Question

a consumer's utility function is given as U(x,y)= ln( x+2*y-y^2/2) where x and y are two goods of consumption . (a) find indirect utility function of the consumer (b) examine if roy's law is satisfied by the consumer's demand functionfor y. (c) find the expenditure function of the consumer e(p,u) where price of x=1 and price of y=p (d) find the hicksian demand function hy (p,u) for commodity y, where the price of x is 1 and the price of y is p.