ajaz_204_2009_lecture_10

ajaz_204_2009_lecture_10 - University of Toronto Department...

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University of Toronto Department of Economics ECO 204 2009 2010 Sayed Ajaz Hussain Lecture 10 1 Ajaz Hussain. Department of Economics. University of Toronto (St. George)
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Today ± Modeling Firms ² Cost Minimization Problem (CMP) ² Some observations o Price of owned (not leased) capital o Target output o Innovation ± Production function ² Long vs. Short Run ² Returns to scale ² Isoquants and Technical Rate of Substitution ± Cobb Douglas CMP Ajaz Hussain. Department of Economics. University of Toronto (St. George) 2
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Consumer vs. Producer Choice (N = 2) Ajaz Hussain. Department of Economics. University of Toronto (St. George) 3 Consumer Utility = f(Q 1 , Q 2 ) Price Taker Producer q = f(Input 1 , Input 2 ) Consumer Problem for 2 Commodities Producer Problem for 2 Inputs
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Target Output q Firm chooses target output separately Examples Ajaz Hussain. Department of Economics. University of Toronto (St. George) 4
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“Fixed”, “Variable” Inputs ECO 100: Fixed and variable inputs Fixed (“unavoidable”) costs arise from fixed inputs Variable (“avoidable”) costs arise from variable inputs For now assume inputs either fixed or variable Later ( Prestige Telephone Company ) inputs will be quasi fixed, quasi variable Ajaz Hussain. Department of Economics. University of Toronto (St. George) 5
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UMP vs. CMP Ajaz Hussain. Department of Economics. University of Toronto (St. George) 6 U TILITY M AXIMIZATION P ROBLEM (UMP) Choose goods to maximize utility such that expenditure Income Max Utility s.t. P 1 Q 1 + P 2 Q 2 Y C OST M INIMIZATION P ROBLEM (CMP) Choose inputs to minimize cost such that Output Target q Min Cost = P 1 Input 1 + P 2 Input 2 s.t. Output
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Utility vs. Production Function (N =2) U TILITY F UNCTION U = f(Q 1 , Q 2 ) Utility ordinal + Monotonic Transformation gives another utility function representing preferences Ajaz Hussain. Department of Economics. University of Toronto (St. George) 7 P RODUCTION F UNCTION Q = f(A, Input 1 , Input 2 ) Output cardinal + Monotonic Transformation doesn’t give another production function representing technology
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Production Function with L and K Q = f(A, Input 1 , Input 2 ) Assume Input 1 = Labor (L), Input 2 = Capital (K) Of course, there can be more or fewer inputs If all inputs “variable”: long run production function If at least 1 input “variable”: short run production function Ajaz Hussain. Department of Economics. University of Toronto (St. George) 8
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Input Prices: Remarks Firm “purchases” inputs as a price taker If Input 1 = Labor, Input 2 = Capital Price of Labor = P L Price of Capital = P K Assume labor hired and capital leased in competitive markets. Later, we’ll have to impute P K for firms that own capital Ajaz Hussain. Department of Economics.
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ajaz_204_2009_lecture_10 - University of Toronto Department...

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