Question:

a) Show that the Cobb-Douglas production function is homogeneous of degree (a+b) in labor and capital and that the marginal products of labor and capital are each homogeneous of degree (a+b-1) in labor and capital.

b) For the following functions find numerical values of x and y that satisfy the first order conditions a maximum.

i. f(x,y)=ln(xy)-(x+y)²

ii. f(x,y)=3ln(x-a)+ln(y-x-by)

c) Find the total differential of each of the following functions:

i. f(x,y)=ax²+bxy+cy²

ii. f(x,y)=(xy)^1/2

iii. f(x,y,z)=Ax^ay^bz^c