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lecture12

# lecture12 - Prof Jay Bhattacharya Spring 2001 The Theory of...

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Prof. Jay Bhattacharya Spring 2001 Econ 11--Lecture 12 1 Spring 2001 Econ 11--Lecture 12 1 The Theory of the Firm II Last lecture we covered: – production functions • Today: – Cost minimization – Firm’s supply under cost minimization – Short vs. long run cost curves Spring 2001 Econ 11--Lecture 12 2 Firm Objectives Profit maximization: firms choose that level of output and that combination of inputs which yields the highest level of profits Cost minimization: firms choose that combination of inputs to produce a certain level of output at minimum cost. Cost minimization should hold even for non-profit firms. Spring 2001 Econ 11--Lecture 12 3 Cost Minimization— Mathematical Approach ( ) L K F Q t s rK wL L K , . . , min = + ( ) ( ) L K F Q rK wL G , + = λ Spring 2001 Econ 11--Lecture 12 4 First order conditions ( ) 0 , 0 0 = = = = = = = = L K F Q G MP w L F w L G MP r K F r K G L K λ λ λ λ λ L K MP MP w r = Spring 2001 Econ 11--Lecture 12 5 Input demand equations Solving the three first order conditions simultaneously yields two input demand equations: Plugging these back into the total input expenditure identity (Expend. = wL + rK ) yields the minimum total cost curve: ( ) Q r w L L , , * = ( ) Q r w K K , , * = ( ) Q r w C wL rK TC , , * * = + = Spring 2001 Econ 11--Lecture 12 6 Cost Minimization— Graphical Approach ( ) L K F Q , = L K Decreasing costs r w slope = K L MP MP slope =

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Prof. Jay Bhattacharya Spring 2001 Econ 11--Lecture 12 2 Spring 2001 Econ 11--Lecture 12 7 Firm Optimization Tangency Condition – increase use of an input until its marginal product is equal to its real price – if MP L /MP K > w/r then increasing use of L (while decreasing use of K) will decrease costs – if MP L /MP K < w/r then decreasing use of L (while increasing use of K) will decrease costs Technology Constraint Spring 2001 Econ 11--Lecture 12 8 Example Problem For Cobb-Douglass Production Q = K a L b , what are the input demand functions for K and L? What is the minimum cost function?
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lecture12 - Prof Jay Bhattacharya Spring 2001 The Theory of...

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