Lect16310-1W2012Cost and Duality [Compatibility Mode]

# Lect16310-1W2012Cost and Duality [Compatibility Mode] -...

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Unformatted text preview: Northwestern University ECON 310-1: Microeconomic Theory Professors Jim Hornsten and Ron Braeutigam Winter 2012 Costs and Duality (B&B Chapter 7) Notes for Lecture #16 Northwestern University ECON 310-1: Microeconomic Theory Professors Jim Hornsten and Ron Braeutigam Winter 2012 Three Representations of Technology Factor Prices Factors (Amounts of Inputs/Month) Product (Output / Month) w or P L (wage rate) L -- Labor (# of worker-hours) r or P K (rental P of K) K-- Capital (Blast Furnaces) m or P m (price of ore) M-- raw materials (iron ore) Three Questions a Production Manager Might Ask: Suppose the boss tells us how much to produce (target is Q). Factor prices (w, r, m) are exogenously determined in competitive markets. 1) What possible combinations of K, L, and M can we hire to meet the production target? Production Function Q(K,L,M) 2) How much of each factor should we hire if we want to produce Q at the lowest cost? Factor Demand Equations: K(Q,r,w,m), L(Q,r,w,m), M(Q,r,w,m) 3) What is the lowest total cost we will incur to meet the production target? Cost Function C(Q,w,r,m) Learning Outcome #6 on Syllabus: By the end of this course you will be able to explain how a production manager would choose inputs to minimize the total cost of producing any required level of output…You will be able to apply the optimal choice model for producers to show the relationship between production functions, cost curves and supply curves in the short run and in the long run. Production Process Q Amount of Steel Northwestern University ECON 310-1: Microeconomic Theory Professors Jim Hornsten and Ron Braeutigam Winter 2012 Minimizing Costs: Setting the Stage L K • Qo = 100 • • • • Assume the firm must produce Q = 100 Exogenous Variable: Q Endogenous Variables: K and L Constraint: Firm must choose K and L so that f(K,L) = Q . Question: Which point on the isoquant should the firm choose? Answer: The one that minimizes cost! The firm’s ability to choose K and L may also depend on other constraints. In the short run the firm may not be able to choose the levels of all factors. Long Run: A time period (planning horizon) for the firm long enough for the firm to vary all factors of production as the firm desires. Short Run: A time period (planning horizon) in which the firm regards one or more factors of production as fixed. Northwestern University ECON 310-1: Microeconomic Theory Professors Jim Hornsten and Ron Braeutigam Winter 2012 Minimizing Costs in the Long Run K L C 3 / r Q= 20 A D B Directions of increasing cost C 2 / r C 1 / r C / r C C 1 C 2 C 3 The cost-minimizing exercise (in the long run): Let w = the factor price of labor (i.e., the wage rate) r = the factor price of capital (equivalent rental price) C = the total expenditure of the firm = wL + rK Production target is Q = 20....
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## This note was uploaded on 02/16/2012 for the course ECON 310-1 taught by Professor Schulz during the Winter '08 term at Northwestern.

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Lect16310-1W2012Cost and Duality [Compatibility Mode] -...

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