Chapter Seven. Topics. Economic Cost. Measuring Costs. Short-Run Costs. Long-Run Costs. Lower Costs in the Long Run. Cost of Producing Multiple Goods.
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1 Chapter Seven Costs Topics Measuring Costs. Short-Run Costs. Long-Run Costs. Lower Costs in the Long Run. Cost of Producing Multiple Goods Pearson Addison-Wesley. All rights reserved. 7-2 Economic Cost Economic cost or opportunity cost - the value of the best alternative use of a resource. 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. 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
2 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. 7-4 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. 7-5 Marginal Cost. marginal cost (MC) - the amount by which a firm s cost changes if the firm produces one more unit of output. ΔC MC = Δ q And since only variable costs change with output: ΔVC MC = Δq 2009 Pearson Addison-Wesley. All rights reserved
3 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 Pearson Addison-Wesley. All rights reserved. 7-7 Table 7.1 Variation of Short-Run Cost with Output 2009 Pearson Addison-Wesley. All rights reserved. 7-8 Figure 7.1 Short- Run Cost Curves (a) Cost, $ 400 C VC A B 48 F Quantity, q, Units per day (b) Cost per unit, $ 60 MC b a AC AVC 8 AFC Quantity, q, Units per day 2009 Pearson Addison-Wesley. All rights reserved
4 Relationship between average and marginal cost curves Cost per unit, $ When MC is lower than When AC, MC AC is is lower decreasing than AVC, AVC is decreasing b and when MC is and larger when than MC AC, is larger AC is than increases AVC, AVC is increases a MC AC so MC = AC, at AVC the lowest point of the AC curve! so MC = AVC, at the lowest point of the AVC curve! Quantity, q, Units per day 2009 Pearson Addison-Wesley. All rights reserved Figure 7.2 Variable Cost and Total Product of Labor 2009 Pearson Addison-Wesley. All rights reserved Shape of the Marginal Cost Curve MC = ΔVC/Δq. But in the short run, ΔVC = w (can you tell why?) Therefore, MC = w/δq The additional output created by every additional unit of labor is: Δq/ ΔL = MP L Therefore, MC = w/ MP L 2009 Pearson Addison-Wesley. All rights reserved
5 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 2009 Pearson Addison-Wesley. All rights reserved Application Short-Run Cost Curves for a Furniture Manufacturer 2009 Pearson Addison-Wesley. All rights reserved Table 7.2 Effect of a Specific Tax of $10 per Unit on Short-Run Costs 2009 Pearson Addison-Wesley. All rights reserved
6 Figure 7.3 Effect of a Specific Tax on Cost Curves Costs per unit, $ 80 A $10.00 tax shifts both the AVC and MC by exactly $10 MC a = MC b + 10 MC b $10 AC a = AC b $10 AC b q, Units per day 2009 Pearson Addison-Wesley. All rights reserved 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 Solved Problem Pearson Addison-Wesley. All rights reserved
7 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 2009 Pearson Addison-Wesley. All rights reserved Input Choice line - all the combinations of inputs that require the same (iso-) total expenditure (cost). The firm s total cost equation is: C = wl + rk. Capital Labor Costs Costs 2009 Pearson Addison-Wesley. All rights reserved Input Choice (Cont). The firm s 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 = C r - w L r 2009 Pearson Addison-Wesley. All rights reserved
8 Table 7.3 Bundles of Labor and Capital That Cost the Firm $ Pearson Addison-Wesley. All rights reserved Figure 7.4 A Family of Isocost Lines K, Units of capital per year $ = $ e For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant. d c Slope = -1/2 = w/r ΔK = 2.5 b ΔL = 5 $100 Isocost Equation C K = - w L r r Initial Values C = $100 w = $5 r = $10 a $100 $5 = 20 L, Units of labor per year 2009 Pearson Addison-Wesley. All rights reserved Figure 7.4 A Family of Isocost Lines K, Units of capital per year $ = $10 $ = $10 e Isocost Equation C K = - w L r r An increase in C. Initial Values C = $150 w = $5 r = $10 $100 $150 L, Units of labor per year 2009 Pearson Addison-Wesley. All rights reserved a $100 $5 = 20 $150 $5 = 30 8
