# Finding optimal combination of inputs

Answer the following questions based upon the information given below

Q = K^(1/2)L^(1/2), WK = $20 WL = $5

1. What relative amounts of capital and labor will be employed to

maximize output?

a. equal amounts of capital and labor

b. four times as much labor as capital

c. twice as much capital as labor

d. none of the above

2 Having a budget of $16,000, what amounts of capital and labor will be

employed?

a. 200 units of K and 200 units of L

b. 400 units of K and 1600 units of L

c. 200 units of K and 1600 units of L

d. 100 units of K and 40 units of L

e. none of the above

3. If the proper amounts of K and L are employed

a. MRS should equal WL/WK

b. MPL/MPK should equal WL/WK

c. WK/MPL should equal WL/MPK

d. all of the above

e. two of the above

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#### Solution Preview

1. What relative amounts of capital and labor will be employed to

maximize output?

a. equal amounts of capital and labor

b. four times as much labor as capital

c. twice as much capital as labor

d. none of the above

Q = K^1/2L^1/2

Marginal Product of capital=MPK=dQ/dK=1/2*K^(-1/2)*L^1/2=0.5K^(-0.5)L^0.5

Marginal Product of labor=MPL=dQ/dL=K^1/2*(1/2)*L^(-1/2)=0.5K^0.5L^(-0.5)

For profit maximization, firm will employ its capital and labor such that

MPK/WK=MPL/WL

Given ...

#### Solution Summary

Solution describes the steps to calculate optimal combination of inputs.

Finding Optimal Combination of Inputs

Let the production function be given by

Q = K^1/2*L^1/2, WL=$5, WK=$20,

Suppose the plant size (K) is fixed in the short run at 100.

A. With K = 100, how many units of L are required to produce 400 units of

output?

a. 400

b. 100

c. 1600

d. 3200

e. none of the above

B. If this amount of labor (found in question A) is combined with 100 units of K:

a. MPL/WL = MPK/WK

b. MPL/WL > MPK/WK

c. MRS = WL/WK

d. MPK/WK > MPL/WL

e. Two of the above.