Question

A manufacturer has modeled its yearly production function P (the monetary value of its entire production in millions of dollars) as a Cobb-Douglas function P(L, K) = 1.47L0.65K0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). Find P(120, 30) and interpret it. (Round your answers to one decimal place.) P(120, 30) = , so when the manufacturer invests $ million in capital and thousand hours of labor are completed yearly, the monetary value of the production is about $ million.

Answer 1

Answer: P(120,30)= $1,218,365.5

So when the manufacturer invests $30 million in capital and 120,000 hours in labour yearly, the monetary value of production is about $1.2 million.

Explanation:

The Cobb-Douglas production function expresses the technological relationship between two inputs (labour and capital).

Since  

P(L,K)=1.47L^0.65 K^0.35 (equation 1)

we simply substitute L=120,000 and K=30,000,000 into equation 1.  

Thus, P(120,30)= 1.47(120,000)^0.65 (30,000,000)^0.35

(Recall that L is in thousand of hours and K is in millions of dollars).

P(120, 30)= 1.47(2002.02)(413.99)

Thus, P(120,30)= 1218365.475

P(120,30)= $1,218,365.5

P(120, 30)= $1.2 million

So when the manufacturer invests $30 million in capital and 120,000 hours in labour yearly, the monetary value of production is about $1.2 million