Chapter 7 The Cost of Production

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

Chapter 7Slide 3 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

Chapter 7Slide 4 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?

Chapter 7Slide 5 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?

Chapter 7Slide 6 Sunk Cost Expenditure that has been made and cannot be recovered Should not influence a firm’s decisions. Measuring Cost: Which Costs Matter?

Chapter 7Slide 7 An Example A firm pays $500,000 for an option to buy a building. The cost of the building is $5 million or a total of $5.5 million. The firm finds another building for $5.25 million. Which building should the firm buy? Measuring Cost: Which Costs Matter?

Chapter 7Slide 8 Choosing the Location for a New Law School Building Northwestern University Law School 1) Current location in downtown Chicago 2) Alternative location in Evanston with the main campus

Chapter 7Slide 9 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) Choosing the Location for a New Law School Building

Chapter 7Slide 10 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” Choosing the Location for a New Law School Building

Chapter 7Slide 11 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

Chapter 7Slide 12 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

Chapter 7Slide 13 Fixed Cost Cost paid by a firm that is in business regardless of the level of output Sunk Cost Cost that has been incurred and cannot be recovered Measuring Cost: Which Costs Matter?

Chapter 7Slide 14 Personal Computers: most costs are variable Components, labor Software: most costs are sunk Cost of developing the software Measuring Cost: Which Costs Matter?

Chapter 7Slide 15 Pizza Largest cost component is fixed Measuring Cost: Which Costs Matter?

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

Chapter 7Slide 17 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.

Chapter 7Slide 18 Cost in the Short Run For Example: Assume the wage rate (w) is fixed relative to the number of workers hired. Then:

Chapter 7Slide 19 Cost in the Short Run Continuing:

Chapter 7Slide 20 Cost in the Short Run Continuing:

Chapter 7Slide 21 Cost in the Short Run In conclusion: …and a low marginal product (MP) leads to a high marginal cost (MC) and vise versa.

Chapter 7Slide 22 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

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

Chapter 7Slide 24 Cost Curves for a Firm Output Cost ($ per year) 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

Chapter 7Slide 25 Cost Curves for a Firm Output (units/yr.) Cost ($ per unit) MC ATC AVC AFC

Chapter 7Slide 26 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 P FC VC A TC

Chapter 7Slide 27 Cost in the Long Run User Cost of Capital = Economic Depreciation + (Interest Rate)(Value of Capital) The User Cost of Capital

Chapter 7Slide 28 Cost in the Long Run Example Delta buys a Boeing 737 for $150 million with an expected life of 30 years  Annual economic depreciation = $150 million/30 = $5 million  Interest rate = 10% The User Cost of Capital

Chapter 7Slide 29 Cost in the Long Run Example User Cost of Capital = $5 million + (.10)($150 million – depreciation)  Year 1 = $5 million + (.10)($150 million) = $20 million  Year 10 = $5 million + (.10)($100 million) = $15 million The User Cost of Capital

Chapter 7Slide 30 Cost in the Long Run Rate per dollar of capital r = Depreciation Rate + Interest Rate The User Cost of Capital

Chapter 7Slide 31 Cost in the Long Run Airline Example Depreciation Rate = 1/30 = 3.33%/yr Rate of Return = 10%/yr User Cost of Capital r = = 13.33%/yr The User Cost of Capital

Chapter 7Slide 32 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

Chapter 7Slide 33 Cost in the Long Run Question If capital was rented, would it change the value of r ? The User Cost of Capital The Cost Minimizing Input Choice

Chapter 7Slide 34 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

Chapter 7Slide 35 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

Chapter 7Slide 36 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 cost C 0. C0C0 C1C1 C2C2 C O C 1 C 2 are three isocost lines A K1K1 L1L1 K3K3 L3L3 K2K2 L2L2

Chapter 7Slide 37 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/L). Labor per year Capital per year

Chapter 7Slide 38 Cost in the Long Run Isoquants and Isocosts and the Production Function

Chapter 7Slide 39 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.

Chapter 7Slide 40 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?

Chapter 7Slide 41 The Effect of Effluent Fees on Firms’ Input Choices Firms that have a by-product to production produce an effluent. An effluent fee is a per-unit fee that firms must pay for the effluent that they emit. How would a producer respond to an effluent fee on production?

Chapter 7Slide 42 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. The Effect of Effluent Fees on Firms’ Input Choices

Chapter 7Slide 43 The Cost-Minimizing Response to an Effluent Fee Waste Water (gal./month) Capital (machine hours per month) Output of 2,000 Tons of Steel per Month A 10,00018,00020, ,000 Slope of isocost = -10/40 = ,000 1,000 4,000 3,000 5,000

Chapter 7Slide 44 The Cost-Minimizing Response to an Effluent Fee Output of 2,000 Tons of Steel per Month 2,000 1,000 4,000 3,000 5,000 10,00018,00020, ,000 Capital (machine hours per month) E 5,000 3,500 Slope of isocost = -20/40 = B Following the imposition of the effluent fee of $10/gallon the slope of the isocost changes reflecting the higher cost of water to capital so now combination B is selected. A 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. C F Waste Water (gal./month)

Chapter 7Slide 45 Observations: The more easily factors can be substituted, the more effective the fee is in reducing the effluent. The greater the degree of substitution, the less the firm will have to pay (for example: $50,000 with combination B instead of $100,000 with combination A) The Effect of Effluent Fees on Firms’ Input Choices

Chapter 7Slide 46 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 A $2000 Isocost Line 200 Unit Isoquant B $3000 Isocost Line 300 Unit Isoquant C

Chapter 7Slide 47 A Firm’s Long-Run Total Cost Curve Output, Units/yr Cost per Year Long-Run Total Cost D E F

Chapter 7Slide 48 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)?

Chapter 7Slide 49 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

Chapter 7Slide 50 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

Chapter 7Slide 51 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

Chapter 7Slide 52 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

Chapter 7Slide 53 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

Chapter 7Slide 54 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

Chapter 7Slide 55 Long-Run Average and Marginal Cost Output Cost ($ per unit of output LAC LMC A

Chapter 7Slide 56 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

Chapter 7Slide 57 Measuring Economies of Scale E c = percent change in cost from a 1% increase in output Long-Run Versus Short-Run Cost Curves

Chapter 7Slide 58 Measuring Economies of Scale Long-Run Versus Short-Run Cost Curves

Chapter 7Slide 59 Therefore, the following is true: E C < 1: MC < AC  economies of scale E C = 1: MC = AC  constant economies of scale E C > 1: MC > AC  diseconomies of scale Long-Run Versus Short-Run Cost Curves

Chapter 7Slide 60 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

Chapter 7Slide 61 Long-Run Cost with Constant Returns to Scale Output Cost ($ per unit of output) Q3Q3 SAC 3 SMC 3 Q2Q2 SAC 2 SMC 2 Q1Q1 SAC 1 SMC 1 LAC = LMC With many plant sizes with minimum SAC = $10 the LAC = LMC and is a straight line $10

Chapter 7Slide 62 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

Chapter 7Slide 63 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? Long-Run Cost with Constant Returns to Scale