Chapter Seven. Costs
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1 Chapter Seven Costs
2 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
3 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. 7-3
4 Economic Vs Accounting Cost According to Bookkeepers: The purpose of cost estimation: a. To minimize firm s tax for this year b. To reflect good impression for stock holders about the firm s performance SO: Accounting Profits = TR TC Where TC = Explicit costs, such as: - Wages - Salaries - Rent - Row material payment - Amortization OR (Depreciation) 2009 Pearson Addison-Wesley. All rights reserved. 7-4
5 Economic Vs Accounting Cost According to Economists: To run a firm profitably, a manager acts like an economist and consider all relevant costs: SO: Econ. Profits = TR TC Where TC = Explicit cost + Implicit cost - Explicit costs do not contain depreciation, economists amortizes capital using the rule of the best rental rate for capital, which is an implicit cost - Implicit cost: Such as: a. Opportunity cost for capital, or the best alternative use (Rental rate) b. Opportunity cost for the production factors owned to owner, or the best alternative use Pearson Addison-Wesley. All rights reserved. 7-5
6 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. 7-6
7 Marginal Cost. marginal cost (MC) - the amount by which a firm s cost changes if the firm produces one more unit of output. C MC q And since only variable costs change with output: MC VC q 2009 Pearson Addison-Wesley. All rights reserved. 7-7
8 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. 7-8
9 Table 7.1 Variation of Short-Run Cost with Output 2009 Pearson Addison-Wesley. All rights reserved. 7-9
10 Cost per unit, $ Cost, $ Figure 7.1 Short- Run Cost Curves (a) 400 C VC B A F (b) Quantity, q, Units per day 60 MC b a AC AVC 8 AFC Quantity, q, Units per day 2009 Pearson Addison-Wesley. All rights reserved. 7-10
11 Cost per unit, $ Relationship between average and marginal cost curves When MC is When lower MCthan is lower AC, than AC is AVC, decreasing AVC is decreasing b and when MC is and larger when than MCAC, is larger AC is than increases AVC, AVC is increases a MC AC AVC so MC = AC, at 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. 7-11
12 Figure 7.2 Variable Cost and Total Product of Labor 2009 Pearson Addison-Wesley. All rights reserved. 7-12
13 Shape of the Marginal Cost Curve MC = VC/ q. But in the short run, VC = w. L (can you tell why?) Therefore, MC = w.( L/ q) The additional output created by every additional unit of labor is: q/ L = MP L Therefore, MC = w/ MP L 2009 Pearson Addison-Wesley. All rights reserved. 7-13
14 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. 7-14
15 Application Short-Run Cost Curves for a Furniture Manufacturer 2009 Pearson Addison-Wesley. All rights reserved. 7-15
16 Table 7.2 Effect of a Specific Tax of $10 per Unit on Short-Run Costs 2009 Pearson Addison-Wesley. All rights reserved. 7-16
17 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 AC a = AC b $10 AC b q, Units per day 2009 Pearson Addison-Wesley. All rights reserved. 7-17
18 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. 7-18
19 Solved Problem Pearson Addison-Wesley. All rights reserved. 7-19
20 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. 7-20
21 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 = wl + rk. Labor Costs Capital Costs 2009 Pearson Addison-Wesley. All rights reserved. 7-21
22 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. 7-22
23 Table 7.3 Bundles of Labor and Capital That Cost the Firm $ Pearson Addison-Wesley. All rights reserved. 7-23
24 K, Units of capital per year Figure 7.4 A Family of Isocost Lines 10 = $100 $ e For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant. d K = 2.5 c L = 5 Isocost Equation C K = - w L r r Initial Values C = $100 w = $5 r = $10 Slope = -1/2 = w/r b $100 isocost a $100 $5 = 20 L, Units of labor per year 2009 Pearson Addison-Wesley. All rights reserved. 7-24
25 Figure 7.4 A Family of Isocost Lines Isocost Equation K, Units of capital per year 15 = 10 = $150 $10 $100 $10 e C K = - w L r r An increase in C. Initial Values C = $150 w = $5 r = $10 $100 isocost $150 isocost 2009 Pearson Addison-Wesley. All rights reserved a $100 $5 = 20 $150 $5 = 30 L, Units of labor per year
