1. For each of the following statements, define all of the underlined terms. Then, explain why the statement is true, false or uncertain.

(a) If a consumer views two goods as perfect substitutes then their optimal choice will be a corner solution.

(b) The substitution effect from a price increase states that the consumer will always choose a smaller amount of that good to consume. However, the income effect states that consumption can move in either direction.

(c) Suppose Alf and Bo have convex indifference curves. Alf likes units of "X" more than units of "Y" but Bo likes units of "Y" much more than units of "X." Then, in the optimum, Alf's marginal rate of substitution will be different from Bo's even if they face the same prices.

(d) All Giffen goods are normal goods, but not all normal goods are Giffen goods.

(e) Economists assume that preferences are ordinal. This implies that given two utility functions and one is a monotonic transformation of the other, then they represent the same preferences over bundles of goods.

2. A Californian student consumes Internet services (I) and books (B). Her preferences are represented by a Cobb-Douglas utility function of the type: U(I, B) = I 0.5B0.5 . Initially Y = 100, PI = PB = 1. Lately, however, because of the electricity shortage, the price of the Internet services has increased to 2. The government has decided to give a transfer to the student so that she can recover her initial welfare. In order to determine the transfer the government has hired three consultants who have made the following suggestions:

Consultant A: The transfer should allow the student to buy her initial bundle.

Consultant B: The transfer should allow the student to get her initial level of utility.

Consultant C: The government should give her a transfer of 20.

(a) Using the expenditure function, find the amount of the transfer implied by consultant A.

(b) Find the amount of the transfer implied by consultant B.

(c) Determine whether the consumer is better or worse off from Consultant C's suggestion than before the price increases.

3. A Californian student consumes Internet services (I) and books (B). Her preferences are represented by a Cobb-Douglas utility function: U(I, B) = I 1/4B1/4 The prices of each good is $2 and the student has an income of $200. Over the course of the past year, the price of internet services has risen to $4, but the price of books has remained the same. The government has decided provide this student with additional money to compensate for the higher price of internet services. In order to determine the transfer the government has two consultants who have made the following suggestions:

Consultant A: The student's income should be increased by a percentage found using a consumer price index (CP I).

Consultant B: The additional income should allow the student to get her initial level of utility.

(a) Find the consumer's optimal bundle before the increase in price occurs.

(b) Find the consumer's optimal bundle after the increase in price occurs with income still at $200.

(c) Find the amount of the transfer implied by consultant A.

(d) Is the student necessarily better or worse off than before from such a transfer implied by consultant A? Explain why.

(e) Is the transfer implied by consultant B more or less than the amount implied by A? Explain. What is the precise dollar amount implied by consultant B?