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

© 2008 Pearson Addison Wesley. All rights reserved

Chapter Six

Firms and Production

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. 6-2

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.


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.


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.


The Ownership of Firms

• Limited Liability–condition whereby the personal assets of the owners of the corporation 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.


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.


What Owners Want

• Economists usually assume that a firm’s owners try to maximize profit.

• profit ( )–the difference between revenues, R, and costs, C: ＝ R － C

• To maximize profits, a firm must produce as efficiently as possible as we will consider in this chapter.


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.


Production

• A firm uses a technology or production process to transform inputs or factors of production into outputs.

–Capital (K)–Labor (L)–Materials (M)


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. 6-11

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.


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


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


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 is the fixed number of units of capital.


K

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, or a figure, Figure 6.1.



Figure 6.1Production Relationships with Variable Labor

Marginal Product of Labor

• marginal product of labor (MPL)

–the change in total output, , resulting from using an extra unit of labor, , holding other factors constant.

–The marginal product of labor is the partial derivative of the production function with respect to labor,


q ( , )

f L K

MPLL L

q

L

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


Relationship of the Product Curves

• The average product of labor curve slopes upward where the marginal product of labor curve is above it and slopes downward where the marginal product curve is below it.


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.


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.


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.



Equation 6.4

Isoquants

• isoquant

–a curve that shows the efficient combinations of labor and capital that can produce a single (iso) level of output (quantity)

• We can use these isoquants to illustrate what happens in the short run when capital is fixed and only labor varies.



Equation 6.5

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.



Figure 6.2Family of Isoquants for a U.S. Electronics Manufacturing Firm

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 production function is

q = x + y


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).



Figure 6.3 (a) and (b)Substitutability of Inputs


Figure 6.3 (c)Substitutability of Inputs

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).



Equation 6.6


Equation 6.7

Solved Problem 6.3

• What is the marginal rate of technical substitution for a general Cobb-Douglas production function,

q = ALaKb ?



Equation 6.8

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.



Figure 6.4How the Marginal Rate of Technical Substitution Varies Along an Isoquant

The Elasticity of Substitution

• The elasticity of substitution, , is the percentage change in the capital-labor ratio divided by the percentage change in the MRTS.

• This measure reflects the ease with which a firm can substitute capital for labor.



Equation 6.9


Equation 6.10


• 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.



Equation 6.11


Equation 6.12


Equation 6.13


Equation 6.14


• Special cases of the constant elasticity production functions:

- Linear Production Function:

is infinite

- Cobb-Douglas Production Function:

= 1

- Fixed-Proportion Production Function:

= 0



Equation 6.15: Cobb-Douglas Production Function


Equation 6.16

Returns to Scale

• How much output changes if a firm increases all its inputs proportionately? The answer helps a firm determine its scale or size in the long run.


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



• 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(2L, 2K) > 2f(L, K)



• 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(2L, 2K) < 2f(L, K)



Figure 6.5Varying Scale Economies

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.


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: 100q/q*.


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. 6-58


Table 6.1Annual Percentage Rates of Neutral Productivity Growth for Computer and Related Capital Goods

Innovations

• 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.


Organizational Change

• Organizational changes may also alter the production function and increase the amount of output produced by a given amount of inputs.


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