Chapter 7 Cost Analysis

1. Chapter 7Cost Analysis

2. Relevant costs: In deciding among alternative courses of actions, consider only the differential revenues and costs of the alternatives Opportunity cost: Foregone benefits of next-best choice Accounting profit: Revenues less expenses Total costs: Explicit costs plus opportunity costs Economic profit: Revenue less total cost Fixed costs: Costs that do not change with the level of output Sunk cost: Expense already incurred which cannot be recovered Cost Analysis Definitions

3. Given P = 24 – Q where P is in dollars and Q is hundreds of copies sold. Bookstore pays $12 per copy of the book. There is no shelf-space constraint Problem: How many copies should the bookseller order? What price should the bookseller charge? Bookseller Example

4. Decision Rule: MC = MR Find MR P = 24 – Q TR = P Q = 24 Q – Q2 MR = 24 – 2 Q Apply decision rule MC = MR 12 = 24 – 2 Q 2 Q = 12 Q = 6 hundred books Bookseller Example (continued)

5. Find P for Q = 6 P = 24 – Q P = 24 – 6 P = $18 Bookseller Example (continued)

6. Given P = 24 – Q where P is in dollars and Q is hundreds of copies sold. Bookstore pays $12 per copy of the book. Shelf space is constrained; profit per typical book is $4 Problem: How many copies should the bookseller order? What price should the bookseller charge? Bookseller Example (continued)

7. Decision Rule: MC = MR Find MR MR = 24 – 2 Q Find MC MC is the $12 cost of the best seller PLUS the $4 profit that is foregone by using shelf space for the best seller. Bookseller Example (continued)

8. Decision Rule: MC = MR 16 = 24 – 2 Q 2Q = 8 Q = 4 hundred books Find P P = 24 – Q P = 24 – 4 P = $20 Bookseller Example (continued)

9. Given Bookstore ordered 4 hundred copies of the book. Bookstore pays $12 per copy of the book. Shelf space is constrained; profit per typical book is $4. Demand is actually P = 18 – 2 Q Cost of returning a book to the publisher is $6 Problem: Should the bookstore return any books and, if so, how many? Bookseller Example (continued)

10. Decision Rule: MC = MR Find MR P = 18 – 2 Q TR = P Q = 18 Q – 2 Q2 MR = 18 – 4 Q Find MC Since the books have already been purchased, the $12 cost is not relevant. The MC is the $4 profit from a typical book plus the $6 foregone if you keep the book to sell. Consequently, MC = $10 Bookseller Example (continued)

11. Decision Rule: MC = MR 10 = 18 – 4Q 4Q = 8 Q = 2 hundred Return 200 books Find P P = 18 – 2Q P = 18 – 2 (2) P = $14 Bookseller Example (continued)

12. Cost function Fixed costs Variable costs Average cost = average total cost Average variable cost Marginal cost Average fixed cost Short-Run Cost of Production – Definitions

13. Cost Function

14. Marginal cost is the extra cost from increasing output by one unit. In the short-run that is achieved by increasing labor SMC = ?C / ? Q SMC = (? C / ? L) (? Q / ? L) SMC = PL / MPL SMC increases if PL increases or MPL decreases The law of diminishing marginal productivity says MPL decreases as L increases So, short-run marginal cost (SMC) has a positive slope Short-Run Marginal Cost (SMC)

15. Short-run average cost is total cost divided by the level of output. SAC = TC / Q Since TC = FC + VC SAC = FC / Q + VC /Q At low levels of output, FC / Q will be relatively large and VC / Q will be relatively small, so SAC will be high. As Q increases, FC / Q decreases. If SMC < SAC, then increasing Q decreases SAC. If SAC = SMC, then SAC is at its minimum. Beyond that point, increases in Q increase SAC. Short-Run Average Cost (SAC)

16. Marginal and Average Costs

17. All inputs are variable. Total costs = variable costs Firm selects plant size and other long-term assets for a given level of output. Firm produces at global minimum average cost only if firm produces at planned output level. If short-term output varies from planned output, short-term average costs > long-term average costs. Slope of the long-run cost curve shows returns to scale. Long-Run Average Costs

18. Long-Run Average Cost Curve

19. Two products, different productivities, two countries, two wages, one exchange rate Assumptions: US wage $15; Japan wage ¥1,000 Exchange rate: $1 = ¥100 Productivity Trade and Comparative Advantage

20. Trade and Comparative Advantage (continued) Costs are productivity times wages Convert Japanese costs to dollars Costs

21. Comparative advantage depends on Productivity in each product in each country Wages in each country Exchange rates If wages increase in one country relative to the other, the change favors the country with the constant wages. If exchange rate of dollar appreciates (depreciates), the change favors the country with the depreciating (appreciating) currency. Trade and Comparative Advantage (continued)

22. Trade and Comparative Advantage – Wage Change

23. Trade and Comparative Advantage – Dollar Appreciates

24. Returns to scale determine the shape of the long-run average cost curve. U-shaped curve shows Increasing returns to scale at low levels of output. Constant returns to scale in the intermediate output range. Decreasing returns to scale at high levels of output. Returns to Scale

