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Chapter Seven Costs Slide 2 2009 Pearson Addison-Wesley. All rights reserved. 7-2 Topics Measuring Costs. Short-Run Costs. Long-Run Costs. Lower Costs in the Long Run. Cost of Producing Multiple Goods. Slide 3 2009 Pearson Addison-Wesley. All rights reserved. 7-3 Economic Cost Economic cost or opportunity cost - the value of the best alternative use of a resource. Explicit costs - firms 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. Implicit costs cost of use inputs that may not have an explicit price. value of the working time of the firms owner Slide 4 2009 Pearson Addison-Wesley. All rights reserved. 7-4 Capital Costs Durable good- a product that is usable for years. Sunk cost - an expenditure that cannot be recovered Slide 5 2009 Pearson Addison-Wesley. All rights reserved. 7-5 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 firms variable cost and fixed cost: C = VC + F Slide 6 2009 Pearson Addison-Wesley. All rights reserved. 7-6 Marginal Cost. marginal cost (MC) - the amount by which a firms cost changes if the firm produces one more unit of output. And since only variable costs change with output: Slide 7 2009 Pearson Addison-Wesley. All rights reserved. 7-7 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. Slide 8 2009 Pearson Addison-Wesley. All rights reserved. 7-8 Table 7.1 Variation of Short-Run Cost with Output Slide 9 2009 Pearson Addison-Wesley. All rights reserved. 7-9 Figure 7.1 Short- Run Cost Curves 120 216 400 48 0610 428 Quantity,q, Units per day Quantity,q, Units per day 6 b a B A 428 C F 1 1 27 20 VC MC AC AVC AFC Cost, $ Cost per unit, $ (a) (b) 60 28 27 20 8 0 Slide 10 2009 Pearson Addison-Wesley. All rights reserved. 7-10 Relationship between average and marginal cost curves 10 Quantity,q, Units per day 6 b a 428 MC AC AVC Cost per unit, $ 60 28 27 20 8 0 When MC is lower than AVC, AVC is decreasing and when MC is larger than AVC, AVC is increases so MC = AVC, at the lowest point of the AVC curve! When MC is lower than AC, AC is decreasing and when MC is larger than AC, AC is increases so MC = AC, at the lowest point of the AC curve! Slide 11 2009 Pearson Addison-Wesley. All rights reserved. 7-11 Figure 7.2 Variable Cost and Total Product of Labor Slide 12 2009 Pearson Addison-Wesley. All rights reserved. 7-12 Shape of the Marginal Cost Curve MC = VC / q. But in the short run, VC = w (can you tell why?) Therefore, MC = w / q The additional output created by every additional unit of labor is: q/ L = MP L Therefore, MC = w / MP L Slide 13 2009 Pearson Addison-Wesley. All rights reserved. 7-13 Shape of the Average Cost Curves AVC = VC/q. But in the short-run, with only labor as an input: AVC = VC/q = wL/q And since q/L = AP L, then AVC = VC/q = w/APL L Slide 14 2009 Pearson Addison-Wesley. All rights reserved. 7-14 Application Short-Run Cost Curves for a Furniture Manufacturer Slide 15 2009 Pearson Addison-Wesley. All rights reserved. 7-15 Table 7.2 Effect of a Specific Tax of $10 per Unit on Short-Run Costs Slide 16 2009 Pearson Addison-Wesley. All rights reserved. 7-16 Figure 7.3 Effect of a Specific Tax on Cost Curves Costs per unit, $ 1558100 q, Units per day 80 37 27 $10 AC a = AC b + 10AC b MC b MC a =MC b A $10.00 tax shifts both the AVC and MC by exactly $10 Slide 17 2009 Pearson Addison-Wesley. All rights reserved. 7-17 Solved Problem 7.1 What is the effect of a lump-sum franchise tax on the quantity at which a firms after tax average cost curve reaches its minimum? (Assume that the firms before-tax average cost curve is U-shaped.) Slide 18 2009 Pearson Addison-Wesley. All rights reserved. 7-18 Solved Problem 7.1 Slide 19 2009 Pearson Addison-Wesley. All rights reserved. 