Question

Solve the following:

a)If production is Y=K^1/2L^1/2 and the rental rate is $10 while wages are $5; if the firm produces then the firm will use:

A) it is not possible to tell with the information given

B) a greater number of machines than laborers

C) Zero of either inputs since profits are negative

D) a greater of laborers than machines

E) an equal number of laborers and machines

b) If the marginal product of labor is higher than the marginal product of capital: then the firm will

A) always use more labor than machines

B) always use labor than machine

C) always use more machines if rental rates are sufficiently low

D) always use equal amounts of labor and machines

c) if the production function is Y= min (K, L) and the rental rate is $25 while wages are $5; if the firm produces then the firm will use

A) a greater of laborers than machines

B) a greater of machines than laborers

C) zero laborers

D) an equal number of laborers and machines  

E) Zero machines

d) Nadine has a production function Y=4k+L. If r=$10 and W=$1, how much will the cost her to produce 70 units of output?

A) 140

B) 70

C) 700

D) 1,260

E) 105

e) if q = 2K + L and r=w$5 and c=300 then

A) k=20, l=40

B) k=60, l= 0

C) k=30, l=30

D) k=40, l=20

E) k = 0, l=60

Answer 1

a) D) a greater of laborers than machines
(Firm will use the combination where MRTS = w/r
MRTS = MPL/MPK = (dY/dL)/(dY/dK) = K1/2(1/2)L(1/2)-1/(1/2)K(1/2)-1L1/2 = K1/2L-1/2/K-1/2L1/2 = K/L
So, K/L = 5/10 = 1/2
So, K = L/2
Thus, more L will be used.)

b) A) always use more labor than machines
(As MPL is higher, so more L will be used.)

c) D) an equal number of laborers and machines  
(For such a function, K = L)

d) B) 70
(MRTS = MPL/MPK = (dY/dL)/(dY/dK) = 1/4 = 0.25 > w/r = 1/10 = 0.1
So, only L will be used.
Y = 70 = L
Cost = wL = 1*70 = 70)

e) B) k=60, l= 0
(MRTS = MPL/MPK = (dY/dL)/(dY/dK) = 1/2 = 0.5 < w/r = 1/1 =1
So, only K will be used.
rK = 5K = 300
So, K = 300/5 = 60)