1. Chapter 7 The Cost of Production

2. Chapter 7Slide 2 Topics to be Discussed Measuring Cost: Which Costs Matter? Cost in the Short Run Cost in the Long Run Long-Run Versus Short-Run Cost Curves

3. Chapter 7Slide 3 Introduction The production technology measures the relationship between input and output. Given the production technology, managers must choose how to produce. To determine the optimal level of output and the input combinations, we must convert from the unit measurements of the production technology to dollar measurements or costs.

4. Chapter 7Slide 4 Measuring Cost: Which Costs Matter? Accounting Cost Actual expenses plus depreciation charges for capital equipment Economic Cost Cost to a firm of utilizing economic resources in production, including opportunity cost Economic Cost vs. Accounting Cost

5. Chapter 7Slide 5 Opportunity cost. Cost associated with opportunities that are foregone when a firm’s resources are not put to their highest-value use. An Example A firm owns its own building and pays no rent for office space Does this mean the cost of office space is zero? Measuring Cost: Which Costs Matter?

6. Economic versus Accountants Copyright © 2004 South-Western Revenue How an Economist Views a Firm How an Accountant Views a Firm Revenue Economic profit Implicit costs Explicit costs Explicit costs Accounting profit

7. Chapter 7Slide 7 Total output is a function of variable inputs and fixed inputs. Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or… Costs in the short-run: Fixed and Variable Costs

8. Chapter 7Slide 8 Fixed Cost Does not vary with the level of output Variable Cost Cost that varies as output varies Measuring Cost: Which Costs Matter? Fixed and Variable Costs

9. Chapter 7Slide 9 Fixed Cost Cost paid by a firm that is in business regardless of the level of output Sunk Cost Cost that have been incurred and cannot be recovered Decision makers should ignore sunk costs to maximize profit or minimize losses Measuring Cost: Which Costs Matter?

10. A Firm’s Short-Run Costs ($) 050 050------------ 15050100505050100 2507812828253964 350981482016.732.749.3 4501121621412.52840.5 55013018018102636 650150200208.32533.3 750175225257.12532.1 850204254296.325.531.8 950242292385.626.932.4 10503003505853035 1150385435854.53539.5 Rate ofFixedVariableTotalMarginalAverageAverageAverage OutputCostCostCostCostFixedVariableTotal (FC)(VC)(TC)(MC)CostCostCost (AFC)(AVC)(ATC)

11. Chapter 7Slide 11 Cost in the Short Run Marginal Cost (MC) is the cost of expanding output by one unit. Since fixed cost have no impact on marginal cost, it can be written as:

12. Chapter 7Slide 12 Cost in the Short Run Average Total Cost (ATC) is the cost per unit of output, or average fixed cost (AFC) plus average variable cost (AVC). This can be written:

13. Chapter 7Slide 13 Cost in the Short Run The relationship between the production function and cost can be exemplified by either increasing returns and cost or decreasing returns and cost. Increasing returns and cost  With increasing returns, output is increasing relative to input and variable cost and total cost will fall relative to output. Decreasing returns and cost  With decreasing returns, output is decreasing relative to input and variable cost and total cost will rise relative to output.

14. Chapter 7Slide 14 Cost in the Short Run For Example: Assume the wage rate (w) is fixed relative to the number of workers hired. Then:

15. Chapter 7Slide 15 Cost in the Short Run Continuing:

16. Chapter 7Slide 16 Cost in the Short Run In conclusion: …and a low marginal product (MP) leads to a high marginal cost (MC) and vise versa.

17. Chapter 7Slide 17 Cost in the Short Run Consequently (from the table): MC decreases initially with increasing returns  0 through 4 units of output MC increases with decreasing returns  5 through 11 units of output

18. A Firm’s Short-Run Costs ($) 050 050------------ 15050100505050100 2507812828253964 350981482016.732.749.3 4501121621412.52840.5 55013018018102636 650150200208.32533.3 750175225257.12532.1 850204254296.325.531.8 950242292385.626.932.4 10503003505853035 1150385435854.53539.5 Rate ofFixedVariableTotalMarginalAverageAverageAverage OutputCostCostCostCostFixedVariableTotal (FC)(VC)(TC)(MC)CostCostCost (AFC)(AVC)(ATC)

19. Chapter 7Slide 19 Cost Curves for a Firm Output Cost ($ per year) 100 200 300 400 012345678910111213 VC Variable cost increases with production and the rate varies with increasing & decreasing returns. TC Total cost is the vertical sum of FC and VC. FC 50 Fixed cost does not vary with output

