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 Production with Two Outputs-- Economies of Scope

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.

4. Chapter 7Slide 4 Introduction 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.

5. Chapter 7Slide 5 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

6. Chapter 7Slide 6 Opportunity cost. Cost associated with opportunities that are foregone when a firm’s resources are not put to their highest-value use. Measuring Cost: Which Costs Matter?

7. Chapter 7Slide 7 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?

8. Chapter 7Slide 8 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… Measuring Cost: Which Costs Matter? Fixed and Variable Costs

9. Chapter 7Slide 9 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

10. Chapter 7Slide 10 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 Measuring Cost: Which Costs Matter?

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 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:

14. Chapter 7Slide 14 Cost in the Short Run The Determinants of Short-Run Cost The relationship between the production function and cost can be exemplified by either increasing returns and cost or decreasing returns and cost.

15. Chapter 7Slide 15 Cost in the Short Run The Determinants of Short-Run 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.

16. Chapter 7Slide 16 Cost in the Short Run For Example: Assume the wage rate (w) is fixed relative to the number of workers hired. Then:

17. Chapter 7Slide 17 Cost in the Short Run Continuing:

18. Chapter 7Slide 18 Cost in the Short Run Continuing:

19. Chapter 7Slide 19 Cost in the Short Run In conclusion: …and a low marginal product (MP) leads to a high marginal cost (MC) and vise versa.

20. 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)

21. Chapter 7Slide 21 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

22. Chapter 7Slide 22 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

23. Chapter 7Slide 23 Cost Curves for a Firm Output (units/yr.) Cost ($ per unit) 25 50 75 100 0 1 234567891011 MC ATC AVC AFC

24. Chapter 7Slide 24 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

25. Chapter 7Slide 25 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

26. Chapter 7Slide 26 Cost in the Long Run User Cost of Capital = Economic Depreciation + Interest Rate (Value of Capital) The User Cost of Capital

27. Chapter 7Slide 27 Cost in the Long Run Assumptions Two Inputs: Labor ( L ) & capital ( K ) Price of labor: wage rate (w) The price of capital  r = depreciation rate + interest rate The Cost Minimizing Input Choice

28. Chapter 7Slide 28 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

29. Chapter 7Slide 29 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

30. Chapter 7Slide 30 Choosing Inputs We will address how to minimize cost for a given level of output. We will do so by combining isocosts with isoquants

31. Chapter 7Slide 31 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 not 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

32. Chapter 7Slide 32 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 increases, the isocost curve becomes steeper due to the change in the slope -(w/r). Labor per year Capital per year

33. Chapter 7Slide 33 Cost in the Long Run Isoquants and Isocosts and the Production Function

34. Chapter 7Slide 34 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.

35. Chapter 7Slide 35 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

36. Chapter 7Slide 36 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

37. Chapter 7Slide 37 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)?

38. Chapter 7Slide 38 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

39. Chapter 7Slide 39 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

40. Chapter 7Slide 40 Long-Run Average and Marginal Cost Output Cost ($ per unit of output LAC LMC A

41. Chapter 7Slide 41 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

42. Chapter 7Slide 42 Measuring Economies of Scale Long-Run Versus Short-Run Cost Curves

43. Chapter 7Slide 43 Measuring Economies of Scale Long-Run Versus Short-Run Cost Curves

44. Chapter 7Slide 44 Therefore, the following is true: E C < 1: MC < AC  Average cost indicate economies of scale E C = 1: MC = AC  Average cost indicate constant economies of scale E C > 1: MC > AC  Average cost indicate diseconomies of scale Long-Run Versus Short-Run Cost Curves

45. Chapter 7Slide 45 Economies of scope exist when the joint output of a single firm is greater than the output that could be achieved by two different firms each producing a single output. What are the advantages of joint production? Consider an automobile company producing cars and tractors Production with Two Outputs--Economies of Scope

46. Chapter 7Slide 46 Advantages 1)Both use capital and labor. 2)The firms share management resources. 3)Both use the same labor skills and type of machinery. Production with Two Outputs--Economies of Scope

47. Chapter 7Slide 47 Observations There is no direct relationship between economies of scope and economies of scale.  May experience economies of scope and diseconomies of scale  May have economies of scale and not have economies of scope Production with Two Outputs--Economies of Scope

48. Chapter 7Slide 48 The degree of economies of scope measures the savings in cost and can be written: C(Q 1 ) is the cost of producing Q 1 C(Q 2 ) is the cost of producing Q 2 C(Q 1 Q 2 ) is the joint cost of producing both products Production with Two Outputs--Economies of Scope

49. Chapter 7Slide 49 Interpretation: If SC > 0 -- Economies of scope If SC < 0 -- Diseconomies of scope Production with Two Outputs--Economies of Scope

50. Chapter 7Slide 50 Learning A firm’s average cost of production can fall over time if the firm “learns” how to produce more effectively.

51. Chapter 7Slide 51 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.

52. Chapter 7Slide 52 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.

53. Chapter 7Slide 53 Summary The firm’s expansion path describes how its cost-minimizing input choices vary as the scale or output of its operation increases.

54. Chapter 7Slide 54 Summary A firm enjoys economies of scale when it can double its output at less than twice the cost. Economies of scope arise when the firm can produce any combination of the two outputs more cheaply than could two independent firms that each produced a single product.

55. End of Chapter 7 The Cost of Production