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A7+Optimum+Long+Run+Choice+and+Expansion+Path

# A7+Optimum+Long+Run+Choice+and+Expansion+Path - (1 Lamda =...

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Frank Chapter 10 (Blue Book) Assume the production function q = 16K .5 N .25 represents a family farm. In this case, the family owns acres of land (N) that it can farm or rent each year. The rental rate for the land is f. The family can also lease machinery time from the local cooperative equipment shed. The charge for the machine use is r. The family’s harvest in thousands of bushels is represented by q. 1. What is the cost equation of this production function? (7 points) 2. What is the Expansion Path of this production function? (7 points)

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Cost Function i) Isocost curves ii) Minimize cost to a given output (1) Tangency solution iii) Maximize output to a given cost (1) Tangency solution iv) Lagrangian: Cost subject to Output
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Unformatted text preview: (1) Lamda = Marginal cost of output (2) Factor cost = marginal cost * marginal product of that factor = marginal revenue product of that factor (3) Solving for lamda and substituting, ratio of prices equals ratio of marginal products, which s mrts, hence, optimal solution is tangency between lines. v) Expansion path (1) Since w and v are fixed, a series of tangencies can be defined to show the mix of inputs for each level of output (2) Solve w/v = mrts for K and you have an expansion path Answers 1 TC = rK + fN 2 K = 2 (f/r) N N = (1/2) (r/f) K mp N = 4 K 1/2 N-3/4 mp K = 8 K-1/2 N 1/4 mp N = w = 4 K 1/2 N-3/4 mp K r 8 K-1/2 N 1/4 Solve for K (or N)...
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A7+Optimum+Long+Run+Choice+and+Expansion+Path - (1 Lamda =...

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