20. Chapter 7Slide 20 Cost Curves for a Firm Output (units/yr.) Cost ($ per unit) 25 50 75 100 0 1 234567891011 MC ATC AVC AFC

21. Chapter 7Slide 21 Cost Curves for a Firm The line drawn from the origin to the tangent of the variable cost curve: Its slope equals AVC The slope of a point on VC equals MC Therefore, MC = AVC at 7 units of output (point A) Output Cost 100 200 300 400 0123456789101112 13 FC VC A TC

22. Chapter 7Slide 22 Cost Curves for a Firm Unit Costs AFC falls continuously When MC < AVC or MC < ATC, AVC & ATC decrease When MC > AVC or MC > ATC, AVC & ATC increase Output (units/yr.) Cost ($ per unit) 25 50 75 100 0 1 2345678910 11 MC ATC AVC AFC

23. Chapter 7Slide 23 Cost Curves for a Firm Unit Costs MC = AVC and ATC at minimum AVC and ATC Minimum AVC occurs at a lower output than minimum ATC due to FC Output (units/yr.) Cost ($ per unit) 25 50 75 100 0 1 2345678910 11 MC ATC AVC AFC

24. Chapter 7Slide 24 Cost in the Long Run The Isocost Line C = wL + rK Isocost: A line showing all combinations of L & K that can be purchased for the same cost The User Cost of Capital The Cost Minimizing Input Choice

25. Chapter 7Slide 25 Cost in the Long Run Rewriting C as linear: K = C/r - (w/r)L Slope of the isocost:  is the ratio of the wage rate to rental cost of capital.  This shows the rate at which capital can be substituted for labor with no change in cost. The Isocost Line

26. Chapter 7Slide 26 Choosing Inputs We will address how to minimize cost for a given level of output. We will do so by combining isocosts with isoquants

27. Chapter 7Slide 27 Producing a Given Output at Minimum Cost Labor per year Capital per year Isocost C 2 shows quantity Q 1 can be produced with combination K 2 L 2 or K 3 L 3. However, both of these are higher cost combinations than K 1 L 1. Q1Q1 Q 1 is an isoquant for output Q 1. Isocost curve C 0 shows all combinations of K and L that can produce Q 1 at this cost level. C0C0 C1C1 C2C2 C O C 1 C 2 are three isocost lines A K1K1 L1L1 K3K3 L3L3 K2K2 L2L2

28. Isocost The combinations of inputs that produce a given level of output at the same cost: wL + rK = C Rearranging, K= (1/r)C - (w/r)L For given input prices, isocosts farther from the origin are associated with higher costs. Changes in input prices change the slope of the isocost line. K L C1C1 L K New Isocost Line for a decrease in the wage (price of labor: w 0 > w 1 ). C1/rC1/r C1/wC1/w C0C0 C0/wC0/w C0/rC0/r C/w0C/w0 C/w1C/w1 C/rC/r New Isocost Line associated with higher costs (C 0 < C 1 ).

29. Chapter 7Slide 29 Input Substitution When an Input Price Change C2C2 This yields a new combination of K and L to produce Q 1. Combination B is used in place of combination A. The new combination represents the higher cost of labor relative to capital and therefore capital is substituted for labor. K2K2 L2L2 B C1C1 K1K1 L1L1 A Q1Q1 If the price of labor changes, the isocost curve becomes steeper due to the change in the slope -(w/r). Labor per year Capital per year

30. Chapter 7Slide 30 Cost in the Long Run Isoquants and Isocosts and the Production Function

31. Chapter 7Slide 31 Cost in the Long Run The minimum cost combination can then be written as: Minimum cost for a given output will occur when each dollar of input added to the production process will add an equivalent amount of output.

32. Chapter 7Slide 32 Cost in the Long Run Question If w = $10, r = $2, and MP L = MP K, which input would the producer use more of? Why?

33. Chapter 7Slide 33 Cost minimization with Varying Output Levels A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output. Cost in the Long Run

34. Chapter 7Slide 34 A Firm’s Expansion Path Labor per year Capital per year Expansion Path The expansion path illustrates the least-cost combinations of labor and capital that can be used to produce each level of output in the long-run. 25 50 75 100 150 100 50 150300200 A $2000 Isocost Line 200 Unit Isoquant B $3000 Isocost Line 300 Unit Isoquant C

35. Chapter 7Slide 35 A Firm’s Long-Run Total Cost Curve Output, Units/yr Cost per Year Long Run Total Cost 1000 100300200 2000 3000 D E F

36. Chapter 7Slide 36 Long-Run Versus Short-Run Cost Curves What happens to average costs when both inputs are variable (long run) versus only having one input that is variable (short run)?

