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Chapter 7 The Cost of Production. Topics to be Discussed n Measuring Cost: Which Costs Matter? n Costs in the Short Run n Cost in the Long Run n Long-Run.

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Presentation on theme: "Chapter 7 The Cost of Production. Topics to be Discussed n Measuring Cost: Which Costs Matter? n Costs in the Short Run n Cost in the Long Run n Long-Run."— Presentation transcript:

1 Chapter 7 The Cost of Production

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

3 Topics to be Discussed n Production with Two Outputs--Economies of Scope n Dynamic Changes in Costs--The Learning Curve n Estimating and Predicting Cost

4 Introduction n The production function measures the relationship between input and output. n Given the production technology, managers must choose how to produce.

5 Introduction n To determine the optimal level of output and the input combinations, we must convert from the unit measurements of the production function to dollar measurements or costs.

6 Measuring Cost: Which Cost Matter? n Accounting Cost Consider only explicit cost, the out of pocket cost for such items as wages, salaries, materials, and property rentals

7 Measuring Cost: Which Cost Matter? n Economic Cost Considers explicit and opportunity cost. – Opportunity cost is the cost associated with opportunities that are foregone by not putting resources in their highest valued use. n Sunk Cost An expenditure that has been made and cannot be recovered--they should not influence a firm’s decisions.

8 Example: Choosing the Location for a New Law School Building n Northwestern University Law School 1) Current location in downtown Chicago 2) Alternative location in Evanston with the main campus

9 Example: Choosing the Location for a New Law School Building n Northwestern University Law School 3) Choosing a Site – Land owned in Chicago – Must purchase land in Evanston – Chicago location might appear cheaper without considering the opportunity cost of the downtown land (i.e. what it could be sold for)

10 Example: Choosing the Location for a New Law School Building n Northwestern University Law School 3) Choosing a Site – Chicago location chosen--very costly – Justified only if there is some intrinsic values associated with being in Chicago – If not, it was an inefficient decision if it was based on the assumption that the downtown land was “free”

11 Cost in the Short Run n Total output is a function of variable inputs and fixed inputs. n 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

12 Cost in the Short Run n Fixed costs do not change with changes in output n Variable costs increase as output increases.

13 A Firm’s Short-Run Costs ($) Rate ofFixedVariableTotalMarginalAverageAverageAverage OutputCostCostCostCostFixedVariableTotal (FC)(VC)(TC)(MC)CostCostCost (AFC)(AVC)(ATC)

14 Cost in the Short Run n 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:

15 Cost in the Short Run n 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:

16 Cost in the Short Run n 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.

17 Cost in the Short Run n 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.

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

19 Cost in the Short Run n Continuing:

20 Cost in the Short Run n Continuing:

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

22 Cost in the Short Run n 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

23 A Firm’s Short-Run Costs ($) Rate ofFixedVariableTotalMarginalAverageAverageAverage OutputCostCostCostCostFixedVariableTotal (FC)(VC)(TC)(MC)CostCostCost (AFC)(AVC)(ATC)

24 Cost in the Short Run n AVC and the Production Function

25 Cost in the Short Run n AVC and the Production Function

26 Cost in the Short Run n Observations If a firm is experiencing increasing returns, AP is increasing and AVC will decrease. If a firms is experiencing decreasing returns, AP is decreasing and AVC will increase.

27 Cost in the Short Run n Summary The production function (MP & AP) shows the relationship between inputs and output. The cost measurements show the impact of the production function in dollar terms.

28 Cost Curves for a Firm Output (units per year) Price ($ per year)

29 Cost Curves for a Firm Output (units per year) Price ($ per year) FCFC Fixed costs are the same at all levels of output.

30 Cost Curves for a Firm Output (units per year) Price ($ per year) FCFC Variable cost increases with production and the rate varies with increasing & decreasing returns. VC

31 Cost Curves for a Firm Output (units per year) Price ($ per year) FCFC VC Total cost is the vertical sum of FC and VC. TC

32 Cost Curves for a Firm Output (units per year) Price ($ per year) FCFC VC A TC

33 Cost Curves for a Firm Output (units per year) Price ($ per year) FCFC VC A TC B

34 Cost Curves for a Firm Output (units per year) Price ($ per unit)

35 Cost Curves for a Firm Output (units per year) Price ($ per unit) AFC Average fixed cost fall continuously

36 Cost Curves for a Firm Output (units per year) Price ($ per unit) AFC Average variable cost decreases initially then increases. AVC

37 Cost Curves for a Firm Output (units per year) Price ($ per unit) AFC AVC ATC Average total cost decreases initially then increases.