26 Figure 7.4 A Family of Isocost Lines Isocost Equation K, Units of capital per year 15 = 10 = $150 $10 $100 $10 e C K = - w L r r A decrease in C. Initial Values C = $50 w = $5 r = $10 5 = $50 $10 $50 isocost $100 isocost $150 isocost $50 $5 = Pearson Addison-Wesley. All rights reserved a $100 $5 = 20 $150 $5 = 30 L, Units of labor per year
27 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 Pearson Addison-Wesley. All rights reserved. 7-27
28 Figure 7.5 Cost Minimization K, Units of capital per hour $3,000 isocost $2,000 isocost q = 100 isoquant Which of these three Isocost would allow the firm to produce the 100 units of output at the lowest possible cost? Isocost Equation C K = - w L r r Isoquant Slope MP L - = MRTS MP K 100 $1,000 isocost x Initial Values q = 100 C = $2,000 w = $24 r = $ L, Units of labor per hour 2009 Pearson Addison-Wesley. All rights reserved. 7-28
29 Figure 7.5 Cost Minimization K, Units of capital per hour 303 $3,000 isocost $2,000 isocost q = 100 isoquant y Isocost Equation C K = - w L r r Isoquant Slope MP L - = MRTS MP K $1,000 isocost 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. 7-29
30 Cost Minimization At the point of tangency, the slope of the isoquant equals the slope of the isocost. Therefore, MRTS MRTS MP MP MP w L K L w r MP MP w r MP r K L K 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 Pearson Addison-Wesley. All rights reserved. 7-30
31 2009 Pearson Addison-Wesley. All rights reserved. K, Units of capital per hour Figure 7.5 Cost Minimization $3,000 isocost $2,000 isocost $1,000 isocost q = 100 isoquant y MP L w = x MP L = 0.6q/L MP K = 0.4q/K Initial Values q = 100 C = $2,000 w = $24 r = $8 MP K 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
32 2009 Pearson Addison-Wesley. All rights reserved. K, Units of capital per hour Figure 7.5 Cost Minimization $3,000 isocost $2,000 isocost $1,000 isocost q = 100 isoquant y MP L 2.5 = w 24 = 0.1 MP K 0.13 r = 8 = 0.02 x MP L = 0.6q/L MP K = 0.4q/K Initial Values q = 100 C = $2,000 w = $24 r = $8 if So the the firm shifts firm should one dollar shiftfrom capital even more to labor, resources output falls from by capital because to labor which there is less capital but increases also increases the marginal by 0.1 product because there of capital is more and labor decreases for a net the gain of marginal more product output of at labor. the same cost. 28 z L, Units of labor per hour
33 Figure 7.6 Change in Factor Price Minimizing Cost Rule K, Units of capital per hour 100 Original isocost, $2,000 New isocost, $1,032 q = 100 isoquant 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. 7-33
34 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. 7-34
35 K, Units of capital per hour Figure 7.7(a) Expansion Path $4,000 isocost $3,000 isocost $2,000 isocost Expansion path x y z q = 300 Isoquant q = 200 Isoquant q = 100 Isoquant L, Workers per hour 2009 Pearson Addison-Wesley. All rights reserved. 7-35
36 Figure 7.7(b) Expansion Path and Long-Run Cost Curve (cont d) 2009 Pearson Addison-Wesley. All rights reserved. 7-36
37 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. 7-37
38 Figure 7.8 Long- Run Cost Curves 2009 Pearson Addison-Wesley. All rights reserved. 7-38
39 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. 7-39
40 Table 7.4 Returns to Scale and Long-Run Costs 2009 Pearson Addison-Wesley. All rights reserved. 7-40
41 Table 7.5 Shape of Average Cost Curves in Canadian Manufacturing 2009 Pearson Addison-Wesley. All rights reserved. 7-41
42 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. 7-42
43 Average cost, $ Figure 7.9 Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves SRAC 3 LRAC 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. 7-43
44 Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines 2009 Pearson Addison-Wesley. All rights reserved. 7-44
45 Application Long-Run Cost Curves in Furniture Manufacturing and Oil Pipelines 2009 Pearson Addison-Wesley. All rights reserved. 7-45
46 Application Choosing an Ink-Jet or a Laser Printer 2009 Pearson Addison-Wesley. All rights reserved. 7-46
47 Figure 7.10 Long-Run and Short-Run Expansion Paths 2009 Pearson Addison-Wesley. All rights reserved. 7-47
48 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. 7-48
49 Figure 7.11 Learning by Doing 2009 Pearson Addison-Wesley. All rights reserved. 7-49
50 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. 7-50
51 Figure 7.12 Joint Production 2009 Pearson Addison-Wesley. All rights reserved. 7-51
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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