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.

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Business

Duckling

7 December, 08:21

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.

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Logan Brennan · 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