1. 1 Chapter 8: Cost Curves A firm aims to MAXIMIZE PROFITS In order to do this, one must understand how to MINIMIZE COSTS Therefore understanding of cost curves is essential to maximizing profits

2. 2 Chapter 8: Costs Curves In this chapter we will cover: 8.1 Long Run Cost Curves 8.1.1 Total Cost 8.1.2 Marginal Cost and Average Cost 8.2 Economies of Scale 8.3 Short Run Cost Curves 8.3.1 Total Cost, Variable Cost, Fixed Cost 8.3.2 Marginal Cost and Average Cost 8.4 Economies of Scope 8.5 Economies of Experience

3. 3 8.1 Long Run Cost Curves In the long run, a firm’s costs equal zero when zero production is undertaken As production (Q) increases, the firm must use more inputs, thus increasing its cost By minimizing costs, a firm’s long run cost curve is as follows:

4. 4 Q (units per year) L (labor services per year) K TC ($/yr) 0 0 LR Total Cost Curve Q0Q0 Q1Q1 TC 0 =wL 0 +rK 0 L0L0 L1L1 K0K0 K1K1 Q0Q0 Q1Q1 TC = TC 1 TC = TC 0 TC 1 =wL 1 +rK 1

5. 5 An increase in the price of only 1 input will cause a firm to change its optimal choice of inputs However, the increase in input costs will always cause a firm’s costs to increase: -(This is only not true in the case of perfect substitutes when the productivity per dollar of each substitute is originally equal)

6. 6 L K Q0Q0 0 B A TC 0 /r TC 1 /r Slope=w 1 /r Slope=w 2 /r C2C2 C1C1 C3C3 C 1 : Original isocost curve (TC = $200) C 2 : Isocost curve after Price change (TC = $200) C 3 : Isocost curve after Price change (TC = $300)

7. 7 Q (units/yr) TC ($/yr) TC(Q) old TC(Q) new Change in Input Prices -> A Shift in the Total Cost Curve Q0Q0 300 200

8. 8 Let Q=2(LK) 1/2 MRTS=K/L, W=5, R=20, Q=40 What occurs to costs when rent falls to 5? Initially: MRTS=W/R K/L=5/20 4K=L Q=2(LK) 1/2 40=2(4KK) 1/2 40=4K 10=K 40=L

9. 9 Let Q=2(LK) 1/2 MRTS=K/L, W=5, R=20, Q=40 What occurs to costs when rent falls to 5? After Price Change: MRTS=W/R K/L=5/5 L=K Q=2(LK) 1/2 40=2(LL) 1/2 40=2L 20=L 20=K

10. 10 What occurs when rent falls to 5? Initial: L=40, K=10 Final: L=K=20 W=5, R=20, Q=40 Initial: TC=wL+rK TC=5(40)+20(10) TC=400 Final:TC=5(20)+5(20) TC=200 Due to the fall in rent, total cost falls by $200.

11. 11 Q (units/yr) TC ($/yr) TC(Q) final TC(Q) initial Change in Rent 40 400 200

12. 12 To calculate total cost, simply substitute labour and capital demand into your cost expression: Q= 50L 1/2 K 1/2 (From Chapter 7, slide 38:) L*(Q,w,r) = (Q 0 /50)(r/w) 1/2 K*(Q,w,r) = (Q 0 /50)(w/r) 1/2 TC = wL +rK TC= w [(Q 0 /50)(r/w) 1/2 ] +r[(Q 0 /50)(w/r) 1/2 ] TC= [(Q 0 /50)(wr) 1/2 ] +[(Q 0 /50)(wr) 1/2 ] TC = 2Q 0 (wr) 1/2 /50

13. 13 Let Q= L 1/2 K 1/2, MP L /MP K =K/L, w=10, r=40. Calculate total cost. MRTS=w/r K/L=10/40 K=4L Q= L 1/2 K 1/2 = L 1/2 (4L) 1/2 Q= 2L L=Q/2