9 Figure 7.4 A Family of Isocost Lines K, Units of capital per year $ = $10 $ = $10 e A decrease in C. Isocost Equation C K = - w L r r Initial Values C = $50 w = $5 r = $10 $50 5 = $10 $50 $100 $150 $50 $5 = 10 $100 $5 = 20 $150 $5 = Pearson Addison-Wesley. All rights reserved a L, Units of labor per year Combining Cost and Production Information. The firm can choose any of three equivalent approaches to minimize its cost: Lowest- rule - pick the bundle of inputs where the lowest line touches the isoquant. Tangency rule - pick the bundle of inputs where the isoquant is tangent to the 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 Pearson Addison-Wesley. All rights reserved Figure 7.5 Cost Minimization K, Units of capital per hour 100 $3,000 $2,000 $1,000 q = 100 isoquant Which of these three Isocost would allow the firm to produce the 100 units of output at the lowest possible cost? x Isocost Equation C K = - w L r r Isoquant Slope MP L - =MRTS MP K Initial Values q = 100 C = $2,000 w = $24 r = $ L, Units of labor per hour 2009 Pearson Addison-Wesley. All rights reserved
10 Figure 7.5 Cost Minimization K, Units of capital per hour 303 $3,000 $2,000 q = 100 isoquant y Isocost Equation C K = - w L r r Isoquant Slope MP L - =MRTS MP K $1,000 x Initial Values q = 100 C = $2,000 w = $24 r = $8 z L, Units of labor per hour 2009 Pearson Addison-Wesley. All rights reserved Cost Minimization At the point of tangency, the slope of the isoquant equals the slope of the. Therefore, w MRTS = last-dollar rule: cost is r MPL MRTS = MPK MPL w = MPK r MPL MPK = w r 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 Pearson Addison-Wesley. All rights reserved K, Units of capital per hour Figure 7.5 Cost Minimization $3,000 $2,000 $1,000 q = 100 isoquant y MP L MP w = K r x MP L = 0.6q/L MP K = 0.4q/K Initial Values q = 100 C = $2,000 w = $24 r = $ = 24 = = Spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital. 28 z L, Units of labor per hour 2009 Pearson Addison-Wesley. All rights reserved. 10
11 K, Units of capital per hour Figure 7.5 Cost Minimization $3,000 $2,000 $1,000 q = 100 isoquant y MP L = 0.6q/L MP K = 0.4q/K Initial Values q = 100 C = $2,000 w = $24 r = $8 MP L 2.5 = w 24 = 0.1 if So the the firm shifts firm one dollar should from shift capital to MP K 0.13 labor, even output more falls by r = because there 8 = 0.02 resources from is capital less capital to labor but also which increases by 0.1 the because marginal there is more product labor of for capital a net gain and of decreases more x output the marginal at the same cost. product of labor. 28 z L, Units of labor per hour 2009 Pearson Addison-Wesley. All rights reserved. Figure 7.6 Change in Factor Price Minimizing Cost Rule K, Units of capital per hour 100 q = 100 isoquant Original, $2,000 New, $1,032 A decrease in w. x MP L MP w = K r Initial Values q = 100 C = $2,000 w = $24 r = $8 w 2 = $8 C 2 = $1, v L, Workers per hour 2009 Pearson Addison-Wesley. All rights reserved 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
12 Solved Problem Pearson Addison-Wesley. All rights reserved 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 Figure 7.7(a) Expansion Path K, Units of capital per hour $4,000 $3,000 Expansion path $2, y z 100 x q = 200 Isoquant q = 150 Isoquant q = 100 Isoquant L, Workers per hour 2009 Pearson Addison-Wesley. All rights reserved
13 Figure 7.7(b) Expansion Path and Long-Run Cost Curve (cont d) 2009 Pearson Addison-Wesley. All rights reserved 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 Pearson Addison-Wesley. All rights reserved Figure 7.8 Long- Run Cost Curves 2009 Pearson Addison-Wesley. All rights reserved
14 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 Pearson Addison-Wesley. All rights reserved Table 7.4 Returns to Scale and Long-Run Costs 2009 Pearson Addison-Wesley. All rights reserved Table 7.5 Shape of Average Cost Curves in Canadian Manufacturing 2009 Pearson Addison-Wesley. All rights reserved
15 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 firm s long-run decision determines its short-run cost Pearson Addison-Wesley. All rights reserved Figure 7.9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves Average cost, $ LRAC SRAC 3 SRAC 1 SRAC 3 SRAC a b c d e 0 q 1 q 2 q, Output per day 2009 Pearson Addison-Wesley. All rights reserved Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines 2009 Pearson Addison-Wesley. All rights reserved
16 Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines 2009 Pearson Addison-Wesley. All rights reserved Application Choosing an Ink-Jet or a Laser Printer 2009 Pearson Addison-Wesley. All rights reserved Figure 7.10 Long-Run and Short-Run Expansion Paths 2009 Pearson Addison-Wesley. All rights reserved
17 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 Figure 7.11 Learning by Doing 2009 Pearson Addison-Wesley. All rights reserved 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
18 Figure 7.12 Joint Production 2009 Pearson Addison-Wesley. All rights reserved
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