Draw an indifference map for each of the following functions. U(x,y) = x2y3 U (x, y) = 2x + 3y U (x, y) =x + ln(y) U (x, y) = min{2x, 3y} U (x, y) = max{3x, 2y}

(b) It is thought that a consumer measures the utility, u(x, y), of possessing a quantity, z, of apples and a quantity, y, of oranges by the formula u(x, y) = rªyla, where a is a constant. Suppose that apples cost p dollars each and oranges q dollars each. If the consumer has M dollars to spend on apples and oranges, use the method of Lagrange multipliers to find the quantity of each that he will buy in terms of a, p, q and M. [You are not required to justify the use of the method of Lagrange multipliers here.] For equally priced apples and oranges when he has one dollar to spend, he is actually observed buying one apple and two oranges. What value of a does this imply?

A consumer has an annual budget constraint for two goods: “housing sq. ft." and "$ for everything else". Draw the budget constraint for this consumer if income (v) = $50,000 and price per sq. ft. of housing, ph, is S200. Please be sure to fully label your graph (i.e., slope, intercept, etc.). Note: plot "housing sq. ft." on the x-axis. How would this consumer's budget line change if she received a $5,000 raise and the price of housing increased to $250? Include a graph with your answer. How did the economic rate of substitution (ERS) between housing and $ for everything else change when pa changed? Please interpret the ERS both before and after the price change.

3. Let there be two goods x and y with prices px and py respectively, and let M be the consumer's income. Let the consumer's preferences be represented by the utility function min(2x, y). Find the consumer's expenditure function. Note: you cannot use the Lagrange method as the utility function is not differentiable - but you have used the min U = utility function before. (4)