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Chapter Seven Costs Chapter Seven Costs

Topics § Measuring Costs. § Short-Run Costs. § Long-Run Costs. § Lower Costs in Topics § Measuring Costs. § Short-Run Costs. § Long-Run Costs. § Lower Costs in the Long Run. § Cost of Producing Multiple Goods. © 2009 Pearson Addison-Wesley. All rights reserved. 2

Economic Cost § Economic cost or opportunity cost the value of the best alternative Economic Cost § Economic cost or opportunity cost the value of the best alternative use of a resource. w Explicit costs - firm’s direct, out-of-pocket payments for inputs to its production process during a given time period. , Workers’ wages, managers’ salaries, etc. and payments for materials. w Implicit costs – cost of use inputs that may not have an explicit price. value of the working time of the firm’s owner © 2009 Pearson Addison-Wesley. All rights reserved. 3

Capital Costs § Durable good- a product that is usable for years. § Sunk Capital Costs § Durable good- a product that is usable for years. § Sunk cost - an expenditure that cannot be recovered © 2009 Pearson Addison-Wesley. All rights reserved. 4

Short-Run Cost Measures § Fixed cost (F) - a production expense that does not Short-Run Cost Measures § Fixed cost (F) - a production expense that does not vary with output. § Variable cost (VC) - a production expense that changes with the quantity of output produced. § Cost (total cost, C) - the sum of a firm’s variable cost and fixed cost: C = VC + F © 2009 Pearson Addison-Wesley. All rights reserved. 5

Marginal Cost. § marginal cost (MC) - the amount by which a firm’s cost Marginal Cost. § marginal cost (MC) - the amount by which a firm’s cost changes if the firm produces one more unit of output. w And since only variable costs change with output: © 2009 Pearson Addison-Wesley. All rights reserved. 6

Average Costs. § average fixed cost (AFC) - the fixed cost divided by the Average Costs. § average fixed cost (AFC) - the fixed cost divided by the units of output produced: AFC = F/q. § average variable cost (AVC) - the variable cost divided by the units of output produced: AVC = VC/q. § average cost (AC) - the total cost divided by the units of output produced: AC = C/q AC = AFC + AVC. © 2009 Pearson Addison-Wesley. All rights reserved. 7

Table 7. 1 Variation of Short-Run Cost with Output © 2009 Pearson Addison-Wesley. All Table 7. 1 Variation of Short-Run Cost with Output © 2009 Pearson Addison-Wesley. All rights reserved. 8

400 Cost, $ Figure 7. 1 Short. Run Cost Curves (a) C VC 27 400 Cost, $ Figure 7. 1 Short. Run Cost Curves (a) C VC 27 A 216 1 20 1 B 120 48 0 F 2 4 6 8 Cost per unit, $ (b) 10 Quantity, q, Units per day 60 MC 28 27 a b 20 AC AVC 8 AFC 0 © 2009 Pearson Addison-Wesley. All rights reserved. 2 4 6 10 8 Quantity, q, Units per day 9

Cost per unit, $ Relationship between average and marginal cost curves 60 When MC Cost per unit, $ Relationship between average and marginal cost curves 60 When MC is lower than When MC is AC, AC is lower than decreasing… AVC, AVC is decreasing… and when MC is larger than is and when MCAC, AC than AVC, largeris increases AVC is increases 28 27 a b 20 8 0 2 MC 4 © 2009 Pearson Addison-Wesley. All rights reserved. 6 AC AVC …so MC = AC, at the lowest point of the AC curve! …so MC = AVC, at the lowest point of the AVC curve! 10 8 Quantity, q, Units per d ay 10

Figure 7. 2 Variable Cost and Total Product of Labor © 2009 Pearson Addison-Wesley. Figure 7. 2 Variable Cost and Total Product of Labor © 2009 Pearson Addison-Wesley. All rights reserved. 11

Shape of the Marginal Cost Curve MC = DVC/Dq. § But in the short Shape of the Marginal Cost Curve MC = DVC/Dq. § But in the short run, DVC = w (can you tell why? ) w Therefore, MC = w/Dq § The additional output created by every additional unit of labor is: Dq/ DL = MPL w Therefore, MC = w/ MPL © 2009 Pearson Addison-Wesley. All rights reserved. 12

Shape of the Average Cost Curves AVC = VC/q. w But in the short-run, Shape of the Average Cost Curves AVC = VC/q. w But in the short-run, with only labor as an input: AVC = VC/q = w. L/q w And since q/L = APL, then AVC = VC/q = w/APLL © 2009 Pearson Addison-Wesley. All rights reserved. 13

