Lecture%205%20-%20Cost%2c%20Profit%2c%20Supply

Lecture%205%20-%20Cost%2c%20Profit%2c%20Supply - 1 Fin 501...

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Unformatted text preview: 1 Fin 501 Financial Economics Lecture 5: Cost Functions, Profit Maximization, Supply Functions. Professor Nolan Miller 2 Announcements Sorry for the cancelation. Problem Set #2 is available on Compass, due next Thursday. Ill decide what to do about problem set #3. Copies of the texts are available on the library reserve shelf. Nicholson & Snyder Intermediate Microeconomics, Microeconomic Theory Books that may be useful references when we cover finance applications, game theory, macroeconomics. 3 Production & Supply Firms have production functions. A profit maximizing firm must minimize cost. CMP: choose inputs to min. cost of producing Q units of output. Solution to CMP is conditional factor demand function. Cost Function gives minimum cost of producing Q units of output. 4 Production & Supply More about costs Total cost, average cost, marginal cost. Graphing cost curves Profit Maximization Supply Functions Short Run vs. Long Run considerations 5 Cost Minimization Now, we turn to the question of how the firm chooses K and L to minimize cost. Let v be the price of capital, w be the wage. The cost of (L,K) is: w L + v K. Suppose the firm wants to produce Q units of output. Then it solves the Cost Minimization Problem (CMP): min w L + v K subject to: F(K,L) Q Since producing output is costly, we know that the firm will not choose to produce more than Q. 6 Isocost Curves The firm wants to minimize cost. The set of (K,L) that has cost C is given by: v K + w L = C, or K = -w/v * L + C/v Isocost curves are lines with slope w/v. Lower costs are closer to the origin. K L K 1 L 1 These points have the same cost as (L 1 ,K 1 ) Cost decreases 7 Cost Minimization: Graphically Q 1 K L Can this point be optimal? Isocost line No. This point is cheaper and still produces Q 1 . But, is it optimal? Optimal point: tangency between isoquant and isocost line 8 Cost Minimization: Algebraically The cost-minimizing way to produce Q units of output: 1. Satisfies the production constraint: F(K * ,L * ) = Q . 1. Sets the MRTS = |slope of isocost|: These two conditions determine the solution. L K MP w MRTS MP v = - = 9 Interpreting the Tangency Condition The tangency condition can be rewritten as: w/MP L and v/MP K are the cost of producing a little more output using labor and capital, respectively....
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Lecture%205%20-%20Cost%2c%20Profit%2c%20Supply - 1 Fin 501...

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