38 Cost Curves for a Firm Marginal cost decreases initially then increases. Output (units per year) Price ($ per unit) AFC AVC ATC MC

39 Cost Curves for a Firm n 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 P FCFC VC A TC B

40 Cost Curves for a Firm n The ray drawn from the origin to the tangent of the total cost curve: The slope of a tangent equals the slope of the point. ATC at 8 units = MC Output = 8 units. Output P FCFC VC TC A B

41 Cost Curves for a Firm n Unit Costs AFC falls continuously When MC < AVC or MC < ATC, AVC & ATC decrease When MC > AVC or MC > ATC, AVC & ATC increase Output P AFC AVC ATC MC

42 Cost Curves for a Firm n 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 P AFC AVC ATC MC

43 Cost in the Long Run n Choosing Inputs Assumptions – Two Inputs: Labor ( L ) & capital ( K ) – Wage rate for labor (w) and rental rate for capital (r) are determined in competitive markets

44 Cost in the Long Run n Choosing Inputs A Decision Model – C = wL + rK – Isocost: A line showing all combinations of L & K that can be purchased for the same cost

45 Cost in the Long Run n Choosing Inputs 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.

46 Choosing Inputs n We will address how to minimize cost for a given level of output. We will do so by combining isocosts with isoquants

47 Producing a Given Output at Minimum Cost Labor per year Capital per year

48 Producing a Given Output at Minimum Cost Labor per year Capital per year C0C0 C O C 1 C 2 are three isocost lines

49 Producing a Given Output at Minimum Cost Labor per year Capital per year C0C0 C1C1 C O C 1 C 2 are three isocost lines

50 Producing a Given Output at Minimum Cost Labor per year Capital per year C O C 1 C 2 are three isocost lines C0C0 C1C1 C2C2

51 Producing a Given Output at Minimum Cost Labor per year Capital per year Q 1 is an isoquant for output Q 1. Isocost curve C 0 shows not combination of K and L can produce Q 1 at this cost level. C0C0 C1C1 C2C2 Q1Q1

52 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. C0C0 C1C1 C2C2 K1K1 L1L1 K3K3 L3L3 K2K2 L2L2 A Q1Q1

53 Producing a Given Output at Minimum Cost Labor per year Capital per year Isocost C 1 shows quantity Q 1 can be produced with combination K 1 L 1.. This is the low cost combination because it is tangent to Q 1. C0C0 C1C1 C2C2 K1K1 L1L1 A Q1Q1

54 Input Substitution When an Input Price Change Labor per year Capital per year C1C1 K1K1 L1L1 If the price of labor changes, the isocost curve becomes steeper due to the change in the slope -(w/L). A Q1Q1

55 Input Substitution When an Input Price Change Labor per year Capital per year C1C1 K1K1 L1L1 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 C2C2 A B Q1Q1

56 Cost in the Long Run n Isoquants and Isocosts and the Production Function

57 Cost in the Long Run n 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.

58 Cost in the Long Run n Question: If w = $10, r = $2, and MP L = MP K, which input would the producer use more of? Why?

59 Example: The Effect of Effluent Fees on Firms’ Input Choices n Firms that have a by-product to production produce an effluent. n An effluent fee is a per-unit fee that firms must pay for the effluent that they emit. n How would a producer respond to an effluent fee on production?

60 Example: The Effect of Effluent Fees on Firms’ Input Choices n The Scenario: Steel Producer 1)Located on a river: Low cost transportation and emission disposal (effluent). 2) EPA imposes a per unit effluent fee to reduce the environmentally harmful effluent.

61 Example: The Effect of Effluent Fees on Firms’ Input Choices n The Scenario: Steel Producer 3)How should the firm respond?

