels per year can be produced with different combinations of labor and capital. The more capital-intensive production process is shown as point A, the more labor- intensive process as point B. The marginal rate of technical substitution between A and B is 10/260 = 0.04. Figure 6.9 shows one isoquant, associated with the production function, corresponding to an output of 13,800 bushels of wheat per year. The manager of the farm can use this isoquant to decide whether it is profitable to hire more labor or use more machinery. The exact labor/capital combination to use depends on input prices, a subject that we discuss in Chapter 7.

6.3 Returns to Scale (1 of 3) returns to scale Rate at which output increases as inputs are increased proportionately. INCREASING RETURNS TO SCALE increasing returns to scale Situation in which output more than doubles when all inputs are doubled. CONSTANT RETURNS TO SCALE constant returns to scale Situation in which output doubles when all inputs are doubled. DECREASING RETURNS TO SCALE decreasing returns to scale Situation in which output less than doubles when all inputs are doubled. The automobile assembly line is a famous example of increasing returns. Constant returns: a large travel agency might provide the same service per client and use the same ratio of capital (office space) and labor (travel agents) as a small agency that services fewer clients. The decreasing returns case is likely to be associated with the problems of coordinating tasks and maintaining a useful line of communication between management and workers.

6.3 Returns to Scale (2 of 3) Describing Returns to Scale Returns to scale need not be uniform across all possible levels of output. For example, at lower levels of output, the firm could have increasing returns to scale, but constant and eventually decreasing returns at higher levels of output. In Figure 6.10 (a), the firm’s production function exhibits constant returns. Twice as much of both inputs is needed to produce 20 units, and three times as much is needed to produce 30 units. In Figure 6.10 (b), the firm’s production function exhibits increasing returns to scale. Less than twice the amount of both inputs is needed to increase production from 10 units to 20; substantially less than three times the inputs are needed to produce 30 units. Returns to scale vary considerably across firms and industries. Other things being equal, the greater the returns to scale, the larger the firms in an industry are likely to be.

6.3 Returns to Scale (3 of 3) FIGURE 6.10 RETURNS TO SCALE When a firm’s production process exhibits constant returns to scale as shown by a movement along line 0A in part (a), the isoquants are equally spaced as output increases proportionally. However, when there are increasing returns to scale as shown in (b), the isoquants move closer together as inputs are increased along the line.

Example 6.5 Returns to Scale in the Carpet Industry Innovations have reduced costs and greatly increased carpet production. Innovation along with competition have worked together to reduce real carpet prices. Carpet production is capital intensive. Over time, the major carpet manufacturers have increased the scale of their operations by putting larger and more efficient tufting machines into larger plants. At the same time, the use of labor in these plants has also increased significantly. The result? Proportional increases in inputs have resulted in a more than proportional increase in output for these larger plants. Most smaller carpet manufacturers have found that small changes in scale have little or no effect on output. We can therefore characterize the carpet industry as one in which there are constant returns to scale for relatively small plants but increasing returns to scale for larger plants.

Copyright