Application Short-Run Cost Curves for a Furniture Manufacturer © 2009 Pearson Addison-Wesley. All rights Application Short-Run Cost Curves for a Furniture Manufacturer © 2009 Pearson Addison-Wesley. All rights reserved. 14

Table 7. 2 Effect of a Specific Tax of $10 per Unit on Short-Run Table 7. 2 Effect of a Specific Tax of $10 per Unit on Short-Run Costs © 2009 Pearson Addison-Wesley. All rights reserved. 15

Costs per unit, $ Figure 7. 3 Effect of a Specific Tax on Cost Costs per unit, $ Figure 7. 3 Effect of a Specific Tax on Cost Curves 80 A $10. 00 tax shifts both the AVC and MC by exactly $10… MC a = MC b + 10 MC b $10 37 AC a = AC b + 10 $10 AC b 27 0 5 © 2009 Pearson Addison-Wesley. All rights reserved. 8 10 15 q, Units per day 16

Solved Problem 7. 1 § What is the effect of a lump-sum franchise tax Solved Problem 7. 1 § What is the effect of a lump-sum franchise tax on the quantity at which a firm’s after tax average cost curve reaches its minimum? (Assume that the firm’s before-tax average cost curve is U -shaped. ) © 2009 Pearson Addison-Wesley. All rights reserved. 17

Solved Problem 7. 1 © 2009 Pearson Addison-Wesley. All rights reserved. 18 Solved Problem 7. 1 © 2009 Pearson Addison-Wesley. All rights reserved. 18

Long-Run Costs § Fixed costs are avoidable in the long run. w in the Long-Run Costs § Fixed costs are avoidable in the long run. w in the long F = 0. w As a result, the long-run total cost equals: C = VC © 2009 Pearson Addison-Wesley. All rights reserved. 19

Input Choice § isocost line - all the combinations of inputs that require the Input Choice § isocost line - all the combinations of inputs that require the same (iso-) total expenditure (cost). § The firm’s total cost equation is: C = w. L + r. K. Capital Labor Costs © 2009 Pearson Addison-Wesley. All rights reserved. 20

Input Choice (Cont). § The firm’s total cost equation is: C = w. L Input Choice (Cont). § The firm’s total cost equation is: C = w. L + r. K. w We get the Isocost equation by setting fixing the costs at a particular level: C = w. L + r. K. w And then solving for K (variable along y-axis): K= © 2009 Pearson Addison-Wesley. All rights reserved. C r w L r 21

Table 7. 3 Bundles of Labor and Capital That Cost the Firm $100 © Table 7. 3 Bundles of Labor and Capital That Cost the Firm $100 © 2009 Pearson Addison-Wesley. All rights reserved. 22

K, Units of capital per year Figure 7. 4 A Family of Isocost Lines K, Units of capital per year Figure 7. 4 A Family of Isocost Lines For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant. 10 = $100 $10 e d 7. 5 5 2. 5 c DK = 2. 5 Isocost Equation C - w L K= r r Initial Values C = $100 w = $5 r = $10 Slope = -1/2 = w/r b DL = 5 $100 isocost a 5 10 15 $100 = 20 $5 L, Units of labor per year © 2009 Pearson Addison-Wesley. All rights reserved. 23

Figure 7. 4 A Family of Isocost Lines K, Units of capital per year Figure 7. 4 A Family of Isocost Lines K, Units of capital per year Isocost Equation 15 = $150 $10 10 = $100 $10 e C - w L K= r r An increase in C…. Initial Values C = $150 w = $5 r = $100 isocost $150 isocost a $100 = 20 $5 $150 = 30 $5 L, Units of labor per year © 2009 Pearson Addison-Wesley. All rights reserved. 24

Figure 7. 4 A Family of Isocost Lines K, Units of capital per year Figure 7. 4 A Family of Isocost Lines K, Units of capital per year Isocost Equation C - w L r r Initial Values C = $50 w = $5 r = $10 K= 15 = $150 $10 10 = $100 $10 5= $50 $10 A decrease in C…. e $50 isocost $100 isocost $150 isocost a $50 = 10 $5 $100 = 20 $5 $150 = 30 $5 L, Units of labor per year © 2009 Pearson Addison-Wesley. All rights reserved. 25

Combining Cost and Production Information. § The firm can choose any of three equivalent Combining Cost and Production Information. § The firm can choose any of three equivalent approaches to minimize its cost: w Lowest-isocost rule - pick the bundle of inputs where the lowest isocost line touches the isoquant. w Tangency rule - pick the bundle of inputs where the isoquant is tangent to the isocost line. w Last-dollar rule - pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input. © 2009 Pearson Addison-Wesley. All rights reserved. 26

