The production function for producing parkas is given by q=100KL. If the price o

Question

The production function for producing parkas is given by q=100KL. If the price of capital is $120 per day and the price of labor is $30 per day, what is the optimal combination of capital and labor that minimizes the cost of producing 100,000 parkas? Need a Letter Answer

A. 10, 400 B. 400,10 C. 5, 200 D. 200,5

The production function for producing parkas is given by q=100KL. If the price of capital is $120 per day and the price of labor is $30 per day, what is the optimal combination of capital and labor that minimizes the cost of producing 100,000 parkas? Need a Letter Answer

A. 10, 400 B. 400,10 C. 5, 200 D. 200,5

Explanation / Answer

optimum compbination will be obtained when MPL/MPK = w/r

here MPL = dq/dL

=d(100KL)/dL

= 100k

and MPK =dq/dK

=d/dK(100KL)

=100L

so as w=$30 and r=$120

so from equation MPL/MPK = w/r

=> 100K/100L =30/120

=> K/L = 1/4 ---(1)

also as given q= 100,000

so 100,000 = 100KL

=> KL =1000---(2)

so solving (1) and (2) , we get

K= 5 ,L=200

so ans:C

ans: C

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