With the following condition: UxxUx^2-2UxyYxUy+uyyUy^2<0 check the convexity of the indifference curves for each of the following functions and describe the precise relationship between diminishing marginal utility and quasi-concavity for each case.

A. U(x,y)=3x+y

B.U(x,y)=(x.y)^1/2

C.U(x,y)=(x)^1/2+y

D.U(x,y)=(x^2-y^2)^1/2

E.U(x,y)=(xy)/(x+y)

(^1/2 used inplace for square root)

54. Explanation

Suppose there are two firms in an industry with marginal abatement cost curves:

MACA= 1,200-2EA

MACB= 800-2EB

If the regulator wants to use a transferable emission permit scheme to achieve industry abatement of 50%:

a. How many permits will it need to issue?

b. If each firm receives one -half of the permits at no charge initially, explain what permit trading will take place and calculate the total compliance cost of each firm under this form of regulation.

c. Compute gains of each party from the TEPs