Lecture11.ppt

# Lecture11.ppt - Cost Constraint/Isocost Line COST...

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Cost Constraint/Isocost Line

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COST CONSTRAINT C= wL + rK (m = p 1 x 1 +p 2 x 2 ) w: wage rate (including fringe benefits, holidays, PRSI, etc) r: rental rate of capital Rearranging: K=C/r-(w/r)L
COST CONSTRAINT L K Represents society’s willingness to trade the factors of production C=wL+rK C/w C/r Slope of the isocost = K/ L= K/ L= (-) w/r (-) w/r

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EQUILIBRIUM L K Y e rK wL C
EQUILIBRIUM We can either Minimise cost subject to e and C Y Y or Maximise output subject to e and Y C C equilibrium equilibrium

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EQUILIBRIUM L K f Y rK wL L , * rL wL C K L f L ) , ( * Minimise cost subject to output or Maximise output subject to costs Lagrangian method
Lagrange Method Set up the problem (same as with utility maximisation subject to budget constraint). Find the first order conditions. It is easier to maximise output subject to a cost constraint than to minimise costs subject to an output constraint. The answer will be the same (in essence ) either way.

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Example: Cobb-Douglas Equilibrium Set up the problem rK wL C L AK L a a 1 * Multiply out the part in brackets rK wL C L AK L a a 1 * Derive a demand function for Capital and Labour by maximising output subject to a cost constraint. Let L* be Lagrange, L be labour and K be capital.
Cobb-Douglas: Equilibrium Find the First Order Conditions by differentiation with respect to K, L and 0 1 1 * r L AaK K L a a 1 st FOC 0 1 * w L K a A L L a a 2 nd FOC 0 * rK wL C L 3 rd FOC

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Cobb-Douglas: Equilibrium Rearrange the 1 st FOC and the 2 nd
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