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*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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