K, Units of capital per hour Figure 7. 5 Cost Minimization q = 100 K, Units of capital per hour Figure 7. 5 Cost Minimization q = 100 isoquant $3, 000 isocost Which of these three Isocost would allow the firm to produce the 100 units of output at the lowest possible cost? $2, 000 isocost $1, 000 isocost 100 0 x 50 © 2009 Pearson Addison-Wesley. All rights reserved. Isocost Equation K= C - w L r r Isoquant Slope MPL = MRTS MPK Initial Values q = 100 C = $2, 000 w = $24 r = $8 L, Units of labor per hour 27

K, Units of capital per hour Figure 7. 5 Cost Minimization Isocost Equation q K, Units of capital per hour Figure 7. 5 Cost Minimization Isocost Equation q = 100 isoquant C - w L K= r r Isoquant Slope MPL = MRTS MPK $3, 000 isocost y 303 $2, 000 isocost $1, 000 isocost x 100 28 0 24 50 © 2009 Pearson Addison-Wesley. All rights reserved. Initial Values q = 100 C = $2, 000 w = $24 r = $8 z 116 L, Units of labor per hour 28

Cost Minimization § At the point of tangency, the slope of the isoquant equals Cost Minimization § At the point of tangency, the slope of the isoquant equals the slope of the isocost. Therefore, last-dollar rule: cost is minimized if inputs are chosen so that the last dollar spent on labor adds as much extra output as the last dollar spent on capital. © 2009 Pearson Addison-Wesley. All rights reserved. 29

K, Units of capital per hour Figure 7. 5 Cost Minimization MPL = 0. K, Units of capital per hour Figure 7. 5 Cost Minimization MPL = 0. 6 q/L MPK = 0. 4 q/K q = 100 isoquant $3, 000 isocost y 303 1. 2 MPL MPK 0. 4 = r = 24 = 8 = 0. 05 w $2, 000 isocost Spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital. $1, 000 isocost x 100 z 28 0 Initial Values q = 100 C = $2, 000 w = $24 r = $8 24 50 © 2009 Pearson Addison-Wesley. All rights reserved. 116 L, Units of labor per hour 30

K, Units of capital per hour Figure 7. 5 Cost Minimization MPL = 0. K, Units of capital per hour Figure 7. 5 Cost Minimization MPL = 0. 6 q/L MPK = 0. 4 q/K q = 100 isoquant $3, 000 isocost y 303 $2, 000 isocost $1, 000 isocost MPL = w MPK r = x 100 if So …theshifts one the firm dollar from capital to should shift labor, output falls by even more 0. 017 because there resources from iscapital to labor— less capital but also increases by 0. 1 which increases because there is the marginal more labor for a net product of capital gain of 0. 083 more and decreases output at the same the marginal cost…. of labor. product z 28 0 2. 5 24 = 0. 13 0. 02 8 = Initial Values q = 100 C = $2, 000 w = $24 r = $8 24 50 © 2009 Pearson Addison-Wesley. All rights reserved. 116 L, Units of labor per hour 31

Figure 7. 6 Change in Factor Price K, Units of capital per hour Minimizing Figure 7. 6 Change in Factor Price K, Units of capital per hour Minimizing Cost Rule q = 100 isoquant Original isocost, $2, 000 A decrease in w…. New isocost, $1, 032 100 x v 52 0 MPL MPK w = r Initial Values q = 100 C = $2, 000 w = $24 r = $8 w 2 = $8 C 2 = $1, 032 50 © 2009 Pearson Addison-Wesley. All rights reserved. 77 L, Workers per hour 32

Solved Problem 7. 3 § If it manufactures at home, a firm faces input Solved Problem 7. 3 § If it manufactures at home, a firm faces input prices for labor and capital of wˆ and rˆ and produces qˆ units of output using L ˆ units of labor and K ˆ units of capital. Abroad, the wage and cost of capital are half as much as at home. If the firm manufactures abroad, will it change the amount of labor and capital it uses to produce qˆ? What happens to its cost of producing qˆ? © 2009 Pearson Addison-Wesley. All rights reserved. 33

Solved Problem 7. 3 © 2009 Pearson Addison-Wesley. All rights reserved. 34 Solved Problem 7. 3 © 2009 Pearson Addison-Wesley. All rights reserved. 34

How Long-Run Cost Varies with Output § expansion path - the cost-minimizing combination of How Long-Run Cost Varies with Output § expansion path - the cost-minimizing combination of labor and capital for each output level © 2009 Pearson Addison-Wesley. All rights reserved. 35

