Unit V

1. Unit V Production Costs (Chapter 12)

2. In this chapter, look for the answers to these questions: • What is a production function? What is marginal product? How are they related? • What are the various costs, and how are they related to each other and to output? • How are costs different in the short run vs. the long run? • What are “economies of scale”?

3. 0 Short Run and Long run • The Short Run: Fixed Plant • The short run is a time frame in which the quantities of some resources are fixed. • In the short run, a firm can usually change the quantity of labor it uses but not the quantity of capital. • The Long Run: Variable Plant • The long run is a time frame in which the quantities of all resources can be changed. • A sunk cost is irrelevant to the firm’s decisions.

4. 0 Short Run Production • To increase output with a fixed plant, a firm must increase the quantity of labor it uses. • We describe the relationship between output and the quantity of labor by using three related concepts: • Total product • Marginal product • Average product

5. 0 The Production Function • A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good. • It can be represented by a table, equation, or graph. • Example: • Farmer Jack grows wheat. • He has 5 acres of land. • He can hire as many workers as he wants.

6. 0 The Production Function • Total Product • Total product (TP) is the total quantity of a good produced in a given period. • Total product is an output rate—the number of units produced per unit of time. • Total product increases as the quantity of labor employed increases.

7. 0 The Production Function • The figure shows the total product and the total product curve. • Points A through H on the curve correspond to the columns of the table. • The TP curve is like the PPF: It separates attainable points and unattainable points.

8. L(no. of workers) Q(bushels of wheat) 3,000 2,500 0 0 2,000 1 1000 1,500 Quantity of output 2 1800 1,000 3 2400 500 4 2800 0 0 1 2 3 4 5 5 3000 No. of workers 0 EXAMPLE: Farmer Jack’s Production Function

9. ∆Q ∆L 0 Marginal Product • Marginal product is the change in total product that results from a one-unit increase in the quantity of labor employed. • Marginal product tells us the contribution to total product of adding one more worker. • E.g., if Farmer Jack hires one more worker, his output rises by the marginal product of labor. • Notation: ∆ (delta) = “change in…” • Examples: ∆Q = change in output, ∆L = change in labor • Marginal product of labor (MPL) =

10. 0 Marginal Product • The figure shows total product and marginal product. • We can illustrate marginal product as the orange bars that form steps along the total product curve. • The height of each step represents marginal product.

11. 0 Marginal Product • The table calculates marginal product and the orange bars in part (b) illustrate it. • Notice that the steeper the slope of the TP curve, the greater is marginal product.

12. 0 Marginal Product • The total product and marginal product curves in this figure incorporate a feature of all production processes: • Increasing marginal returns initially • Decreasing marginal returns eventually • Negative marginal returns

13. L(no. of workers) Q(bushels of wheat) 0 0 ∆Q = 1000 ∆L = 1 1 1000 ∆Q = 800 ∆L = 1 2 1800 ∆L = 1 ∆Q = 600 3 2400 ∆Q = 400 ∆L = 1 4 2800 ∆L = 1 ∆Q = 200 5 3000 0 EXAMPLE: Total & Marginal Product MPL 1000 800 600 400 200

14. 3,000 2,500 2,000 Quantity of output 1,500 1,000 500 0 0 1 2 3 4 5 No. of workers 0 EXAMPLE: MPL = Slope of Prod Function L(no. of workers) Q(bushels of wheat) MPL MPL equals the slope of the production function. Notice that MPL diminishes as L increases. This explains why the production function gets flatter as L increases. 0 0 1000 1 1000 800 2 1800 600 3 2400 400 4 2800 200 5 3000

15. Why MPL Is Important • Rational people think at the margin. • When Farmer Jack hires an extra worker, • his costs rise by the wage he pays the worker • his output rises by MPL • Comparing them helps Jack decide whether he would benefit from hiring the worker.

16. Increasing Marginal Returns • Increasing marginal returnsoccur when the marginal product of an additional worker exceeds the marginal product of the previous worker. • Increasing marginal returns occur when a small number of workers are employed and arise from increased specialization and division of labor in the production process.

17. Why MPL Diminishes • Decreasing marginal returns occur when the marginal product of an additional worker is less than the marginal product of the previous worker. • E.g., Farmer Jack’s output rises by a smaller and smaller amount for each additional worker. Why? • If Jack increases workers but not land, the average worker has less land to work with, so will be less productive. • In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.).

18. Why MPL Diminishes • Decreasing marginal returns are so pervasive that they qualify for the status of a law: • The law of decreasing returnsstates that: As a firm uses more of a variable input, with a given quantity of fixed inputs, the marginal product of the variable input eventually decreases.