37. Chapter 7Slide 37 Long-Run Expansion Path The long-run expansion path is drawn as before.. The Inflexibility of Short-Run Production Labor per year Capital per year L2L2 Q2Q2 K2K2 D C F E Q1Q1 A B L1L1 K1K1 L3L3 P Short-Run Expansion Path

38. Chapter 7Slide 38 Long-Run Average Cost (LAC) Constant Returns to Scale  If input is doubled, output will double and average cost is constant at all levels of output. Long-Run Versus Short-Run Cost Curves

39. Chapter 7Slide 39 Long-Run Average Cost (LAC) Increasing Returns to Scale  If input is doubled, output will more than double and average cost decreases at all levels of output. Long-Run Versus Short-Run Cost Curves

40. Chapter 7Slide 40 Long-Run Average Cost (LAC) Decreasing Returns to Scale  If input is doubled, the increase in output is less than twice as large and average cost increases with output. Long-Run Versus Short-Run Cost Curves

41. Chapter 7Slide 41 Long-Run Average Cost (LAC) In the long-run:  Firms experience increasing and decreasing returns to scale and therefore long-run average cost is “U” shaped. Long-Run Versus Short-Run Cost Curves

42. Chapter 7Slide 42 Long-Run Average and Marginal Cost Output Cost ($ per unit of output LAC LMC A

43. Chapter 7Slide 43 Long-Run Average Cost (LAC) Long-run marginal cost leads long-run average cost:  If LMC < LAC, LAC will fall  If LMC > LAC, LAC will rise  Therefore, LMC = LAC at the minimum of LAC Long-Run Versus Short-Run Cost Curves

44. Chapter 7Slide 44 Question What is the relationship between long- run average cost and long-run marginal cost when long-run average cost is constant? Long-Run Versus Short-Run Cost Curves

45. Chapter 7Slide 45 Economies and Diseconomies of Scale Economies of Scale  Increase in output is greater than the increase in inputs. Diseconomies of Scale  Increase in output is less than the increase in inputs. Long-Run Versus Short-Run Cost Curves

46. Long-Run Average Costs LRAC $ Q Economies of Scale Diseconomies of Scale Q*

47. Chapter 7Slide 47 The Relationship Between Short-Run and Long-Run Cost We will use short and long-run cost to determine the optimal plant size Long-Run Versus Short-Run Cost Curves

48. Chapter 7Slide 48 Long-Run Cost with Constant Returns to Scale Output Cost ($ per unit of output Q3Q3 SAC 3 SMC 3 Q2Q2 SAC 2 SMC 2 LAC = LMC With many plant sizes with SAC = $10 the LAC = LMC and is a straight line Q1Q1 SAC 1 SMC 1

49. Chapter 7Slide 49 Observation The optimal plant size will depend on the anticipated output (e.g. Q 1 choose SAC 1,etc). The long-run average cost curve is the envelope of the firm’s short-run average cost curves. Question What would happen to average cost if an output level other than that shown is chosen? Long-Run Cost with Constant Returns to Scale

50. Chapter 7Slide 50 Long-Run Cost with Economies and Diseconomies of Scale Output Cost ($ per unit of output SMC 1 SAC 1 SAC 2 SMC 2 LMC If the output is Q 1 a manager would chose the small plant SAC 1 and SAC $8. Point B is on the LAC because it is a least cost plant for a given output. $10 Q1Q1 $8 B A LAC SAC 3 SMC 3

51. Chapter 7Slide 51 What is the firms’ long-run cost curve? Firms can change scale to change output in the long-run. The long-run cost curve is the dark blue portion of the SAC curve which represents the minimum cost for any level of output. Long-Run Cost with Constant Returns to Scale

52. Chapter 7Slide 52 Observations The LAC does not include the minimum points of small and large size plants? Why not? Long-Run Cost with Constant Returns to Scale

53. Chapter 7Slide 53 Summary Managers, investors, and economists must take into account the opportunity cost associated with the use of the firm’s resources. Firms are faced with both fixed and variable costs in the short-run.

54. Chapter 7Slide 54 Summary When there is a single variable input, as in the short run, the presence of diminishing returns determines the shape of the cost curves. In the long run, all inputs to the production process are variable.

55. Chapter 7Slide 55 Summary The firm’s expansion path describes how its cost-minimizing input choices vary as the scale or output of its operation increases. The long-run average cost curve is the envelope of the short-run average cost curves. A firm enjoys economies of scale when it can double its output at less than twice the cost.

56. End of Chapter 7 The Cost of Production