# Production functions and cost

Please see the attached file for full problem description.

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4

The production of barstools (q) is characterized by a production function of the form

a. Derive general expressions for average productivity of labor and capital for barstool production as functions of K and L. (Hint: By definition, = q/L and = q/K)

b. Graph and curve for K=100

c. Graph the q= 10 isoquant. Show all K-L combinations in a table.

d. The point K=10, L=10 is one point on the q =10 isoquant. What value of K corresponds to L= 11 on that isoquant? What is the approximate value for the RTS at K = 10, L=10?

5

Qin is a wheat farmer in the southern part of China. Being one of many, he is a price taker in the market for wheat. The current market price of wheat is 1400 yuan1 per ton. The costs of producing wheat are given by

Total cost = 0.5 q2 + 400 q + 1000 Marginal cost = q + 400

where q = the quantity of wheat (in tons) Qin chooses to produce every season

a. What is the profit maximizing quantity that Qin should produce?

b. Calculate Qin's maximum profits.

c. Derive the expression for average cost. Draw AC, MC and MR and show the Qin's profit maximizing choice in your graph.

6

The costs of production are given as follows:

Total cost = 50,000 + 200q + 0.5 q2 Marginal cost = 200 + q

a. Compute the level of output that minimizes AC.

b. Calculate AC and MC at the cost minimizing level of output.

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