62 The Cost-Minimizing Response to an Effluent Fee Waste Water (gallons per month) Capital (machine hours per month) C Output of 2,000 Tons of Steel per Month A 10,00018,00020, ,000 Prior to regulation the firm chooses to produce an output using 10,000 gallons of water and 2,000 machine-hours of capital at A. Slope of isocost = -10/40 = ,000 1,000 4,000 3,000 5,000

63 The Cost-Minimizing Response to an Effluent Fee Waste Water (gallons per month) Capital (machine hours per month) C Output of 2,000 Tons of Steel per Month 2,000 A 1,000 4,000 3,000 5,000 10,00018,00020, ,000 E 3,500 Following the imposition of the effluent fee of $10/gallon the slope of the isocost changes which the higher cost of water to capital so now combination B is selected. Slope of isocost = -20/40 = B

64 Example: The Effect of Effluent Fees on Firms’ Input Choices n Observations: The more easily factors can be substituted, the more effective the fee is in reducing the effluent. The greater the degree of substitutes, the less the firm will have to pay (for example: $50,000 with combination B instead of $100,000 with combination A)

65 Long-Run Versus Short-Run Cost Curves n 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.

66 A Firm’s Expansion Path Labor per year Capital per year The first step in drawing a firm’s expansion path is to calculate the cost-minimizing input quantities for each output level and resulting cost.

67 A Firm’s Expansion Path Next, locate the tangency of the isocost line with each isoquant. Labor per year Capital per year A

68 A Firm’s Expansion Path Next, locate the tangency of the isocost line with each isoquant. Labor per year Capital per year A B

69 A Firm’s Expansion Path Next, locate the tangency of the isocost line with each isoquant. Labor per year Capital per year A B C

70 A Firm’s Expansion Path Next, locate the tangency of the isocost line with each isoquant. Labor per year Capital per year A B C D

71 A Firm’s Expansion Path Next, locate the tangency of the isocost line with each isoquant. Labor per year Capital per year A B C D E

72 A Firm’s Expansion Path Labor per year Capital per year A B C D E 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.

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

74 The Inflexibility of Short-Run Production Labor per year Capital per year Q1Q1 L1L1 B K1K1 Begin with Q 1 and isocost AB which yields K 1 L 1.

75 The Inflexibility of Short-Run Production Labor per year Q1Q1 L1L1 Q2Q2 A B P K1K1 Assume K is fixed (short-run) and output is increased to Q 2. Combination K 1 L 3 would have to be used on isocost EF. Capital per year F E L3L3

76 The Inflexibility of Short-Run Production Labor per year Capital per year Q1Q1 K2K2 L1L1 Q2Q2 A BL2L2 DF C E K1K1 If K is flexible (long-run), isocost line CD is used yielding combination K 2 L 2. CD is a lower cost level than EF. In the long-run, the firm substitutes cheaper K for L.

77 The Inflexibility of Short-Run Production Labor per year Capital per year Q1Q1 K2K2 L1L1 Expansion Path Q2Q2 A BL2L2 DF C E K1K1 The long-run expansion path is drawn as before..

78 Long-Run Versus Short-Run Cost Curves n 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.

79 Long-Run Versus Short-Run Cost Curves n 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.

80 Long-Run Versus Short-Run Cost Curves n 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.

81 Long-Run Versus Short-Run Cost Curves n Long-Run Average Cost (LAC) In the long-run: – Firms experience increasing and decreasing returns to scale and therefor long-run average cost is “U” shaped.

82 Long-Run Versus Short-Run Cost Curves n 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

83 Long-Run Average and Marginal Cost Output Cost ($ per unit of output

84 Long-Run Average and Marginal Cost Output Cost ($ per unit of output LMC

85 Long-Run Average and Marginal Cost Output Cost ($ per unit of output LMC LAC

86 Long-Run Versus Short-Run Cost Curves n Question What is the relationship between long-run average cost and long-run marginal cost when long-run average cost is constant?

87 Long-Run Versus Short-Run Cost Curves n 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.

88 Long-Run Versus Short-Run Cost Curves n Measuring Economies of Scale

89 Long-Run Versus Short-Run Cost Curves n Measuring Economies of Scale

90 Long-Run Versus Short-Run Cost Curves n Therefore, the following is true: E C < 1: MC < AC – Average cost indicate decreasing economies of scale E C = 1: MC = AC – Average cost indicate constant economies of scale E C > 1: MC > AC – Average cost indicate increasing diseconomies of scale

91 Long-Run Versus Short-Run Cost Curves n The Relationship Between Short-Run and Long-Run Cost We will use short and long-run cost to determine the optimal plant size

92 Long-Run Cost with Constant Returns to Scale Output Cost ($ per unit of output Known: The SAC for three plant sizes with constant returns to scale.