14. 14 Let Q= L 1/2 K 1/2, MRTS=K/L, w=10, r=40. Calculate total cost. K=4L L=K/4 L=Q/2 Q= L 1/2 K 1/2 Q= (K/4) 1/2 K 1/2 Q=1/2 K K=2Q TC = wL +rK TC = 10(Q/2) +40(2Q) TC=85Q

15. 15 When the price of all inputs change by the same (percentage) amount, the optimal input combination does not change The same combination of inputs are purchased at higher prices

16. 16 L (labor services/yr) K (capital services/yr) 0 A Q0Q0 C 1 =Isocost curve before ($200) and after ($220) a 10% increase in input prices C1C1

17. 17 Q (units/yr) TC ($/yr) TC(Q) old TC(Q) new Example: A Shift in the Total Cost Curve When Input Prices Rise 10% Q0Q0 220 200

18. 18 Definition: The long run average cost function is the long run total cost function divided by output, Q. That is, the LRAC function tells us the firm’s cost per unit of output…

19. 19 Definition: The long run marginal cost function is rate at which long run total cost changes with a change in output The (LR)MC curve is equal to the slope of the (LR)TC curve

20. 20 Q (units/yr) TC ($/yr) TC(Q) post Average vrs. Marginal Costs Q0Q0 TC 0 Slope=LRMC Slope=LRAC

21. 21  When marginal cost is less than average cost, average cost is decreasing in quantity. That is, if MC(Q) < AC(Q), AC(Q) decreases in Q. When marginal cost is greater than average cost, average cost is increasing in quantity. That is, if MC(Q) > AC(Q), AC(Q) increases in Q. When marginal cost equals average cost, average cost does not change with quantity. That is, if MC(Q) = AC(Q), AC(Q) is flat with respect to Q.

22. 22 Q (units/yr) AC, MC ($/yr) 0 MC AC AC at minimum when AC(Q)=MC(Q) “typical” shape of AC, MC

23. 23 If average cost decreases as output rises, all else equal, the cost function exhibits economies of scale. -large scale operations have an advantage If average cost increases as output rises, all else equal, the cost function exhibits diseconomies of scale. -small scale operations have an advantage

24. 24 Why Economies of scale? -Increasing Returns to Scale for Inputs -Specialization of Labour -Indivisible Inputs (ie: one factory can produce up to 1000 units, so increasing output up to 1000 decreases average costs for the factory)

25. 25 Why Diseconomies of scale? -Diminishing Returns from Inputs -Managerial Diseconomies -Growing in size requires a large expenditure on managers -ie: One genius cannot run more than 1 branch

26. 26 0Q (units/yr) AC ($/yr) Q* AC(Q) Typical Economies of Scale Economies of scale Diseconomies of scale Minimum Efficient Scale – smallest Quantity where LRAC curve reaches Its min.

27. 27 When the production function exhibits increasing returns to scale, the long run average cost function exhibits economies of scale so that AC(Q) decreases with Q, all else equal. When the production function exhibits decreasing returns to scale, the long run average cost function exhibits diseconomies of scale so that AC(Q) increases with Q, all else equal.

28. 28 When the production function exhibits constant returns to scale, the long run average cost function is flat: it neither increases nor decreases with output. Production Function => Returns to Scale Costs => Economies of Scale

29. 29 Example: Returns to Scale and Economies of Scale CRS IRS DRS Production Function Q = L Q = L 2 Q = L 1/2 Labor Demand L*=Q L*=Q 1/2 L*=Q 2 Total Cost Function TC=wQ wQ 1/2 wQ 2 Average Cost Function AC=w w/Q 1/2 wQ Economies of Scale none EOS DOS

30. 30 Economies of Scale can be measured using output elasticity of total cost; how cost changes when output changes

31. 31 Economies of Scale are also related to marginal cost and average cost

32. 32  If  TC,Q < 1, MC < AC, so AC must be decreasing in Q. Therefore, we have economies of scale.  If  TC,Q > 1, MC > AC, so AC must be increasing in Q. Therefore, we have diseconomies of scale.  If  TC,Q = 1, MC = AC, so AC is just flat with respect to Q.

