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Chapter 6

Chapter 6. Production. Introduction. Production decisions of a firm are similar to consumer decisions Can also be broken down into three steps: Production Technology Describe how inputs can be transformed into outputs Inputs: land, labor, capital and raw materials

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Chapter 6

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  1. Chapter 6 Production

  2. Introduction • Production decisions of a firm are similar to consumer decisions • Can also be broken down into three steps: • Production Technology • Describe how inputs can be transformed into outputs • Inputs: land, labor, capital and raw materials • Outputs: cars, desks, books, etc. Chapter 6

  3. Production Decisions of a Firm • Cost Constraints • Firms must consider pricesof labor, capital and other inputs • Firms want to minimize total production costs partly determined by input prices 3. Input Choices • Given input prices and production technology, the firm must choose how much of each input to use in producing output Chapter 6

  4. The Technology of Production • Production Function: • Indicates the highest output (q) that a firm can produce for every specified combination of inputs • For simplicity, we will consider only labor (L) and capital (K) • Shows what is technically feasible when the firm operates efficiently Chapter 6

  5. The Technology of Production • The production function for two inputs: q = F(K,L) • Output (q) is a function of capital (K) and labor (L) • The production function is true for a given technology • If technology increases, more output can be produced for a given level of inputs Chapter 6

  6. Production: One Variable Input • We will begin by looking at the short run when only one input can be varied • We assume capital is fixed and labor is variable • Output can only be increased by increasing labor • Must know how output changes as the amount of labor is changed (Table 6.1) Chapter 6

  7. The Technology of Production • Short Run • Period of time in which quantities of one or more production factors cannot be changed • These inputs are called fixed inputs • Long Run • Amount of time needed to make all production inputs variable • Short run and long run are not time specific Chapter 6

  8. Production: One Variable Input Chapter 6

  9. Production: One Variable Input • Observations: • When labor is zero, output is zero as well • With additional workers, output (q) increases up to 8 units of labor • Beyond this point, output declines • Increasing labor can make better use of existing capital initially • After a point, more labor is not useful and can be counterproductive Chapter 6

  10. Production: One Variable Input • Average product of Labor - Output per unit of a particular product • Measures the productivity of a firm’s labor in terms of how much, on average, each worker can produce Chapter 6

  11. Production: One Variable Input • Marginal Product of Labor – additional output produced when labor increases by one unit • Change in output divided by the change in labor Chapter 6

  12. Production: One Variable Input Chapter 6

  13. Production: One Variable Input • We can graph the information in Table 6.1 to show • How output varies with changes in labor • Output is maximized at 112 units • Average and Marginal Products • Marginal Product is positive as long as total output is increasing • Marginal Product crosses Average Product at its maximum Chapter 6

  14. D 112 Total Product C 60 B A Production: One Variable Input Output per Month At point D, output is maximized. Labor per Month 0 1 2 3 4 5 6 7 8 9 10 Chapter 6

  15. Marginal Product E Average Product Labor per Month 0 1 2 3 4 5 6 7 8 9 10 Production: One Variable Input Output per Worker • Left of E: MP > AP & AP is increasing • Right of E: MP < AP & AP is decreasing • At E: MP = AP & AP is at its maximum • At 8 units, MP is zero and output is at max 30 20 10 Chapter 6

  16. Product Curves • We can show a geometric relationship between the total product and the average and marginal product curves • Slope of line from origin to any point on the total product curve is the average product • At point B, AP = 60/3 = 20 which is the same as the slope of the line from the origin to point B on the total product curve Chapter 6

  17. C 20 60 B 1 10 9 0 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 Labor Labor Product Curves AP is slope of line from origin to point on TP curve q q/L 112 TP 30 AP 10 MP Chapter 6

  18. Product Curves • Geometric relationship between total product and marginal product • The marginal product is the slope of the line tangent to any corresponding point on the total product curve • For 2 units of labor, MP = 30/2 = 15 which is slope of total product curve at point A Chapter 6

  19. q q 112 30 60 AP 30 10 A MP 0 1 2 3 4 5 6 7 8 9 10 Labor Product Curves MP is slope of line tangent to corresponding point on TP curve TP 15 10 9 0 2 3 4 5 6 7 8 1 Labor Chapter 6

  20. Production: One Variable Input • From the previous example, we can see that as we increase labor the additional output produced declines • Law of Diminishing Marginal Returns: As the use of an inputincreases with other inputs fixed, the resulting additions to output will eventually decrease…..applies only in short run when 1 variable fixed Chapter 6

  21. Law of Diminishing Marginal Returns • Assumes a constant technology • Changes in technology will cause shifts in the total product curve • More output can be produced with same inputs • Labor productivity (output per laborer) can increase if there are improvements in technology, even though any given production process exhibits diminishing returns to labor Chapter 6

  22. C O3 B A O2 O1 Labor per time period 0 1 2 3 4 5 6 7 8 9 10 The Effect of Technological Improvement Moving from A to B to C, labor productivity is increasing over time Output 100 50 Chapter 6

  23. END OF LECTURE 1!!!!!!!!!!!!!!!!!!! Chapter 6

  24. Labor Productivity • Macroeconomics are particularly concerned with labor productivity • The average product of labor for an entire industry or the economy as a whole • Links macro- and microeconomics • Can provide useful comparisons across time and across industries Chapter 6

  25. Labor Productivity • Link between labor productivity and standard of living • Consumption can increase only if productivity increases • Growth of Productivity • Growth in stock of capital – total amount of capital available for production • Technological change – development of new technologies that allow factors of production to be used more efficiently Chapter 6

