5. (30 points total) Suppose the utility function for an individual is u(x1, x2) = x1 0.75 x20.25 . The price of x1 is p1, the price of x2 is p2, and the individual's exogenous income is I.

1. a) (6 points) Set up the utility maximization problem and find the uncompensated demand function for x1.
2. b) (6 points) Derive the compensated demand function for x1.
3. c) (6 points) For a small increase in the price of x1, what is the total change in the quantity demanded for x1? Express your answer in terms of p1, p2, and I. How would you classify this good: normal, inferior, Giffen?
4. d) (6 points) Using the Slutsky Equation, calculate the substitution and income effects for the price change in the previous part. Again, express your answer in terms of p1, p2, and I.
5. e) (6 points) Assume that I = $1,000 and p1 and p2 are both $1. What is the maximum income tax that would not reduce the individual's utility by more than half?