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Chapter 7

Chapter 7. Technology and Production. 1. 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

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Chapter 7

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  1. Chapter 7 Technology and Production 1

  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 2

  3. Production Technologies:An Example • Firm producing garden benches: • 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 3

  4. Production Technologies: An Example

  5. Production Possibilities Set • A production possibilities set contains all combinations of inputs and outputs that are possible given the firm’s technology • 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 5

  6. Figure 7.2: Production Possibility Set for Garden Benches

  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 stage where one or more inputs is fixed • Long run: a stage where all inputs are variable • production process not time • 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 8

  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: 9

  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

  11. Relationship Between AP and MP • Compare MP to AP to see whether AP rises or falls as more of an input is added • MPL 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 11

  12. AP and MP 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 12

  13. Figure 7.4: Marginal Product of Labor

  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

  15. Production with Two Variable Inputs • Most production processes use many variable inputs: labor, capital, materials, and land • 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) 15

  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 16

  17. Isoquants • An isoquant identifies all input combinations that efficiently produce a given level of output • Firm’s family of isoquants consists of the isoquants for all of its possible output levels 17

  18. Figure 7.8: Isoquant Example

  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 19

  20. Figure 7.10: Properties of Isoquants

  21. Figure 7.10: Properties of Isoquants

  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 22

  23. Figure 7.12: MRTS

  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 24

  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

  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 26

  27. Figure 7.14: Perfect Substitutes

  28. Figure 7.15: Fixed Proportions

  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, α, and  are parameters that take specific values for a given firm 29

  30. Cobb-Douglas Production Function • A shows firm’s general productivity level • α and  affect relative productivities of labor and capital • Substitution between inputs: 30

  31. Figure: 7.16: Cobb-Douglas Production Function

  32. Returns to Scale

  33. Figure 7.17: Returns to Scale

  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 34

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