7-19 Long-Run Costs Fixed costs are avoidable in the long run. in the long F = 0. As a result, the long-run total cost equals: C = VC Slide 20 2009 Pearson Addison-Wesley. All rights reserved. 7-20 Input Choice isocost line - all the combinations of inputs that require the same (iso-) total expenditure (cost). The firms total cost equation is: C = wL + rK. Labor Costs Capital Costs Slide 21 2009 Pearson Addison-Wesley. All rights reserved. 7-21 Input Choice (Cont). The firms total cost equation is: C = wL + rK. We get the Isocost equation by setting fixing the costs at a particular level: C = wL + rK. And then solving for K (variable along y-axis): K = r - L w r C Slide 22 2009 Pearson Addison-Wesley. All rights reserved. 7-22 Table 7.3 Bundles of Labor and Capital That Cost the Firm $100 Slide 23 2009 Pearson Addison-Wesley. All rights reserved. 7-23 Figure 7.4 A Family of Isocost Lines K, Units of capital per y ear a d e $100 isocost L, Units of labor peryear $100 $10 10 = $100 $5 = 20 Isocost Equation K = r - L w r C Initial Values C = $100 w = $5 r = $10 15 2.5 10 5 7.5 5 c b L = 5 K = 2.5 For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant. Slope = -1/2 = w/r Slide 24 2009 Pearson Addison-Wesley. All rights reserved. 7-24 Figure 7.4 A Family of Isocost Lines K, Units of capital per y ear a e $150 isocost$100 isocost L, Units of labor peryear $150 $10 15 = $100 $10 10 = $100 $5 = 20 $150 $5 = 30 Isocost Equation K = r - L w r C Initial Values C = $150 w = $5 r = $10 An increase in C. Slide 25 2009 Pearson Addison-Wesley. All rights reserved. 7-25 Figure 7.4 A Family of Isocost Lines K, Units of capital per y ear a e $150 isocost$100 isocost$50 isocost L, Units of labor peryear $150 $10 15 = $100 $10 10 = $50 $10 5 = $50 $5 = 10 $100 $5 = 20 $150 $5 = 30 Isocost Equation K = r - L w r C Initial Values C = $50 w = $5 r = $10 A decrease in C. Slide 26 2009 Pearson Addison-Wesley. All rights reserved. 7-26 Combining Cost and Production Information. The firm can choose any of three equivalent approaches to minimize its cost: Lowest-isocost rule - pick the bundle of inputs where the lowest isocost line touches the isoquant. Tangency rule - pick the bundle of inputs where the isoquant is tangent to the isocost line. 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. Slide 27 2009 Pearson Addison-Wesley. All rights reserved. 7-27 Figure 7.5 Cost Minimization K, Units of capital per hour x 500 L, Units of labor per hour 100 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Isocost Equation K = r - L w r C Initial Values q = 100 C = $2,000 w = $24 r = $8 Isoquant Slope MP L MP K =MRTS - Which of these three Isocost would allow the firm to produce the 100 units of output at the lowest possible cost? Slide 28 2009 Pearson Addison-Wesley. All rights reserved. 7-28 Figure 7.5 Cost Minimization K, Units of capital per hour y x z 11650240 L, Units of labor per hour 100 303 28 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Isocost Equation K = r - L w r C Initial Values q = 100 C = $2,000 w = $24 r = $8 Isoquant Slope MP L MP K =MRTS - Slide 29 2009 Pearson Addison-Wesley. All rights reserved. 7-29 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. Slide 30 2009 Pearson Addison-Wesley. All rights reserved. Figure 7.5 Cost Minimization K, Units of capital per hour y x z 11650240 L, Units of labor per hour 100 303 28 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Initial Values q = 100 C = $2,000 w = $24 r = $8 w r MP L MP K = MP L = 0.6q/L MP K = 0.4q/K = 248 1.2 0.4 = = 0.05 Spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital. Slide 31 2009 Pearson Addison-Wesley. All rights reserved. Figure 7.5 Cost Minimization K, Units of capital per hour y x z 11650240 L, Units of labor per hour 100 303 28 q = 100 isoquant $3,000 isocost $2,000 isocost $1,000 isocost Initial Values q = 100 C = $2,000 w = $24 r = $8 w r MP L MP K MP L = 0.6q/L MP K = 0.4q/K = 24 8 2.5 0.13 = = 0.1 if the firm shifts one dollar from capital to labor, output falls by 0.017 because there is less capital but also increases by 0.1 because there is more labor for a net gain of 0.083 more output at the same cost. = 0.02 So the firm should shift even more resources from capital to laborwhich increases the marginal product of capital and decreases the marginal product of labor. Slide 32 2009 Pearson Addison-Wesley. All rights reserved. 