19. SHORT-RUN PRODUCTION The figure graphs the average product against the quantity of labor employed. The average product curve is AP. When marginal product exceeds average product, average product is increasing.

20. SHORT-RUN PRODUCTION When marginal product is less than average product, average product is decreasing. When marginal product equals average product, average product is at its maximum.

21. SHORT-RUN COST • To produce more output in the short run, a firm employs more labor, which means the firm must increase its costs. • We describe the relationship between output and cost using three cost concepts: • Total cost • Marginal cost • Average cost

22. SHORT-RUN COST • Total Cost • A firm’s total cost (TC) is the cost of all the factors of production the firm uses. • Total Cost divides into two parts: • Fixed cost (FC) is the cost of a firm’s fixed factors of production used by a firm—the cost of land, capital, and entrepreneurship. • Fixed costs don’t change as output changes.

23. SHORT-RUN COST • Variable cost (VC) is the cost of the variable factor of production used by a firm—the cost of labor. • To change its output in the short run, a firm must change the quantity of labor it employs, so total variable cost changes as output changes. • Total cost is the sum of total fixed cost and total variable cost. That is, TC = FC + VC

24. SHORT-RUN COST Fixed cost (FC) is constant—it graphs as a horizontal line. Variable cost (VC) increases as output increases. Total cost (TC) also increases as output increases.

25. SHORT-RUN COST The vertical distance between the total cost curve and the total variable cost curve is total fixed cost, as illustrated by the two arrows.

26. MC = ∆TC ∆Q Marginal Cost • Marginal Cost (MC) is the increase in Total Cost from producing one more unit: Marginal cost tells us how total cost changes as total product changes.

27. MC = ∆TC ∆Q EXAMPLE: Marginal Cost Recall, Marginal Cost (MC)is the change in total cost from producing one more unit: Q TC MC 0 $100 $70 1 170 50 2 220 40 3 260 Usually, MC rises as Q rises, due to diminishing marginal product. Sometimes (as here), MC falls before rising. (In other examples, MC may be constant.) 50 4 310 70 5 380 100 6 480 140 7 620

28. SHORT-RUN COST • Average Cost • There are three average cost concepts: • Average fixed cost (AFC) is total fixed cost per unit of output. • Average variable cost (AVC) is total variable cost per unit of output. • Average total cost (ATC) is total cost per unit of output.

29. TC = TFC + TVC Q Q Q SHORT-RUN COST • The average cost concepts are calculated from the total cost concepts as follows: TC = TFC + TVC • Divide each total cost term by the quantity produced, Q, to give or, ATC = AFC + AVC

30. A C T I V E L E A R N I N G 1: Costs Q VC TC AFC AVC ATC MC Fill in the blank spaces of this table. $50 n.a. 0 n.a. n.a. $10 1 10 $10 $60.00 2 30 80 30 3 16.67 20 36.67 4 100 150 12.50 37.50 5 150 30 60 6 210 260 8.33 35 43.33

31. A C T I V E L E A R N I N G 1: Answers Use AFC = FC/Q Use ATC = TC/Q Use relationship between MC and TC Use AVC = VC/Q Q VC TC AFC AVC ATC MC First, deduce FC = $50 and use FC + VC = TC. 0 $0 $50 n.a. n.a. n.a. $10 1 10 60 $50.00 $10 $60.00 20 2 30 80 25.00 15 40.00 30 3 60 110 16.67 20 36.67 40 4 100 150 12.50 25 37.50 50 5 150 200 10.00 30 40.00 60 6 210 260 8.33 35 43.33

32. n.a. $100 50 33.33 25 20 16.67 14.29 0 EXAMPLE: Average Fixed Cost Average fixed cost (AFC)is fixed cost divided by the quantity of output: AFC = FC/Q Q FC AFC 0 $100 1 100 2 100 3 100 Notice that AFC falls as Q rises: The firm is spreading its fixed costs over a larger and larger number of units. 4 100 5 100 6 100 7 100

33. n.a. $70 60 53.33 52.50 56.00 63.33 74.29 0 EXAMPLE: Average Variable Cost Average variable cost (AVC)is variable cost divided by the quantity of output: AVC = VC/Q Q VC AVC 0 $0 1 70 2 120 3 160 As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. 4 210 5 280 6 380 7 520

