A manufacturer estimates that the annual output at a certain

A manufacturer estimates that the annual output at a certain factory is given by Q(K,L)=32 K^(0.8) L^(0.2) units, where K is the capital expenditure in thousands of dollars and L is the size of the labor force in worker-hours. Suppose that the current capital expenditure is $490000 and the labor level is 610 worker-hours.

a. Find the current marginal productivity of capital QK.

ANSWER:

b. Find the current marginal productivity of labor QL.

ANSWER:

Q = 32K^0.8L^0.2 Q_k = dQ/dK = 32*0.8K^-0.2L^0.2 = 25.6*490^-0.2610^0.2 = 26.746485

And Q_L = dQ/dL = 32*0.2K^0.8L^-0.8 = 6.4*490^0.8610^-0.8 = 21.4848814

A manufacturer estimates that the annual output at a certain factory is given by Q(K,L)=32 K^(0.8) L^(0.2) units, where K is the capital expenditure in thousand

A manufacturer estimates that the annual output at a certain

Solution

Get Help Now

Submit a Take Down Notice