F (Z1, Z2) = (Z1^a)*(Z2^b) Z1 and Z2 are both larger than 0

a.Show that if a + b = 1, the prot maximizing output is for some price vectors (p, w1, w2) equal to zero, for others the optimal supply is anything from zero to innity, and yet again for others it is innity.

b. Suppose a, b > 0 and a + b < 1. Find the prot function, the supply function and the factor demands. Verify that the prot function is convex in (p, w1, w2) and that it is homogeneous of degree 1. Verify that the factor demands are homogeneous of degree zero.