Question

Consider the following firm with its demand, production and cost of production functions:

(1) Demand: Q = 230 – 2.5P + 4*Ps + .5*I, where Ps = 2.5, I = 20.

(2) Inverse demand function [P=f(Q)], holding other factors (Ps = 2.5 and I =20) constant, is, P=100-.4*Q.

(3) Production: Q = 1.2*L - .004L2 + 4*K - .002K2;

(4) Long Run Total Cost: LRTC = 2.46*Q + .00025*Q2 (Note: there are no Fixed Costs);

(5) Total Cost: TC = 1*L + 10*K.

Use equations (2), (3) and (5) to find the profit-maximizing Q and P.

a.) Q (quantity)

b.) P (price)

Based on equations (2), (3) and (5), what is the cost-minimizing combination of L and K for the profit-maximizing level of Q?

c.) cost minimizing L (labor)

d.) cost minimizing K (capital)

Answer 1