1. Albert's utility function is u(x, y) = xy. prepare alternate utility function for Albert's preferences. That is, provide a second utility function which produces same ranking for consumption bundles in Albert's choice set. Briefly describe why two utility functions rank bundles in the same way.
2. Bill's utility function is u(x, y) = (x + 4) y. Bill's income is $20, the price of X is $6 per unit, and price of Y is $1 per unit.
a. Draw indifference curve u(x, y) = 16.
b. How much of each good will Bill purchase?
3. Chris consumes two goods, X and Y. Price of X is $4 per unit and price of Y is $3 per unit. Chris's income is $48.
a. Plot Chris's budget constraint. Illustrate the values for intercepts and the slope.
b. Assume that Chris's utility function is u(x, y) = x^{2}y. How much X will he buy?
c. Now assume that seller of X offers quantity discount of following form.
First 8 units cost $4 per unit, but all subsequent units will cost just $2 each.
i. Depict change to Chris's budget constraint in graph for Part (a). Label any changes to intercepts or slope.
ii. Will the quantity discount affect Chris's consumption of X? If so, will he consume more or less, and how can you tell? (Hint: You mustbe able to answer this problem without doing any extramath if you consider the problem graphically.)