A contractor for the U.S. Defense Department products airplanes from capital (K)

Question

A contractor for the U.S. Defense Department products airplanes from capital (K) and labor (L) by the production function: A = K times L2

The marginal product of labor (MPL) = 2KL

the marginal product of capital (MPK) = L2

The Defense Department is ordering 125 airplanes.

a. How mych labor and capital will the firm employ if labor costs twice that of capital? (Hint: Let 2 = $2 and r = $1. Use MPL/MPk = w/r to find L in terms of K. Then substitute this into the production function for A = 125.)

b. How much capital and labor will the firm use if capital costs twice that of labor ?

Explanation / Answer

A = KL^2

Mpl = 2KL

Mpk =L^2

MRTS = 2KL/ L^2

FOR COST MINIMIZATION ... MRTS = W/R =2 .............. GIVEN

2KL/L^2 = 2

K= L

.......................

PUTTING BACK INTO A ..

125 =A = L^3

K=L= 5

......................................................................................................................

following same procedure as above but using different w and r values as given in second part

IF W =1 AND R =2

2KL/L^2 = 1/2

K=L/4

PUTTING BACK TO A

125= A = L/4 L^2

125*4 =L^3

L = 5*CUBEROOT (4)

K= 5/4 * CUBETOOT (4)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.