25. If the plant is easily replicated (McDonalds restaurant), then Constant average costs apply and The firm has constant returns to scale. If increased output allows Greater automation or mass-production processes Greater capital intensity Specialization of labor Significant fixed expenses, e.g., advertising, distribution Then the firm has decreasing average costs and Increasing returns to scale Returns to Scale Determinants

26. If increased output leads to decreased efficiency of organization, information flows, and control, then Average costs increase as output increases and Decreasing returns to scale apply. Returns to Scale Determinants (continued)

27. Generally, most goods have significant economies of scale at low levels of output, followed by a wide range of outputs where returns to scale are constant. A small number of firms show continuously declining average costs. Natural monopoly since the lowest average cost is achieved when one firm supplies the entire market. Returns to Scale – Empirical Results

28. Returns to Scale

29. Returns to Scale

30. Returns to Scale

31. Returns to Scale

32. Minimum efficient scale (MES) is the lowest output where minimum cost is possible. Optimal number of firms in the industry is total market demand divided by MES. Number of likely participants Sulfuric acid production: 25 firms Electric motors: 6 – 7 firms Commercial aircraft worldwide: 10 firms Why do Airbus and Boeing dominate? Minimum Efficient Scale

33. Based on average cost per student in Maryland, 1979. Elementary and middle schools only. Dependent variable: cost per student Independent variables: school enrollment, teacher training, teacher experience, professional support staff and teacher's aides school utilization rates. Efficient School Size Example

34. If the elementary school has excess capacity and increases from 200 to 300 students, $115 per student is saved from increased enrollment. $97 per student is saved from increased utilization rate. Total savings: $212 per student. If the middle school has excess capacity and increases from 600 to 800 students, $142 per student is saved from increased enrollment. $55 per student is saved from increased utilization rate. Total savings: $197 per student. Efficient School Size Example

35. Area of a Rectangle

36. Area on a graph

37. Area on a graph

38. Area on a graph

39. Area on a graph

40. Occurs if producing two or more products jointly lowers costs. Sources Single production process yields multiple products. Production yields unavoidable by-products which are inputs to other products. Uses formerly underutilized resources. Uses transferable know-how. Demand-related economies of scope decrease costs by providing a cluster of goods consumers use. Economies of Scope

41. As cumulative production increases, average cost declines. Sources: Learning by doing Production workers Management Quality control Design and engineering Different from economies of scale and economies of scope. Learning Curve

42. Learning Curve Graphs

43. Learning Curve Graphs

44. Chemical processing study shows Average costs decrease 11% when plant size doubles. Average costs decrease 20 – 30% when cumulative output doubles. Strategies based on learning curve consider profits over multiple years because cumulative output matters. Base profit calculations on multiple years of output. High volume producer has greatest cost advantage. Accelerate sales with forward pricing, marketing, advertising, etc. Careful: profit, not market share is the goal. Strategic Implications of the Learning Curve

45. MC = MR holds Use demand curve to set price. Fallacy: exploit all economies of scale Equivalent to MC = AC Wrong because the optimal level of output depends on demand as well as costs. Fallacy: to increase profits, raise price. Ignores the relationship between demand and costs. Again, optimal level of output depends on demand as well as costs. Single Product Decisions

46. Single Product Graph

47. Single Product Graph

48. Single Product Graph

49. Single Product Graph

50. Single Product Graph

51. Single Product Graph

52. Single Product Graph

53. Single Product Graph

54. Single Product Graph

55. Single Product Graph

56. Single Product Graph

57. Single Product Graph

58. Single Product Graph

59. Single Product Graph

60. Single Product Graph

61. Single Product Graph

62. In the long-run a firm operates only if economic profits are positive. Short-run considerations are different. In the short-run, a company is operating where MC = MR and pricing according to the demand curve, but ? < 0. TC > TR or AC > P Key idea: Fixed costs will be incurred whether the firm operates or shuts down. If company shuts down, its losses will be FC. Shut-down rule: In the short-run, operate so long as P > AVC. Set MC = MR and price along demand curve. Shut-Down Decision

63. Consider profits ? = TR – TC TR = P Q TC = VC + FC VC = (AVC) (Q) ? = TR – (VC + FC) ? = (TR – VC) – FC ? = P Q – (AVC) (Q) – FC ? = (P – AVC) Q – FC If P > AVC, then operating covers some of FC. Losses will be less than FC. Shut-Down Decision

64. Shut-Down Graph

65. Shut-Down Graph

66. Company pursues economies of scope and produces two products, 1 and 2. Each product has its own variable costs. Products share fixed costs. Define terms VC1 = variable costs from product 1 VC2 = variable costs from product 2 TR1 = revenue from product 1 TR2 = revenues from product 2 TC = FC + VC1 + VC2 TR = TR1 + TR2 Multiple Products

67. ? = TR – TC ? = TR1 + TR2 – (F + VC1 + VC2) ? = (TR1 – VC1) + (TR2 – VC2) – FC The multi-product company operates according to two rules: In the short-run, continue to produce each good so long as it makes a positive contribution to fixed costs. TR1 > VC1 AND TR2 > VC2 OR P1 > AVC1 AND P2 > AVC2 In the long-run, continue to operate so long as total profit is positive. Multiple Products