K, Units of capital per hour Figure 7. 7(a) Expansion Path $4, 000 isocost K, Units of capital per hour Figure 7. 7(a) Expansion Path $4, 000 isocost $3, 000 isocost Expansion path $2, 000 isocost z 200 y 150 x 100 q = 200 Isoquant q = 150 Isoquant q = 100 Isoquant 0 50 © 2009 Pearson Addison-Wesley. All rights reserved. 75 100 L, Workers per hour 36

Figure 7. 7(b) Expansion Path and Long-Run Cost Curve (cont’d) © 2009 Pearson Addison-Wesley. Figure 7. 7(b) Expansion Path and Long-Run Cost Curve (cont’d) © 2009 Pearson Addison-Wesley. All rights reserved. 37

Solved Problem 7. 4 § What is the long-run cost function for a fixed-proportions Solved Problem 7. 4 § What is the long-run cost function for a fixed-proportions production function (Chapter 6) when it takes one unit of labor and one unit of capital to produce one unit of output? Describe the longrun cost curve. © 2009 Pearson Addison-Wesley. All rights reserved. 38

Figure 7. 8 Long. Run Cost Curves © 2009 Pearson Addison-Wesley. All rights reserved. Figure 7. 8 Long. Run Cost Curves © 2009 Pearson Addison-Wesley. All rights reserved. 39

Economies of Scale § economies of scale - property of a cost function whereby Economies of Scale § economies of scale - property of a cost function whereby the average cost of production falls as output expands. § diseconomies of scale - property of a cost function whereby the average cost of production rises when output increases. © 2009 Pearson Addison-Wesley. All rights reserved. 40

Table 7. 4 Returns to Scale and Long -Run Costs © 2009 Pearson Addison-Wesley. Table 7. 4 Returns to Scale and Long -Run Costs © 2009 Pearson Addison-Wesley. All rights reserved. 41

Table 7. 5 Shape of Average Cost Curves in Canadian Manufacturing © 2009 Pearson Table 7. 5 Shape of Average Cost Curves in Canadian Manufacturing © 2009 Pearson Addison-Wesley. All rights reserved. 42

Long-Run Average Cost § In its long-run planning, a firm chooses a plant size Long-Run Average Cost § In its long-run planning, a firm chooses a plant size and makes other investments so as to minimize its long-run cost on the basis of how many units it produces. w Once it chooses its plant size and equipment, these inputs are fixed in the short run. Thus, the firm’s long-run decision determines its short-run cost. © 2009 Pearson Addison-Wesley. All rights reserved. 43

Average cost, $ Figure 7. 9 Long-Run Average Cost as the Envelope of Short-Run Average cost, $ Figure 7. 9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves SRAC 3 SRAC 1 b 12 10 a SRAC 3 LRAC SRAC 2 d c e 0 q 1 © 2009 Pearson Addison-Wesley. All rights reserved. q 2 q, Output per day 44

Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines © 2009 Pearson Addison-Wesley. Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines © 2009 Pearson Addison-Wesley. All rights reserved. 45

Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines © 2009 Pearson Addison-Wesley. Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines © 2009 Pearson Addison-Wesley. All rights reserved. 46

Application Choosing an Ink-Jet or a Laser Printer © 2009 Pearson Addison-Wesley. All rights Application Choosing an Ink-Jet or a Laser Printer © 2009 Pearson Addison-Wesley. All rights reserved. 47

Figure 7. 10 Long-Run and Short-Run Expansion Paths © 2009 Pearson Addison-Wesley. All rights Figure 7. 10 Long-Run and Short-Run Expansion Paths © 2009 Pearson Addison-Wesley. All rights reserved. 48

How Learning by Doing Lowers Costs § learning by doing - the productive skills How Learning by Doing Lowers Costs § learning by doing - the productive skills and knowledge that workers and managers gain from experience © 2009 Pearson Addison-Wesley. All rights reserved. 49

Figure 7. 11 Learning by Doing © 2009 Pearson Addison-Wesley. All rights reserved. 50 Figure 7. 11 Learning by Doing © 2009 Pearson Addison-Wesley. All rights reserved. 50

Cost of Producing Multiple Goods § economies of scope - situation in which it Cost of Producing Multiple Goods § economies of scope - situation in which it is less expensive to produce goods jointly than separately. § production possibility frontier - the maximum amount of outputs that can be produced from a fixed amount of input © 2009 Pearson Addison-Wesley. All rights reserved. 51

Figure 7. 12 Joint Production © 2009 Pearson Addison-Wesley. All rights reserved. 52 Figure 7. 12 Joint Production © 2009 Pearson Addison-Wesley. All rights reserved. 52