Given the Utility function U(X,Y) = X.5 + Y.5

1. Write mathematical expressions for marginal utility of x and marginal utility of y
2. Does the consumer the assumption of non-satiation (more is better) desire more of x and y?
3. If the quantity of Y is held constant, does the marginal utility of x increase, remain constant or diminish as x increases? Prove your answer
4. Derive an expression for the marginal rate of substitution of x for y.
5. If Price of X equals 1 and price of Y equals 1 and income equals $200, what utility maximizing quantity of x and quantity of y will the consumer choose.