33. 33 Let Cost=50+20Q 2 MC=40Q IF Q=1 or Q=2, determine economies of scale (Let Q be thousands of units)

34. 34 TC=50+20Q 2 MC=40Q AC=TC/Q=50/Q+20Q Initially: MC=40(1)=40 AC=50/1+20(1)=70 Elasticity=MC/AC=40/70 – Economies of Scale Finally: MC=40(2)=80 AC=50/2+20(2)=65 E=MC/AC=80/65 – Diseconomies of Scale

35. 35 8.3 Short-Run Cost Curves In the short run, at least 1 input is fixed (ie: (K=K*) Total fixed costs (TFC) are the costs associated with this fixed input (ie: rk) Total variable costs (TVC) are the costs associated with variable inputs (ie:wL) Short-run total costs are fixed costs plus variable costs: STC=TFC+TVC

36. 36 Q (units/yr) TC ($/yr) TVC(Q, K*) TFC rK* STC(Q, K*) rK* Short Run Total Cost, Total Variable Cost and Total Fixed Cost

37. 37 Short Run Costs Example: Minimize the cost to build 80 units if Q=2(KL) 1/2 and K=25. If r=10 and w=20, classify costs. Q=2(KL) 1/2 80=2(25L) 1/2 80=10(L) 1/2 8=(L) 1/2 64=L

38. 38 Short Run Costs Example: K*=25, L=16. If r=10 and w=20, classify costs. TFC=rK*=10(25)=250 TVC=wL=20(64)=1280 STC=TFC+TVC=1530

39. 39 The firm can minimize costs better in the long run because it is less constrained. Hence, the short run total cost curve lies above the long run total cost curve almost everywhere.

40. 40 L K TC 0 /w TC 1 /w TC 2 /w TC 2 /r TC 1 /r TC 0 /r Q0Q0 Long Run Expansion path 0 A C B Q1Q1 Q0Q0 K*K* Only at point A is short run minimized as well as long run Short Run Expansion path

41. 41 Q (units/yr) TC ($/yr) LRTC(Q) A STC(Q) rK *

42. 42 Definition: The short run average cost function is the short run total cost function divided by output, Q. That is, the SAC function tells us the firm’s cost per unit of output…

43. 43 Definition: The short run marginal cost function is rate at which short run total cost changes with a change in input The SMC curve is equal to the slope of the STC curve

44. 44 In the short run, 2 additional average costs exist: average variable costs (AVC) and average fixed costs (AFC)

45. 45

46. 46 To make an omelet, one must crack a fixed number of eggs (E) and add a variable number of other ingredients (O). Total costs for 10 omelets were $50. Each omelet’s average variable costs were $1.50. If eggs cost 50 cents, how many eggs in each omelet? AC=AVC+AFC TC/Q=AVC+AFC 50/10=$1.50+AFC $3.50=AFC

47. 47 To make an omelet, one must crack a fixed number of eggs (E) and add a variable number of other ingredients (O). Total costs for 10 omelets were $50. Each omelet’s average variable costs were $1.50. If eggs cost 50 cents, how many eggs in each omelet? $3.50=AFC $3.50=P E (E/Q) $3.50=0.5 (E/Q) 7=E/Q There were 7 eggs in each omelet.

48. 48 Q (units per year) $ Per Unit 0 AFC Average fixed cost is constantly decreasing, as fixed costs don’t rise with output.

49. 49 Q (units per year) $ Per Unit 0 AVC AFC Average variable cost generally decreases then increases due to economies of scale.

50. 50 Q (units per year) $ Per Unit 0 SAC AVC AFC SAC is the vertical sum of AVC and AFC Equal

51. 51 Q (units per year) $ Per Unit 0 SMC SAC AVC AFC SMC intersects SAC and AVC at their minimum points

52. 52 In the long run, a firm can adjust its capital to a level that is then fixed in the short run. The long run average cost curve (LRAC) therefore forms an “envelope” or boundary around the various short run average cost curves (SAC) corresponding to different capital levels.

