Chapter Six Firms and Production 2008 Pearson Addison

Chapter Six Firms and Production © 2008 Pearson Addison Wesley. All rights reserved

Firms and Production • In this chapter, we examine six topics - The Ownership and Management of Firms - Production - Short-Run Production - Long-Run Production - Returns to Scale - Productivity and Technical Change © 2008 Pearson Addison Wesley. All rights reserved. 6 -4

The Ownership and Management of Firms • Firm – an organization that converts inputs such as labor, materials, energy, and capital into outputs, the goods and services that it sells. © 2008 Pearson Addison Wesley. All rights reserved. 6 -5

The Ownership and Management of Firms • In most countries, for-profit firms have one of three legal forms: – Sole proprietorships are firms owned and run by a single individual. – Partnerships are businesses jointly owned and controlled by two or more people. The owners operate under a partnership agreement. – Corporations are owned by shareholders in proportion to the numbers of shares of stock they hold. The shareholders elect a board of directors who run the firm. © 2008 Pearson Addison Wesley. All rights reserved. 6 -6

The Ownership of Firms • Corporations differ from the other two forms of ownership in terms of personal liability for the debts of the firm. • Corporations have limited liability: The personal assets of the corporate owners cannot be taken to pay a corporation’s debts if it goes into bankruptcy. • Sole proprietors and partnerships have unlimited liability－that is, even their personal assets can be taken to pay the firm’s debts. © 2008 Pearson Addison Wesley. All rights reserved. 6 -7

The Management of Firms • In a small firm, the owner usually manages the firm’s operations. • In larger firms, typically corporations and larger partnerships, a manager or team of managers usually runs the company. © 2008 Pearson Addison Wesley. All rights reserved. 6 -11

What Owners Want • Economists usually assume that a firm’s owners try to maximize profit. • profit ( p ) – the difference between revenues, R, and costs, C: p ＝ R － C • To maximize profits, a firm must produce as efficiently as possible as we will consider in this chapter. © 2008 Pearson Addison Wesley. All rights reserved. 6 -12

What Owners Want • Efficient Production or Technological Efficiency – situation in which the current level of output cannot be produced with fewer inputs, given existing knowledge about technology and the organization of production • If the firm does not produce efficiently, it cannot be profit maximizing－so efficient production is a necessary condition for profit maximization. © 2008 Pearson Addison Wesley. All rights reserved. 6 -13

Production • A firm uses a technology or production process to transform inputs or factors of production into outputs. – Capital (K) – Labor (L) – Materials (M) © 2008 Pearson Addison Wesley. All rights reserved. 6 -14

Production Functions • The various ways inputs can be transformed into output are summarized in the production function: the relationship between the quantities of inputs used and the maximum quantity of output that can be produced, given current knowledge about technology and organization. The production function for a firm that uses only labor (L) and capital (K) is q＝f (L, K), (6. 2) where q units of output are produced. © 2008 Pearson Addison Wesley. All rights reserved. 6 -15

Production Functions • The production function shows only the maximum amount of output that can be produced from given levels of labor and capital, because the production function includes only efficient production processes. © 2008 Pearson Addison Wesley. All rights reserved. 6 -16

Time and the Variability of Inputs • Short Run – a period of time so brief that at least one factor of production cannot be varied practically • Fixed Input – a factor of production that cannot be varied practically in the short run © 2008 Pearson Addison Wesley. All rights reserved. 6 -17

Time and the Variability of Inputs • Variable Input – a factor of production whose quantity can be changed readily by the firm during the relevant time period • Long Run – a lengthy enough period of time that all inputs can be varied © 2008 Pearson Addison Wesley. All rights reserved. 6 -18

Short-Run Production: One Variable and One Fixed Input • In the short run, we assume that capital is fixed input and labor is a variable input. • In the short run, the firm’s production function is (6. 3) where q is output, L is workers, and number of units of capital. © 2008 Pearson Addison Wesley. All rights reserved. is the fixed 6 -19

Total Product of Labor • The exact relationship between output or total product and labor can be illustrated by using a particular function, Equation 6. 3, equation 6. 3 , or a figure, Figure 6. 1. © 2008 Pearson Addison Wesley. All rights reserved. 6 -20

Figure 6. 1 Production Relationships with Variable Labor © 2008 Pearson Addison Wesley. All rights reserved. 6 -21

Marginal Product of Labor • marginal product of labor (MPL) – the change in total output, using an extra unit of labor, factors constant. , resulting from , holding other – The marginal product of labor is the partial derivative of the production function with respect to labor, © 2008 Pearson Addison Wesley. All rights reserved. 6 -22

