Which of the following are monotonic transformations? (1) u = 2v − 13; (2) u = −1/v2; (3) u = 1/v2; (4) u = ln v; (5) u = −e−v; (6) u = v2; (7) u = v2 for v > 0; (8) u = v2 for v < 0.

For what kind of preferences will the consumer be just as well-off facing a quantity tax as an income tax?

If a consumer has a utility function u(x1, x2) = x1x4 2, what fraction of her income will she spend on good 2?

If two goods are perfect substitutes, what is the demand function for good 2?

Suppose that a consumer always consumes 2 spoons of sugar with each cup of coffee. If the price of sugar is p1 per spoonful and the price of coffee is p2 per cup and the consumer has m dollars to spend on coffee and sugar, how much will he or she want to purchase?

Suppose that indifference curves are described by straight lines with a slope of −b. Given arbitrary prices and money income p1, p2, and m, what will the consumer’s optimal choices look like?

. Suppose that you have highly non convex preferences for ice cream and olives, like those given in the text, and that you face prices p1, p2 and have m dollars to spend. List the choices for the optimal consumption bundles.

1. If the consumer is consuming exactly two goods, and she is always spending all of her money, can both of them be inferior goods?

Are hamburgers and buns complements or substitutes?

If the preferences are concave will the consumer ever consume both of the goods together?