Question:

1. 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.
2. 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)=ax ² +bxy+cy ²

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

iii) f(x,y,z)=Ax ^a y ^b z ^c

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