Chapter 7 Technology and Production McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Main Topics Production technologies Production with one variable input Production with two variable inputs Returns to scale Productivity differences and technological change 7-2

Production Technologies Firms produce products or services, outputs they can sell profitably A firm’s production technology summarizes all its production methods for producing its output Different production methods can use the same amounts of inputs but produce different amounts of output A production method is efficient if there is no other way for the firm to produce more output using the same amounts of inputs 7-3

Production Technologies: An Example Firm producing garden benches Assembles benches from pre-cut kits Hired labor is only input that can be varied One worker produces 33 benches in a week Two workers can produce different numbers of benches in a week, depending on how they divide up the assembly tasks Each work alone, produce total of 66 benches Help each other, produce more 7-4

Production Technologies: An Example Table 7.1: Inputs and Output for Various Methods of Producing Garden Benches Production Method Number of Assembly Workers Benches Produced Per Week Efficient? A133Yes B266No C270No D274Yes E4125No F4132Yes 7-5

Production Possibilities Set A production possibilities set contains all combinations of inputs and outputs that are possible given the firm’s technology Output on vertical axis, input on horizontal axis A firm’s efficient production frontier shows the input-output combinations from all of its efficient production methods Corresponds to the highest point in the production possibilities set on the vertical line at a given input level 7-6

Figure 7.2: Production Possibility Set for Garden Benches 7-7

Production Function Mathematically, describe efficient production frontier with a production function Output=F(Inputs) Example: Q=F(L)=10L Q is quantity of output, L is quantity of labor Substitute different amounts of L to see how output changes as the firm hires different amounts of labor Amount of output never falls when the amount of input increases Production function shows output produced for efficient production methods 7-8

Short and Long-Run Production An input is fixed if it cannot be adjusted over any given time period; it is variable if it can be Short run: a period of time over which one or more inputs is fixed Long run: a period over time over which all inputs are variable Length of long run depends on the production process being considered Auto manufacturer may need years to build a new production facility but software firm may need only a month or two to rent and move into a new space 7-9

Average and Marginal Products Average product of labor is the amount of output that is produced per worker: Marginal product of labor measures how much extra output is produced when the firm changes the amount of labor it uses by just a little bit: 7-10

Diminishing Marginal Returns Law of diminishing marginal returns: eventually the marginal product for an input decreases as its use increases, holding all other inputs fixed Table 7.3: Marginal Product of Producing Garden Benches Number of Workers Benches Produced Per Week MP L

Relationship Between AP and MP Compare MP to AP to see whether AP rises or falls as more of an input is added MP L shows how much output the marginal worker adds If he is more productive than average, he brings the average up If he is less productive than average, he drives the average down Relationship between a firm’s AP and MP: When the MP of an input is (larger/smaller/the same as) the AP, the marginal units (raise/lower/do not affect) the AP 7-12

AP and MP Curves When labor is finely divisible, AP and MP are graphed as curves For any point on a short run production function: AP is the slope of the straight line connecting the point to the origin MP equals the slope of the line tangent to the production function at that point 7-13

Figure 7.4: Marginal Product of Labor 7-14

Figure 7.6: Average and Marginal Product Curves AP curve slopes upward when it is below MP AP slopes downward when it is above MP AP is flat where the two curve cross 7-15

Production with Two Variable Inputs Most production processes use many variable inputs: labor, capital, materials, and land Capital inputs include assets such as physical plant, machinery, and vehicles Consider a firm that uses two inputs in the long run: Labor (L) and capital (K) Each of these inputs is homogeneous Firm’s production function is Q = F(L,K) 7-16

Production with Two Variable Inputs When a firm has more than one variable input it can produce a given amount of output with many different combinations of inputs E.g., by substituting K for L Productive Inputs Principle: Increasing the amounts of all inputs strictly increases the amount of output the firm can produce 7-17

Isoquants An isoquant identifies all input combinations that efficiently produce a given level of output Note the close parallel to indifference curves Can think of isoquants as contour lines for the “hill” created by the production function Firm’s family of isoquants consists of the isoquants for all of its possible output levels 7-18

Figure 7.8: Isoquant Example 7-19

Properties of Isoquants Isoquants are thin Do not slope upward The boundary between input combinations that produce more and less than a given amount of output Isoquants from the same technology do not cross Higher-level isoquants lie farther from the origin 7-20

Figure 7.10: Properties of Isoquants 7-21

Figure 7.10: Properties of Isoquants 7-22

Substitution Between Inputs Rate that one input can be substituted for another is an important factor for managers in choosing best mix of inputs Shape of isoquant captures information about input substitution Points on an isoquant have same output but different input mix Rate of substitution for labor with capital is equal to negative the slope Marginal Rate of Technical Substitution for input X with input Y: the rate as which a firm must replace units of X with units of Y to keep output unchanged starting at a given input combination 7-23

Figure 7.12: MRTS 7-24

MRTS and Marginal Product Recall the relationship between MRS and marginal utility Parallel relationship exists between MRTS and marginal product The more productive labor is relative to capital, the more capital we must add to make up for any reduction in labor; the larger the MRTS 7-25

Figure 7.13: Declining MRTS Often assume declining MRTS Here MRTS declines as we move along the isoquant, increasing input X and decreasing input Y 7-26

Extreme Production Technologies Two inputs are perfect substitutes if their functions are identical Firm is able to exchange one for another at a fixed rate Each isoquant is a straight line, constant MRTS Two inputs are perfect complements when They must be used in fixed proportions Isoquants are L-shaped 7-27

Figure 7.14: Perfect Substitutes 7-28

Figure 7.15: Fixed Proportions 7-29

Cobb-Douglas Production Function Common production function in economic analysis Introduced by mathematician Charles Cobb and economist (U.S. Senator) Paul Douglas General form: Where A, , and  are parameters that take specific values for a given firm 7-30

Cobb-Douglas Production Function A shows firm’s general productivity level  and  affect relative productivities of labor and capital Substitution between inputs: 7-31

Figure: 7.16: Cobb-Douglas Production Function 7-32

Returns to Scale Types of Returns to Scale Proportional change in ALL inputs yields… What happens when all inputs are doubled? Constant Same proportional change in output Output doubles Increasing Greater than proportional change in output Output more than doubles Decreasing Less than proportional change in output Output less than doubles 7-33

Figure 7.17: Returns to Scale 7-34

Productivity Differences and Technological Change A firm is more productive or has higher productivity when it can produce more output use the same amount of inputs Its production function shifts upward at each combination of inputs May be either general change in productivity of specifically linked to use of one input Productivity improvement that leaves MRTS unchanged is factor-neutral 7-35