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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 20122013) 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 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. ( ) ( ( ) ) That is, 5. CobbDouglas 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 CobbDouglas 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 20122013) 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 “3D” isoquant curves and isocost lines for this 3 inputs CMP, we can
draw 2D isoquant curves and isocost lines for
for specific fixed values of . For example, we saw the following
graphs in an earlier chapter: these show labor and materials isoquant 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 20122013) 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 ( ) isoquant curve ) isoco...
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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.
 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics

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