Use the production function: q = 4l1/2k1/2. refer to scenario 3. suppose that the price of labor is $5 and the price of capital is $20. your firm desires to produce 200 units of output. how much labor will be hired to minimize the costs of producing 200 units of output?

100 labor will be hired to minimize the costs of producing 200 units of output.

Explanation:

Maximising profit

Profit (Pr) = P*Q - Cost

                = P*Q - 5L - 20K

                 = P*4(LK)^0.5 - 4L - 20K

       dPr/dL= P*2(K/L)^0.5 - 4 = 0

       dPr/dK = P*2(L/K)^0.5 - 20 =0

We know equilibrium condition

MPL/MPK = w/ r

                 = 5/20

                  = 0.25  

MPL = 2(K/L)^0.5  MPK = 2(L/K)^0.5

K/L = 0.25

K = 0.25L

200 = 4(0.25L^2)^0.5

       =4*0.5*L

L = 100

Therefore, 100 labor will be hired to minimize the costs of producing 200 units of output.

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