Question

Suppose a firm has a production function q = f(L, K) =2L + 4K, and the factor prices are w = $2 and r = $2. What is the minimum cost at which the firm is able to produce 20 units of output?

a. $10 b. $30 c. $45 d. $100 e. $50

please explain why

Answer #1

The production function is substitute production function, where the only input used with highest per input per dollar output is higher

MPL=dq/dL=2 and MPK=dq/dK=4 .......... first partial derivative of production function to find MP.

MPL/w=2/2=1

MPK/r=4/2=2

the per input-output is higher from K; it means the firm will use only capital

using the production function

q=2L+4K

20=2*0+4K

4K=20

K=5

the firm will use 5 units of capital to produce 20 units

the cost =K*r=5*2=$10

the cost of 20 units of production is $10

option a

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