53. 53 Q (units per year) $ per unit 0 AC(Q) SAC(Q,K 1 ) SAC(Q,K 2 ) SAC(Q,K 3 ) Q 1 Q 2 Q 3

54. 54 When a firm minimizes cost in the short run, given capital chosen in the long run, -AC=SAC (Point A, next slide) -MC=SMC (Point B, next slide) -SAC is not at its min (in general) (Point C, next slide) At the MES: -AC=SAC=MC=SMC and SAC is at a minimum (two slides hence)

55. 55 Q (units per year) $ per unit 0 AC(Q) SAC(Q,K 1 ) Q 1 Q 2 Q 3 MC(Q) SMC(Q,K 1 ) A B C

56. 56 Q (units per year) $ per unit 0 AC(Q) SAC(Q,K 2 ) Q 1 Q 2 Q 3 MC(Q) Example: Putting It All Together SMC(Q,K 2 ) D

57. 57 Often a firm produces more than one product, and often these products are related: -Pepsi Cola makes Pepsi and Diet Pepsi -HP makes Computers and Cameras -Denny’s Serves Breakfast and Dinner Often a firm benefits from economies of scope by producing goods that are related; they share common inputs (or good A is an input for good B). Efficiencies often exist in producing related products (ie: no shipping between plants).

58. 58 If a firm can produce 2 products at a lower total cost than 2 firms each producing their own product: TC(Q 1,Q 2 )<TC(Q 1,0)+TC(0,Q 2 ) That firm experiences economies of scope.

59. 59 If the cities maintains local roads, it costs are $15 million a year. If a private firm covers park maintenance, it costs are $12 million a year. If the city does both, it costs $25 million a year. TC(Q 1,Q 2 )=$25 million TC(Q 1,0)+TC(0,Q 2 )=$15 million + $12 million TC(Q 1,0)+TC(0,Q 2 )=$27 million TC(Q 1,Q 2 )<TC(Q 1,0)+TC(0,Q 2 ) Economies of scope exist.

60. 60 Often with practice a firm “gets better” at producing a given output; it cuts costs by being able to produce the good faster and with fewer defects. Ie: The first time you worked on elasticities, each question took you 10 minutes and 10% were wrong. By the end of the course you’ll be able to calculate elasticities in 4 minutes with only 5% error (for example).

61. 61 Economies of experience are efficiencies (cost advantages) resulting from accumulated experience (learning-by-doing). The experience curve shows the relationship between average variable cost and cumulative production volume. -As more is produced (more experience is gained), average cost decreases.

62. 62 AVC Eventually the curve Flattens out The Experience Curve Cumulative Output

63. 63 Economies of experience occur once, while economies of scale are ongoing. A large producer benefiting from economies of scale will increase average costs by decreasing production. A large producer benefiting from economies of experience may safely decrease production

64. 64 Chapter 8 Key Concepts  Long-Run Costs:  TC=wL+rK (if labor and capital are the only inputs  AC=TC/Q  MC=∆TC/ ∆ Q  Economies of scale summarize how average cost changes as Q increases  Economies of scale = AC decreases as Q increases  Diseconomies of scale = AC increases as Q increases

65. 65 Chapter 8 Key Concepts  Short-Run Costs  TFC=All costs of the FIXED input  TVC=All total costs of the VARIABLE input  STC=TFC+TVC  SAC=STC/Q  SMC=∆STC/ ∆Q  AFC=TFC/Q  AVC=TVC/Q  SAC=AFC+AVC

66. 66 Chapter 8 Key Concepts  If one firm has lower costs producing two goods than two firms producing the goods individually, that firm enjoys ECONOMIES OF SCOPE  If AC decreases as cumulative output increases, a firm enjoys ECONOMIES OF EXPERIENCE  This effect decreases over time  Calculators are important in Econ 281