7-32 Figure 7.6 Change in Factor Price K, Units of capital per hour x 77500L,Workers per hour 100 52 q = 100 isoquant Original isocost, $2,000 New isocost, $1,032 w r MP L MP K = Minimizing Cost Rule A decrease in w. Initial Values q = 100 C = $2,000 w = $24 r = $8 w 2 = $8 C 2 = $1,032 v Slide 33 2009 Pearson Addison-Wesley. All rights reserved. 7-33 Solved Problem 7.3 If it manufactures at home, a firm faces input prices for labor and capital of w and r and produces q units of output using L units of labor and K 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 q? What happens to its cost of producing q? Slide 34 2009 Pearson Addison-Wesley. All rights reserved. 7-34 Solved Problem 7.3 Slide 35 2009 Pearson Addison-Wesley. All rights reserved. 7-35 How Long-Run Cost Varies with Output expansion path - the cost-minimizing combination of labor and capital for each output level Slide 36 2009 Pearson Addison-Wesley. All rights reserved. 7-36 Figure 7.7(a) Expansion Path K, Units of capital per hour x y z 10075500L,Workers per hour 150 200 100 Expansion path $3,000 isocost $2,000 isocost $4,000 isocost q = 100 Isoquant q = 200 Isoquant q = 300 Isoquant Slide 37 2009 Pearson Addison-Wesley. All rights reserved. 7-37 Figure 7.7(b) Expansion Path and Long-Run Cost Curve (contd) Slide 38 2009 Pearson Addison-Wesley. All rights reserved. 7-38 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 long- run cost curve. Slide 39 2009 Pearson Addison-Wesley. All rights reserved. 7-39 Figure 7.8 Long- Run Cost Curves Slide 40 2009 Pearson Addison-Wesley. All rights reserved. 7-40 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. Slide 41 2009 Pearson Addison-Wesley. All rights reserved. 7-41 Table 7.4 Returns to Scale and Long-Run Costs Slide 42 2009 Pearson Addison-Wesley. All rights reserved. 7-42 Table 7.5 Shape of Average Cost Curves in Canadian Manufacturing Slide 43 2009 Pearson Addison-Wesley. All rights reserved. 7-43 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. Once it chooses its plant size and equipment, these inputs are fixed in the short run. Thus, the firms long-run decision determines its short-run cost. Slide 44 2009 Pearson Addison-Wesley. All rights reserved. 7-44 Figure 7.9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves A v e r age cost, $ a b d e SRAC 1 AC 2 AC 3 AC 3 LRAC c q 2 q 1 q, Output per day 10 0 12 Slide 45 2009 Pearson Addison-Wesley. All rights reserved. 7-45 Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines Slide 46 2009 Pearson Addison-Wesley. All rights reserved. 7-46 Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines Slide 47 2009 Pearson Addison-Wesley. All rights reserved. 7-47 Application Choosing an Ink-Jet or a Laser Printer Slide 48 2009 Pearson Addison-Wesley. All rights reserved. 7-48 Figure 7.10 Long-Run and Short-Run Expansion Paths Slide 49 2009 Pearson Addison-Wesley. All rights reserved. 7-49 How Learning by Doing Lowers Costs learning by doing - the productive skills and knowledge that workers and managers gain from experience Slide 50 2009 Pearson Addison-Wesley. All rights reserved. 7-50 Figure 7.11 Learning by Doing Slide 51 2009 Pearson Addison-Wesley. All rights reserved. 7-51 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 Slide 52 2009 Pearson Addison-Wesley. All rights reserved. 7-52 Figure 7.12 Joint Production