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2. Suppose Geralt provided village defense services (D) using two inputs: silver (R), and steel (L)....

2. Suppose Geralt provided village defense services (D) using two inputs: silver (R), and steel (L). Geralt’s production function is D=R1/4 L1/4 . He sells village defense in a competitive market at a price of 50 orens. Silver costs 4 orens per unit, and steel costs 2 orens per unit.

a. Write down the Geralt’s profit function. (3 points)

b. Suppose in the short run, steel is fixed at L=16. Find the first order condition for the shortrun profit maximizing amount of silver. (4 points)

c. Solve for the amount of silver that Geralt uses in the short run to maximize profit. (5 points)

d. In the long run, both inputs are variable. Find the first order conditions for the long-run profit maximizing amounts of both inputs. (7 points)

e. Solve for the amount of silver and steel that Geralt uses to maximize profit in the long run. (6 points)

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