Average Product of Labor • average product of labor (APL) – the ratio of output, q, to the number of workers, L, used to produce that output: APL = q/L © 2008 Pearson Addison Wesley. All rights reserved. 6 -23

Relationship of the Product Curves • The average product of labor curve slopes upward where the marginal product of labor curve is above it • The average product of labor curve slopes downward where the marginal product of labor curve is below it. © 2008 Pearson Addison Wesley. All rights reserved. 6 -24

Law of Diminishing Marginal Returns • The law of diminishing marginal returns (or diminishing marginal product) holds that, if a firm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will become smaller eventually. • That is, if only one input is increased, the marginal product of that input will diminish eventually. © 2008 Pearson Addison Wesley. All rights reserved. 6 -25

Law of Diminishing Marginal Returns • Where there are “diminishing marginal returns, ” the MPL curve is falling. • Within “diminishing returns, ” extra labor causes output to fall. • Thus saying that there are diminishing returns is much stronger than saying that there are diminishing marginal returns. © 2008 Pearson Addison Wesley. All rights reserved. 6 -26

Long-Run Production: Two Variable Inputs • In the long run, however, both inputs are variable. • With both factors variable, a firm can usually produce a given level of output by using a great deal of labor and very little capital, a great deal of capital and very little labor, or moderate amounts of both. © 2008 Pearson Addison Wesley. All rights reserved. 6 -27

Long-Run Production: Two Variable Inputs • Cobb-Douglas production function • Equation 6. 4 where L is labor (workers) per day and K is capital services per day. © 2008 Pearson Addison Wesley. All rights reserved. 6 -28

Isoquants • isoquant – a curve that shows the efficient combinations of labor and capital that can produce a single (iso) level of output (quantity) • Equation 6. 5 ~ © 2008 Pearson Addison Wesley. All rights reserved. 6 -29

Properties of Isoquants • First, the farther an isoquant is from the origin, the greater the level of output. • Second, isoquants do not cross. • Third, isoquants slope downward. © 2008 Pearson Addison Wesley. All rights reserved. 6 -30

Figure 6. 2 Family of Isoquants for a U. S. Electronics Manufacturing Firm © 2008 Pearson Addison Wesley. All rights reserved. 6 -31

Shape of Isoquants • The curvature of an isoquant shows how readily a firm can substitute one input for another. • If the inputs are perfect substitutes, each isoquant is a straight line. • The linear production function is q=x+y © 2008 Pearson Addison Wesley. All rights reserved. 6 -32

Shape of Isoquants • Sometimes it is impossible to substitute one input for the other: Inputs must be used in fixed proportion. Such a production function is called a fixed-proportions production function. • The fixed-proportions production function is given by: q = min(g, b). © 2008 Pearson Addison Wesley. All rights reserved. 6 -33

Figure 6. 3 (a) and (b) Substitutability of Inputs © 2008 Pearson Addison Wesley. All rights reserved. 6 -34

Figure 6. 3 (c) Substitutability of Inputs © 2008 Pearson Addison Wesley. All rights reserved. 6 -35

Substituting Inputs • The slope of an isoquant shows the ability of a firm to replace one input with another while holding output constant. • The slope of an isoquant is called the marginal rate of technological substitution (MRTS). © 2008 Pearson Addison Wesley. All rights reserved. 6 -36

Substituting Inputs • Marginal rate of technical substitution © 2008 Pearson Addison Wesley. All rights reserved. 6 -37

Solved Problem 6. 3 Cobb-Douglas production function • What is the marginal rate of technical substitution for a general Cobb-Douglas production function, q = ALa. Kb ? • Solution： (6. 8) © 2008 Pearson Addison Wesley. All rights reserved. 6 -38

Diminishing Marginal Rates of Technical Substitution • The marginal rate of technical substitution varies along a curved isoquant. • This decline in the MRTS (in absolute value) along an isoquant as the firm increases labor illustrates diminishing marginal rates of technical substitution. © 2008 Pearson Addison Wesley. All rights reserved. 6 -39

Figure 6. 4 How the Marginal Rate of Technical Substitution Varies Along an Isoquant © 2008 Pearson Addison Wesley. All rights reserved. 6 -40

The Elasticity of Substitution • The elasticity of substitution, s , is the percentage change in the capital-labor ratio divided by the percentage change in the MRTS. (6. 9) • This measure reflects the ease with which a firm can substitute capital for labor. © 2008 Pearson Addison Wesley. All rights reserved. 6 -41

