Short-Run Cost Measures - PDF Free Download

Chapter 7 Costs

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 7-9 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Marginal Cost Marginal cost (MC) - the amount by which a firm s cost changes if the firm produces one more unit of output. And since only variable costs change with output: 7-10 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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. 7-11 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Cost per unit, $ Cost, $ Figure 7.1 Short- Run Cost Curves (a) 400 C VC 216 120 B A 1 1 27 20 48 F 0 2 4 6 8 10 Quantity, q, Units per day (b) 60 MC 28 27 20 b a AC AVC 8 AFC 0 2 4 6 8 10 Quantity, q, Units per day 7-13 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Cost per unit, $ Relationship Between Average and Marginal Cost Curves 60 28 27 20 8 When MC is lower than AC, When ACMC 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 AVC so MC = AC, at the lowest point of the AC curve! so MC = AVC, at the lowest point of the AVC curve! 0 2 4 6 8 10 Quantity, q, Units per day 7-14 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Shape of the Marginal Cost Curve MC = DVC/Dq. But in the short run, DVC = wdl (can you tell why?) Therefore, MC = wdl/dq The additional output created by every additional unit of labor is: Dq/ DL = MP L Therefore, MC = w/ MP L 7-16 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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/ap L 7-18 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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 Now, only concerned with three costs: 1. Total cost (C) 2. Average cost (AC) 3. Marginal cost (MC) 7-26 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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 7-27 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

7-28 Copyright 2012 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 r L

Figure 7.4 A Family of Isocost Lines K, Units of capital per year 10 = $100 $10 7.5 e For each extra unit of capital it uses, the firm must use two fewer units of labor to hold its cost constant. d Isocost Equation C K = - w L r r Initial Values C = $100 w = $5 r = $10 5 2.5 DK = 2.5 c DL = 5 Slope = -1/2 = w/r b $100 isocost a 5 10 15 $100 $5 = 20 L, Units of labor per year 7-30 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Figure 7.4 A Family of Isocost Lines K, Units of capital per year 15 = 10 = $150 $10 $100 $10 e Isocost Equation C K = - w L r r An increase in C. Initial Values C = $150 w = $5 r = $10 $100 isocost $150 isocost a $100 $5 = 20 $150 $5 = 30 L, Units of labor per year 7-31 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Figure 7.4 A Family of Isocost Lines K, Units of capital per year 15 = 10 = $150 $10 $100 $10 e A decrease in C. Isocost Equation C K = - w L r r Initial Values C = $50 w = $5 r = $10 5 = $50 $10 $50 isocost $100 isocost $150 isocost $50 $5 = 10 a $100 $5 = 20 $150 $5 = 30 L, Units of labor per year 7-32 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Properties of Isocost Lines 1. Further from the origin = higher cost. 2. All isocost lines have the same negative slope = -w/r. 3. X-axis and y-axis intercepts are meaningful. Tell how much Labor and Capital can be purchased if the firm spends all money on only that input. 4. Similar to budget constraints, but with one main difference. 7-33 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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. 7-34 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Figure 7.5 Cost Minimization K, Units of capital per hour 100 $3,000 isocost $2,000 isocost $1,000 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? x Isocost Equation C K = - w L r r Isoquant Slope MP L - = MRTS MP K 0 50 L, Units of labor per hour Initial Values q = 100 C = $2,000 w = $24 r = $8 7-35 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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 100 28 $1,000 isocost x z Initial Values q = 100 C = $2,000 w = $24 r = $8 0 24 50 116 L, Units of labor per hour 7-36 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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. 7-37 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Figure 7.6 Change in Factor Price K, Units of capital per hour 100 52 Original isocost, $2,000 New isocost, $1,032 q = 100 isoquant A decrease in w. x v Minimizing Cost Rule MP L MP w = K r Initial Values q = 100 C = $2,000 w = $24 r = $8 w 2 = $8 C 2 = $1,032 0 50 77 L, Workers per hour 7-40 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

K, Units of capital per hour Figure 7.7(a) Expansion Path and Long-Run Cost Curve $4,000 isocost $3,000 isocost $2,000 isocost Expansion path 200 150 100 x y z q = 200 Isoquant q = 150 Isoquant q = 100 Isoquant 0 50 75 100 L, Workers per hour 7-44 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

The Shape of Long Run Cost Curves The shape of long run cost curves is determined by the production function relationship between output and inputs. 7-47 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Figure 7.8 Long- Run Cost Curves Discussion Points: The long-run cost curve C rises less rapidly below q* and more rapidly after q*. Marginals pull averages. Same as before. Intersection of MC and AC at minimum AC. Same as before. But, why is the AC curve still U-shaped even though fixed costs=0? 7-48 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Economies of Scale Economies of scale - property of a cost function whereby the average cost of production falls as output expands (IRS, falling AC). Diseconomies of scale - property of a cost function whereby the average cost of production rises when output increases (DRS, rising AC). 7-49 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Lower Costs in the Long Run 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. 7-52 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

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 2 12 10 a b c d e 0 q 1 q 2 q, Output per day 7-53 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

How Learning by Doing Lowers Costs Learning by doing - the productive skills and knowledge that workers and managers gain from experience 7-58 Copyright 2012 Pearson Addison-Wesley. All rights reserved.

Why Costs Fall over Time 1. Technological or organizational progress may increase productivity. 2. Operating at a larger scale in the long run may lower average costs due to increasing returns to scale. 3. The firm s workers and managers may become more proficient over time due to learning by doing. 7-60 Copyright 2012 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. 7-61 Copyright 2012 Pearson Addison-Wesley. All rights reserved.