The firm will use less labor to produce the same

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Unformatted text preview: eturns, a 1% increase in may reduce labor use and cost by more than, less than or equal to 1%. You should be prepared for test questions where you might be asked to work out ● As we saw earlier, since labor and capital cannot be substituted for each other in the short run, as continues to use the same amount of labor and capital: and . the firm As wages rise, the firm, unable to substitute capital for labor, will see its cost increase where: ( ) 23 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) ( Due to a 1% increase in ) will cost increase by more, equal to, or less than 1%? Let’s find out: ( ) ( ( ) ) ( ) That is, ● Since labor and capital cannot be substituted for each other, as amount of capital and mlabor where you should show that: the firm will use continue to use the same As the price of capital rises rise, the firm, unable to substitute capital for labor, will see its cost increase where: ( ) ( Due to a 1% increase in ) will cost increase by more, equal to, or less than 1%? Let’s find out: 24 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) ( ( ) ) That is, 5. Cobb-Douglas Short Run Cost Minimization Problem (2 Variable inputs and 1 Fixed input) Suppose a company uses labor and materials as variable inputs and fixed capital as a fixed input to produce output according to: where tells us the “returns” to the variable inputs labor and materials7: ⏟ { } { } [ ⏟ Now: As such, the short run Cobb-Douglas CMP becomes: { } [ Where by the envelope theorem we know that: ( 7 ) i.e. as the cost of production will go up (or stay the same) Do not confuse “returns” with “returns to scale” 25 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Unlike the 1 variable and 1 fixed input case where we could solve for the variable input from the constraint that output produced must equal target output, we would have to solve this problem by solving the constrained optimization problem. The FOCS are8: [⏟ [⏟ [ Isolating and equating from the first two FOCs yields: How do we interpret this? While we can’t plot “3-D” iso-quant curves and iso-cost lines for this 3 inputs CMP, we can draw 2-D iso-quant curves and iso-cost lines for for specific fixed values of . For example, we saw the following graphs in an earlier chapter: these show labor and materials iso-quant curves for holding capital fixed at and 8 Marginal product of labor, Marginal Product of Materials 26 ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. The condition must be tangent to the ( says that for a given value of , at the optimal bundle of inputs, the ( ) iso-quant curve ) iso-co...
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This note was uploaded on 03/20/2014 for the course ECON 204 taught by Professor Ajazhussain during the Fall '09 term at University of Toronto.

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