93 Long-Run Cost with Constant Returns to Scale Output Cost ($ per unit of output Q1Q1 SAC 1 SMC 1

94 Long-Run Cost with Constant Returns to Scale Output Cost ($ per unit of output Q1Q1 Q2Q2 SAC 1 SAC 2 SMC 1 SMC 2

95 Long-Run Cost with Constant Returns to Scale Output Cost ($ per unit of output Q1Q1 Q2Q2 Q3Q3 SAC 1 SAC 2 SAC 3 SMC 1 SMC 2 SMC 3

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

97 Long-Run Cost with Constant Returns to Scale n 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. n Question What would happen to average cost if an output level other than that shown is chosen?

98 Long-Run Cost with Economies and Diseconomies of Scale Output Cost ($ per unit of output Known: Three plant sizes with economies and diseconomies of scale.

99 Long-Run Cost with Economies and Diseconomies of Scale Output Cost ($ per unit of output SAC 1 SAC 2 SAC 3 SMC 1 SMC 2 SMC 3

100 Long-Run Cost with Economies and Diseconomies of Scale Output Cost ($ per unit of output LAC SAC 1 SAC 2 SAC 3 SMC 1 SMC 2 SMC 3

101 Long-Run Cost with Economies and Diseconomies of Scale Output Cost ($ per unit of output LAC SAC 1 SAC 2 SAC 3 SMC 1 SMC 2 SMC 3 LMC

102 Long-Run Cost with Economies and Diseconomies of Scale Output Cost ($ per unit of output LAC SAC 1 SAC 2 SAC 3 SMC 1 SMC 2 SMC 3 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

103 Long-Run Versus Short-Run Cost Curves n 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.

104 Long-Run Cost with Economies and Diseconomies of Scale n Observations The LAC does not include the minimum points of small and large size plants? Why not? LMC is not the envelope of the short-run marginal cost. Why not?

105 Production with Two Outputs-- Economies of Scope n Examples: Chicken farm--poultry and eggs Automobile company--cars and trucks University--Teaching and research

106 Production with Two Outputs-- Economies of Scope n 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. n What are the advantages of joint production? Consider an automobile company producing cars and tractors

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

108 Production with Two Outputs-- Economies of Scope n Production: Firms must choose how much of each to produce. The alternative quantities can be illustrated using product transformation curves.

109 Product Transformation Curve Number of cars Number of tractors

110 Product Transformation Curve Number of cars Number of tractors O1O1 Each curve shows combinations of output with a given combination of L & K.

111 Product Transformation Curve Number of cars Number of tractors O1O1 O2O2 O 1 illustrates a low level of output. O 2 illustrates a higher level of output with two times as much labor and capital.

112 Production with Two Outputs-- Economies of Scope n Observations Product transformation curves are negatively sloped Constant returns exist in this example Since the production transformation curve is concave is joint production desirable?

113 Production with Two Outputs-- Economies of Scope n 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

114 Production with Two Outputs-- Economies of Scope n The degree of economies of scope measures the savings in cost 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

115 Production with Two Outputs-- Economies of Scope n Interpretation: If SC > 0 -- Economies of scope If SC < 0 -- Diseconomies of scope

116 Example: Economies of Scope in the Trucking Industry n Issues Truckload versus less than truck load Direct versus indirect routing Length of haul

117 Example: Economies of Scope in the Trucking Industry n Questions: Economies of Scale – Are large-scale, direct hauls cheaper and more profitable than individual hauls by small trucks? – Are there cost advantages from operating both direct and indirect hauls?

118 Example: Economies of Scope in the Trucking Industry n Empirical Findings An analysis of 105 trucking firms examined four distinct outputs. – Short hauls with partial loads – Intermediate hauls with partial loads – Long hauls with partial loads – Hauls with total loads

119 Example: Economies of Scope in the Trucking Industry n Empirical Findings Results – SC = for reasonably large firm – SC = for very large firms Interpretation – Combining partial loads at an intermediate location lowers cost management difficulties with very large firms.


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