# Production Costs ECO61 Udayan Roy Fall 2008. Bundles of Labor and Capital That Cost the Firm \$100

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• Production CostsECO61Udayan RoyFall 2008

• Bundles of Labor and Capital That Cost the Firm \$100

• Isocost LinesK, Units of capital peryearade\$100 isocostL, Units of labor peryearIsocost EquationK = r- L wrInitial ValuesC = \$100w = \$5 r = \$10152.51057.55cbDL = 5DK = 2.5For 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

• A Family of Isocost LinesK, Units of capital peryearae\$150 isocost\$100 isocostL, Units of labor peryearIsocost EquationK = r- L wrInitial ValuesC = \$150w = \$5 r = \$10An increase in C.

• A Family of Isocost LinesK, Units of capital peryearae\$150 isocost\$100 isocost\$50 isocostL, Units of labor peryearIsocost EquationK = r- L wrInitial ValuesC = \$50w = \$5 r = \$10A decrease in C.

• CostsThe firms total cost equation is: C = wL + rK.Therefore,Note that if C is constantas along an isocost linethen a one-unit increase in L requires K to change by w/r units. That is, the slope of the isocost line is w/r.

• 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.

• Cost MinimizationK, Units of capital per hourx500L, Units of labor per hour100Isocost EquationK = r- L wrInitial Valuesq = 100C = \$2,000w = \$24 r = \$8Isoquant SlopeMPLMPK= -MRTS- Which of these three Isocost would allow the firm to produce the 100 units of output at the lowest possible cost?

• Cost MinimizationK, Units of capital per houryxz11650240L, Units of labor per hour10030328Isocost EquationK = r- L wrInitial Valuesq = 100C = \$2,000w = \$24 r = \$8Isoquant SlopeMPLMPK= MRTS-

• Cost MinimizationAt 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 sothat the last dollar spent on labor adds as much extra output as the last dollar spent on capital.

• Cost MinimizationK, Units of capital per houryxz11650240L, Units of labor per hour10030328Initial Valuesq = 100C = \$2,000w = \$24 r = \$8wrMPLMPK= MPL = 0.6q/LMPK = 0.4q/K = 2481.20.4= = 0.05 Spending one more dollar on labor at x gets the firm as much extra output as spending the same amount on capital.

• Cost MinimizationK, Units of capital per houryxz11650240L, Units of labor per hour10030328Initial Valuesq = 100C = \$2,000w = \$24 r = \$8wrMPLMPKMPL = 0.6q/LMPK = 0.4q/K = 2482.50.13= = 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.= 0.02So the firm should shifteven more resources from capital to laborwhich increases the marginal product of capital and decreases the marginal product of labor.

• Change in Input PriceK, Units of capital per hourx77500L,Workers per hour10052wrMPLMPK= Minimizing Cost RuleA decrease in w.Initial Valuesq = 100C = \$2,000w = \$24 r = \$8w2 = \$8C2 = \$1,032v

• How Long-Run Cost Varies with Outputexpansion path - the cost-minimizing combination of labor and capital for each output level

• Expansion PathK, Units of capital per hourxyz10075500L,Workers per hour150200100Expansion pathq = 100 Isoquantq = 200 Isoquantq = 300 Isoquant

• Expansion Path and Long-Run Cost Curve (contd)

• Long-Run Cost Curves

• Economies of Scaleeconomies 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.

• Returns to Scale and Long-Run Costs

• Figure 8.7: Least-Cost Method, No-Overlap Rule Example 8-*

• Figure 8.10: Output Expansion Path and Total Cost Curve 8-*

• Figure 8.28: Returns to Scale and Economies of Scale 8-*

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