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A2+Basic+Production+Function

A2+Basic+Production+Function - The family’s harvest in...

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Frank Chapter 9 (Blue Book) K = 4 q = 4K 1/2 L 1/4 What is the Short Run Production Function? What is the Short Run Average Total Product of Labor? What is the Short Run Marginal Product of Labor? What is the Short Run Average Total Product of Capital? What is the Short Run Marginal Product of Capital? Starting with the production function, q = L 1/3 K 2/3 , answer the following questions 1. Suppose K = 27, how much labor is needed to produce 90 units of output? 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 r. The family can also lease machinery time from the local cooperative equipment shed. The charge for the machine use is v.
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Unformatted text preview: The family’s harvest in thousands of bushels is represented by q. Assume that the family has signed contract with their neighbor to lease out all but 16 acres of their land. They are keeping these 16 acres in production. (7 points) What is the farm’s production function for this period? (7 points) 1) Production Function a) Three Equations i) Why q and not Q ii) Total Product (1) TP = q(X 1 ,X 2 ) iii) Marginal Product (1) MP 1 = δ q(X 1 ,X 2 )/ δ X 1 iv) Average Product (1) ATP 1 = q(X 1 ,X 2 )/X 1 (2) In common parlance, productivity refers to average productivity Answers TP = q = 8L 1/4 AP L = 8L-3/4 MP L = 2L-3/4 AP K = 2L 1/4 MP K = n/a q = L 1/3 (27) 2/3 = 9 L 1/3 = 90 L = 1,000 TP = 32 K 1/2...
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