  26. Production: Two Variable Inputs • Firm can produce output by combining different amounts of labor and capital • In the long run, capital and labor are both variable • We can look at the output we can achieve with different combinations of capital and labor – Table 6.4 Chapter 6

  27. Production: Two Variable Inputs Chapter 6

  28. Production: Two Variable Inputs • The information can be represented graphically using isoquants • Curves showing all possible combinations of inputs that yield the same output • Curves are smooth to allow for use of fractional inputs • Curve 1 shows all possible combinations of labor and capital that will produce 55 units of output Chapter 6

  29. E 5 Capital per year 4 3 A B C 2 q3 = 90 D q2 = 75 1 q1 = 55 1 2 3 4 5 Labor per year Isoquant Map Ex: 55 units of output can be produced with 3K & 1L (pt. A) OR 1K & 3L (pt. D) Chapter 6

  30. Production: Two Variable Inputs • Diminishing Returns to Labor with Isoquants • Holding capital at 3 and increasing labor from 0 to 1 to 2 to 3 • Output increases at a decreasing rate (0, 55, 20, 15) illustrating diminishing marginal returns from labor in the short run and long run Chapter 6

  31. Production: Two Variable Inputs • Diminishing Returns to Capital with Isoquants • Holding labor constant at 3 increasing capital from 0 to 1 to 2 to 3 • Output increases at a decreasing rate (0, 55, 20, 15) due to diminishing returns from capital in short run and long run Chapter 6

  32. E 5 Capital per year 4 3 A B C 2 q3 = 90 D q2 = 75 1 q1 = 55 1 2 3 4 5 Labor per year Diminishing Returns Increasing labor holding capital constant (A, B, C) OR Increasing capital holding labor constant (E, D, C) Chapter 6

  33. Production: Two Variable Inputs • Substituting Among Inputs • Companies must decide what combination of inputs to use to produce a certain quantity of output • There is a trade-off between inputs, allowing them to use more of one input and less of another for the same level of output Chapter 6

  34. Production: Two Variable Inputs • Substituting Among Inputs • Slope of the isoquant shows how one input can be substituted for the other and keep the level of output the same • The negative of the slope is the 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

  35. Production: Two Variable Inputs • The marginal rate of technical substitution equals: Chapter 6

  36. Production: Two Variable Inputs • As labor increases to replace capital • Labor becomes relatively less productive • Capital becomes relatively more productive • Need less capital to keep output constant Chapter 6

  37. 2 1 1 1 Q3 =90 2/3 1 1/3 Q2 =75 1 Q1 =55 Marginal Rate ofTechnical Substitution Capital per year 5 Negative Slope measures MRTS; MRTS decreases as move down the indifference curve 4 3 2 1 Labor per month 1 2 3 4 5 Chapter 6

  38. MRTS and Isoquants • We assume there is diminishing MRTS • Increasing labor in one unit increments from 1 to 5 results in a decreasing MRTS from 1 to 1/2 • Diminishing MRTS occurs because of diminishing returns and implies isoquants are convex • There is a relationship between MRTS and marginal products of inputs Chapter 6

  39. MRTS and Marginal Products • If we increase labor and decrease capital to keep output constant, we can see how much the increase in output is due to the increased labor • Amount of labor increased times the marginal productivity of labor: Chapter 6

  40. MRTS and Marginal Products • Similarly, the decrease in output from the decrease in capital can be calculated • Decrease in output from reduction of capital times the marginal produce of capital: Chapter 6

  41. MRTS and Marginal Products • If we are holding output constant, the net effect of increasing labor and decreasing capital must be zero • Using changes in output from capital and labor we can see: Chapter 6

  42. MRTS and Marginal Products • Rearranging equation, we can see the relationship between MRTS and MPs Chapter 6

  43. Isoquants: Special Cases • Two extreme cases show the possible range of input substitution in production • Perfect substitutes • MRTS is constant at all points on isoquant • Same output can be produced with a lot of capital or a lot of labor or a balanced mix Chapter 6

  44. A B C Q1 Q2 Q3 Perfect Substitutes Capital per month Same output can be reached with mostly capital or mostly labor (A or C) or with equal amount of both (B) Labor per month Chapter 6

  45. Isoquants: Special Cases • Perfect Complements • Fixed proportions production function • The output can be made with only a specific proportion of capital and labor • Cannot increase output unless increase both capital and labor in that specific proportion Chapter 6

  46. Q3 C Q2 B Q1 K1 A L1 Fixed-ProportionsProduction Function Capital per month Same output can only be produced with one set of inputs. Labor per month Chapter 6

  47. 120 A 100 B 90 80 40 Labor 250 500 760 1000 Isoquant Describing theProduction of Wheat Point A is more capital-intensive, and B is more labor-intensive. Capital Output = 13,800 bushels per year Chapter 6

  48. Returns to Scale • How does a firm decide, in the long run, the best way to increase output? • Can change the scale of production by increasing all inputs in proportion • If double inputs, output will most likely increase but by how much? Chapter 6

  49. Returns to Scale • Rate at which output increases as inputs are increased proportionately • Increasing returns to scale • Constant returns to scale • Decreasing returns to scale Chapter 6

  50. Returns to Scale • Increasing returns to scale: output more than doubles when all inputs are doubled • Larger output associated with lower cost (cars) • One firm is more efficient than many (utilities) • The isoquants get closer together Chapter 6

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