A comsumer has the utility function U(x,y)=e^( (y+√x) ^ 1/3 ) where x is the good in concern and y is the money that can be spent on all other goods(so the price of y is normalized to be 1). The income of this consumer is 100.
(a)(10 pts)Derive the demand function of x for this consumer.
(b)(5 pts)Calculate the price elasticity of the demand function in (a). Is it true that the absolute value if the elasticity of the demand decreases as the amount of x increases?
(c)(10 pts)Suppose price if x decreases from 1/2 to 1/4. Calculate the compensating variation of this price change.