(1) suppose you win a state lottery. the prize is $1,000,000 but it is paid over 10 years in equal installments of $100,000 each. what is the prize actually worth?

2. Consider the utility function U(x, y) = 3x - y with MUx = 3 and MUy = -1.
a) Is the assumption that more is better satisfied for good x? Is it satisfied for good y?
b) Does the marginal utility of x diminish, remain constant or increase as the consumer buys more x?
c) What is MRS?
d) Is MRS diminishing, constant or increasing as the consumer substitutes x for y along an indifference curve?
e) On a graph with x on the horizontal axis and y on the vertical axis draw a typical indifference curve when utility level is U1.
f) On the same graph draw a second indifference curve U2 with U2 > U1.

3. Jane's utility function is U(x,y) = 2 x2 y with associated marginal utility functions MUx = 4xy and MUy = 2x2. Jane has income I and prices of x and y are respectively given by Px and Py.
a) Determine Jane's demand for x as a function of income and prices.
b) Assume now that her level of income and prices are set at the following values: I = 30, Px = 2, Py = 1. Determine her choices of x and y and compute the level of utility she gets.

4. Paul consumes apples and bananas. His utility function is U(a,b)=a1/2+b. The price of bananas is Pb=4. The price of apples is initially Pa=1 but then rises to Pa=2. Paul's income is I=10.
a) Compute Paul's demand for apples and bananas before the price change.
b) Compute Paul's demand for apples and bananas after the price change.
c) How much income do we need to give Paul after the price increase in order to keep him as happy as he was before? i.e. in order to keep him at the same level of utility he had before the price change?