# Question: consumers surplus a consumer has the utility function uxy elnxy13...

###### Question details

Consumer's surplus: A consumer has the utility function U(x,y) =e^((ln(X)+Y)^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) (10pts) Derive the demand function of x for this consumer. Make sure that at every price of x, the consumer always has enough income to buy the amount of x as indicated by hiss demand function.

(b) (10pts) Calculate the price elasticity of the demand function in (a). Is it true that the absolute value of the elasticity of the demand decreases as the amount of x increases?

(c) (10pts) Suppose price of x decreases from 2 to 1. Calculate the change in consumer's surplus.

(d) (10pts) Suppose price of x decreases from 2 to 1. Calculate the compensating variation of this price change.

(e) (10pts) Suppose price of x decreases from 2 to 1. Calculate the equivalent variation of this price change .