34. AFC AVC n.a. n.a. n.a. $170 $100 $70 110 50 60 86.67 33.33 53.33 77.50 25 52.50 76 20 56.00 80 16.67 63.33 88.57 14.29 74.29 0 EXAMPLE: Average Total Cost Average total cost (ATC) equals total cost divided by the quantity of output: ATC = TC/Q Q TC ATC 0 $100 1 170 2 220 3 260 Also, ATC = AFC + AVC 4 310 5 380 6 480 7 620

35. $200 $175 $150 $125 Costs $100 $75 $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 EXAMPLE: Average Total Cost Q TC ATC Usually, as in this example, the ATC curve is U-shaped. 0 $100 n.a. 1 170 $170 2 220 110 3 260 86.67 4 310 77.50 5 380 76 6 480 80 7 620 88.57

36. $200 $175 $150 AFC $125 AVC Costs $100 ATC $75 MC $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 EXAMPLE: The Various Cost Curves Together

37. SHORT-RUN COST The vertical distance between these two curves is equal to average fixed cost, as illustrated by the two arrows. REMEMBER -- The marginal cost curve (MC) intersects the average variable cost curve and the average total cost curve at their minimum points.

38. SHORT-RUN COST • Why the Average Total Cost Curve Is U-Shaped • Average total cost, ATC, is the sum of average fixed cost, AFC, and average variable cost, AVC. • The shape of the ATC curve combines the shapes of the AFC and AVC curves. • The U shape of the average total cost curve arises from the influence of two opposing forces: • Spreading total fixed cost over a larger output • Decreasing marginal returns

39. $200 $175 $150 $125 Costs $100 $75 $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 EXAMPLE: Why ATC Is Usually U-shaped As Q rises: Initially, falling AFCpulls ATC down. Eventually, rising AVCpulls ATC up.

40. $200 $175 $150 $125 Costs $100 ATC $75 MC $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 EXAMPLE: ATC and MC When MC < ATC, ATC is falling. When MC > ATC, ATC is rising. The MC curve crosses the ATC curve at the ATC curve’s minimum.

41. SHORT-RUN COST • Cost Curves and Product Curves • The technology that a firm uses determines its costs. • At low levels of employment and output, as the firm hires more labor, marginal product and average product rise, and marginal cost and average variable cost fall. • Then, at the point of maximum marginal product, marginal cost is a minimum. • As the firm hires more labor, marginal product decreases and marginal cost increases.

42. SHORT-RUN COST • But average product continues to rises, and average variable cost continues to fall. • Then, at the point of maximum average product, average variable cost is a minimum. • As the firm hires even more labor, average product decreases and average variable cost increases.

43. SHORT-RUN COST This figure illustrates the relationship between the product curves and cost curves. A firm’s marginal cost curve is linked to its marginal product curve. If marginal product rises, marginal cost falls. If marginal product is a maximum, marginal cost is a minimum.

44. SHORT-RUN COST A firm’s average variable cost curve is linked to its average product curve. If average product rises, average variable cost falls. If average product is a maximum, average variable cost is a minimum.

45. SHORT-RUN COST At small outputs, MP and AP rise and MC and AVC fall. At intermediate outputs, MP falls and MC rises and AP rises and AVC falls. At large outputs, MP and AP fall and MC and AVC rise.

46. SHORT-RUN COST • Shifts in Cost Curves Technology • A technological change that increases productivity shifts the total product curve upward. It also shifts the marginal product curve and the average product curve upward. • With a better technology, the same inputs can produce more output, so an advance in technology lowers the average and marginal costs and shifts the short-run cost curves downward.

47. SHORT-RUN COST • Prices of Factors of Production • An increase in the price of a factor of production increases costs and shifts the cost curves. • But how the curves shift depends on which resource price changes. • An increase in rent or another component of fixed cost • Shifts the fixed cost curves (TFC and AFC) upward. • Shifts the total cost curve (TC) upward. • Leaves the variable cost curves (AVC and TVC) and the marginal cost curve (MC) unchanged.

48. SHORT-RUN COST • An increase in the wage rate or another component of variable cost • Shifts the variable curves (TVC and AVC) upward. • Shifts the marginal cost curve (MC) upward. • Leaves the fixed cost curves (AFC and TFC) unchanged.

49. LONG-RUN COST • Plant Size and Cost • When a firm changes its plant size, its cost of producing a given output changes. • Will the average total cost of producing a gallon of smoothie fall, rise, or remain the same? • Each of these three outcomes arise because when a firm changes the size of its plant, it might experience: • Economies of scale • Diseconomies of scale • Constant returns to scale

50. Economies of Scale • Economies of scale exist if when a firm increases its plant size and labor employed by the same percentage, its output increases by a larger percentage and average total cost decreases. • The main source of economies of scale is greater specialization of both labor and capital.