A6+Short+Run+Cost+Functions

# A6+Short+Run+Cost+Functions - They are keeping these 16...

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Frank Chapter 10 (Blue Book) Starting with the production function, q = L 1/3 K 2/3 , answer the following questions 1. Suppose K = 8, wages are \$4 and the opportunity cost of capital (price of capital) is \$1, what is the total cost function? 1. A firm has fixed costs of \$10,000 and an average variable cost of \$1 + \$0.01q. What is the firm’s short run total cost function? 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 z. 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. Assume that the family has signed contract with their neighbor to lease out all but 16 acres of their land.

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Unformatted text preview: They are keeping these 16 acres in production. (7 points) What is the marginal cost function? (7 points) 1) Formulas a) Cost Equation i) TC = P L L + P K K = wL + vK 2) Cost Function a) Three Equations i) Total Cost – total cost of producing any level of output (1) TC = c(w,v,q) ii) Marginal Cost – cost of adding one more unit of output (1) MP 1 = δ q(w,v,q)/ δ q iii) Average Cost – average cost of production per unit (1) TP = q(w,v)/q iv) Average Variable Cost v) Average Fixed Cost Answers: q = L 1/3 (8) 2/3 = 4L 1/3 L* = q 3 /64 TC = rK = wL = (1) (8) + (4) (q 3 /64) = 8 + q 3 /16 AVC = TC/q TC = AVC * q + FC = (\$1 + \$0.01q) (q) + \$10,000 = \$.01 q 2 + \$1 q + \$10,000 q = 16K 1/2 N 1/4 = 16K 1/2 (16) 1/4 = 32K 1/2 K* = q 2 /1024 TC = rK + zL = r q 2 /1024 + zL MC = TC q = rq/512...
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## This note was uploaded on 04/10/2008 for the course ECON 3150 taught by Professor Tittle during the Spring '08 term at Georgia Tech.

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A6+Short+Run+Cost+Functions - They are keeping these 16...

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