THE TECHNOLOGY OF PRODUCTION
Production The theory of the firm describes how a firm makes cost-minimizing production decisions and how the firm’s resulting cost varies with its output. The Production Decisions of a Firm The production decisions of firms are analogous to the purchasing decisions of consumers, and can likewise be understood in three steps: 1. Production Technology 2. Cost Constraints 3. Input Choices Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 3 of 24 6.1 THE TECHNOLOGY OF PRODUCTION Chapter 6: Production ● factors of production Inputs into the production process (e.g., labor, capital, and materials). The Production Function q = F ( K , L) (6.1) ● production function Function showing the highest output that a firm can produce for every specified combination of inputs. Remember the following: Inputs and outputs are flows. Equation (6.1) applies to a given technology. Production functions describe what is technically feasible when the firm operates efficiently. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 4 of 24 6.1 THE TECHNOLOGY OF PRODUCTION 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. [unique_solution]● long run Amount of time needed to make all production inputs variable. Chapter 6: Production Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 5 of 24 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) Chapter 6: Production TABLE 6.1 Production with One Variable Input Amount Amount Total Average Marginal of Labor (L) of Capital (K) Output (q) Product (q/L) Product (∆q/∆L) 0 10 0 — — 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 8 10 112 14 0 9 10 108 12 -4 10 10 100 10 -8 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 6 of 24 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) 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. Average product of labor ＝ Output/labor input ＝ q/L Marginal product of labor ＝ Change in output/change in labor input ＝ Δq/ΔL Chapter 6: Production Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 7 of 24 Chapter 6: Production 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) The Slopes of the Product Curve Figure 6.1 Production with One Variable Input The total product 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), the marginal product is 20 because the tangent to the total product curve has a slope of 20. At point B in (a) the average product of labor is 20, which is the slope of the line from the origin to B. The average product of labor at point C in (a) is given by the slope of the line 0C. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 8 of 24 Chapter 6: Production 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) The Slopes of the Product Curve Figure 6.1 Production with One Variable Input (continued) To the left of point E in (b), the marginal product is above the average product and the average is increasing; to the right of E, the marginal product is below the average product and the average is decreasing. As a result, E represents the point at which the average and marginal products are equal, when the average product reaches its maximum. At D, when total output is maximized, the slope of the tangent to the total product curve is 0, as is the marginal product. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 9 of 24 Chapter 6: Production 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) 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. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 10 of 24 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) Chapter 6: Production The law of diminishing marginal returns was central to the thinking of political economist Thomas Malthus (1766–1834). Malthus believed that the world’s limited amount of land would not be able to supply enough food as the population grew. He 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. Fortunately, TABLE 6.2 Index of World Food Production per Capita Malthus was wrong Year Index (although he was right 1948-1952 100 about the diminishing 1960 115 marginal returns to 1970 123 labor). 1980 128 1990 138 2000 150 2005 156 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 11 of 24 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) Chapter 6: Production Figure 6.3 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. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 12 of 24 Chapter 6: Production 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) 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 ● 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. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 13 of 24 6.2 PRODUCTION WITH ONE VARIABLE INPUT (LABOR) Chapter 6: Production TABLE 6.3 Labor Productivity in Developed Countries UNITED UNITED JAPAN FRANCE GERMANY STATES KINGDOM Real Output per Employed Person (2006) $82,158 $57,721 $72,949 $60,692 $65,224 Years Annual Rate of Growth of Labor Productivity (%) 1960-1973 2.29 7.86 4.70 3.98 2.84 1974-1982 0.22 2.29 1.73 2.28 1.53 1983-1991 1.54 2.64 1.50 2.07 1.57 1992-2000 1.94 1.08 1.40 1.64 2.22 2001-2006 1.78 1.73 1.02 1.10 1.47 The level of output per employed person in the United States in 2006 was higher than in other industrial countries. But, until the 1990s, productivity in the United States grew on average less rapidly than productivity in most other developed nations. Also, productivity growth during 1974–2006 was much lower in all developed countries than it had been in the past. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 14 of 24 Chapter 6: Production 6.3 PRODUCTION WITH TWO VARIABLE INPUTS Isoquants TABLE 6.4 Production with Two Variable Inputs LABOR INPUT Capital Input 1 2 3 4 5 1 20 40 55 65 75 2 40 60 75 85 90 3 55 75 90 100 105 4 65 85 100 110 115 5 75 90 105 115 120 ● isoquant Curve showing all possible combinations of inputs that yield the same output. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 15 of 24 Chapter 6: Production 6.3 PRODUCTION WITH TWO VARIABLE INPUTS Isoquants ● isoquant map Graph combining a number of isoquants, used to describe a production function. Figure 6.4 Production with Two Variable Inputs 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). Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 16 of 24 6.3 PRODUCTION WITH TWO VARIABLE INPUTS Diminishing Marginal Returns Holding the amount of capital fixed at a particular level—say 3, we can see that each additional unit of labor generates less and less additional output. Chapter 6: Production Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 17 of 24 6.3 PRODUCTION WITH TWO VARIABLE INPUTS 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. Chapter 6: Production Figure 6.5 Marginal Rate of Technical Substitution 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. (MP ) / (MP ) =-(DK / DL) =MRTS (6.2) L K MRTS ＝ − Change in capital input/change in labor input ＝ − K/ΔL (for a fixed level of q) Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall • Microeconomics • Pindyck/Rubinfeld, 7e. 18 of 24 6.3 PRODUCTION WITH TWO VARIABLE INPUTS Production Functions—Two Special Cases Chapter 6: Production Figure 6.6 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.