Answer to Question #250103 in Microeconomics for Nana

Question

A firm has a Cobb-Douglas production function given as q=ALαKβ

a. Solve for the factor demand functions

b. If the firms’ competitive output price is p find the wage rate

c. What is the share of the firm’s revenue paid to labour and capital?

d. If α=0.6, β=0.2 and A=1 find the LR labour and capital demand curve equations

Answer 1

Qn. A

For conditional factor demand of capital we haveα

K=K(r, w,Q)

r=rate, w=wage, Q=Quantity

We maintain w and Q as constants, so we have them as Wo and Qo

Thus resulting to our Capital factor demand function as;

K=K(r)

Similarly, for conditional factor demand in labour we have;

L=L(r, W,Q)

r=rate, W=wage, Q=Quantity

Having W and Q as constants, represented in the function as Wo and Qo

Thus resulting Labour factor demand function is;

L=L(r)

Qn. B

Wage rate= MPL

MPL(AlαKβ)

Wage rate AαKβ

Qn. C

Firm revenue paid to labour is;

MPL*Q

MPL=AαKβ

MPL*Q=Q*(AαKβ)

=Q(AαKβ)

Firm revenue paid to capital is;

MPK*Q

MPK(AlαKβ)

MPK=ALαβ

MPK*Q=Q*(ALαβ)

=Q(ALαβ)

 

Qn. D

q=ALαkβ

Demand equation for labour =(AαKβ)

Replacing the values of α, β and A we have;

Q=0.6K0.2

Q=1.2K

Demand equation for capital =(ALαβ)

Replacing the values of α, β and A we have;

Q=L*0.6*0.2

Q=1.2L