Question

Suppose Gus wants to optimize when choosing quantity to produce too. Gus needs to decide how many hours of Walter's and Jesse's time to employ and how much equipment to buy. The production function is given by Q-KA(1/3) EA(1/3). The price of the product is $60,000, the cost of each unit of equipment is $1,000, and Jesse's wage is now $8,000/hr. Using the optimal ratio of employment to capital, find how much time Gus will have Walter and Jesse work.

Answer 1

Q = k^1/3 E^1/3 optimality condition is MP_L/MP_k = W/r = MP_E/MP_k MP_L = MP_E MP_E = k^1/3 (1/3)E^-2/3 MP_k = (1/3)k^-2/3 (E)^1/3 MP_E/MP_k = (k)^1/3 (1/3)E^-2/3/(1/3)k^-2/3(E)^1/3 = k/E k/E = 8000/1000 k/E = 8 implies k = 8E Q = (8E)^1/3 (E)^1/3 Q = 2E^2/3 implies E = (Q/2)^3/2 time implies E = (Q/2)^3/2