The Elasticity of Substitution • Both the factor ration, K/L, and the absolute value of the MRTS, │MRTS│, are positive numbers, so the logarithm of each is meaningful. • Equation 6. 10 © 2008 Pearson Addison Wesley. All rights reserved. 6 -42

The Elasticity of Substitution • Constant Elasticity of Substitution Production – In general, the elasticity of substitution varies along an isoquant. An exception is the constant elasticity of substitution (CES) production function, where r is a positive constant. © 2008 Pearson Addison Wesley. All rights reserved. 6 -43

The Elasticity of Substitution • For simplicity, we assume that a = b = d = 1, so • The marginal rate of technical substitution for a CES isoquant is: • At every point on a CES isoquant, the constant elasticity of substitutions is: © 2008 Pearson Addison Wesley. All rights reserved. 6 -44

The Elasticity of Substitution • Special cases of the constant elasticity of substitution (CES) production functions: - Linear Production Function: s is infinite - Cobb-Douglas Production Function: s =1 - Fixed-Proportion Production Function: s =0 © 2008 Pearson Addison Wesley. All rights reserved. 6 -45

Solved Problem 6. 4 Cobb-Douglas production function • Cobb-Douglas production function, q = ALa. Kb, rearranging the result equation 6. 8, (6. 15) • From Equation 6. 15 we can get, • The elasticity of substitution for a Cobb-Douglas production function is: © 2008 Pearson Addison Wesley. All rights reserved. 6 -46

Returns to Scale • How much output changes if a firm increases all its inputs proportionately? The answer to this question helps a firm determine its scale or size in the long run. © 2008 Pearson Addison Wesley. All rights reserved. 6 -47

Constant, Increasing, and Decreasing Returns to Scale • constant returns to scale (CRS) – property of a production function whereby when all inputs are increased by a certain percentage, output increases by that same percentage • f(2 L, 2 K) = 2 f(L, K) © 2008 Pearson Addison Wesley. All rights reserved. 6 -48

Constant, Increasing, and Decreasing Returns to Scale • increasing returns to scale (IRS) – property of a production function whereby when output rises more than in proportion to an equal increase in all inputs • A technology exhibits increasing returns to scale if doubling inputs more than doubles the output: f(2 L, 2 K) > 2 f(L, K) © 2008 Pearson Addison Wesley. All rights reserved. 6 -49

Constant, Increasing, and Decreasing Returns to Scale • decreasing returns to scale (DRS) – property of a production function whereby output increase less than in proportion to an equal percentage increase in all inputs • A technology exhibits decreasing returns to scale if doubling inputs causes output to rise less than in proportion: f(2 L, 2 K) < 2 f(L, K) © 2008 Pearson Addison Wesley. All rights reserved. 6 -50

Figure 6. 5 Varying Scale Economies © 2008 Pearson Addison Wesley. All rights reserved. 6 -51

Varying Returns to Scale • Many production functions have increasing returns to scale for small amounts of output, constant returns for moderate amounts of output, and decreasing returns for large amounts of output. • The spacing of the isoquants reflects the returns to scale. © 2008 Pearson Addison Wesley. All rights reserved. 6 -52

Productivity and Technical Change • Relative Productivity – We can measure the relative productivity of a firm by expressing the firm’s actual output, q, as a percentage of the output that the most productive firm in the industry could have produced, q*, from the same amount of inputs: 100 q/q*. © 2008 Pearson Addison Wesley. All rights reserved. 6 -53

Innovations • Technical Progress – an advance in knowledge that allows more output to be produced with the same level of inputs • Neutral Technical Progress – The firm can produce more output using the same ratio of inputs. q = A(t)f(L, K) © 2008 Pearson Addison Wesley. All rights reserved. 6 -54

Table 6. 1 Annual Percentage Rates of Neutral Productivity Growth for Computer and Related Capital Goods © 2008 Pearson Addison Wesley. All rights reserved. 6 -55

Innovations • Nonneutral technical changes – Nonneutral technical changes are innovations that alter the proportion in which inputs are used. • Labor saving innovation: – The ratio of labor to the other inputs used to produce a given level of output falls after the innovation. © 2008 Pearson Addison Wesley. All rights reserved. 6 -56

Innovations • Organizational changes – Organizational changes may also alter the production function and increase the amount of output produced by a given amount of inputs. © 2008 Pearson Addison Wesley. All rights reserved. 6 -57