Exam 7: Slutsky Equation

Jimmy's utility function is U(a, b) = ab, where a is his consumption of apples and b is his consumption of bananas. If prices and income change in such a way that Jimmy's old consumption lies on his new budget line, then Jimmy will not change his consumption bundle.

The Hicks version of the substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indifference curve as before the price change.

Suggest at least one reason why it might be worth the trouble it takes to learn how to decompose the effects of a price change into an income effect and a substitution effect.

Use a diagram to prove that in case there are two goods, the substitution effect of an increase in the price of good x reduces the demand for good x.

A rational consumer prefers more of good x to less. If the price of good x rises and the prices of all other goods remain constant, then the consumer must necessarily demand less of x.

Charlie's utility function is x_Ax_B. The price of apples used to be $1 per unit and the price of bananas was $2 per unit. His income was $40 per day. If the price of apples increased to $2.25 and the price of bananas fell to $1.25, then in order to be able to just afford his old bundle, Charlie would have to have a daily income of

In 2000, Bruce spent his income on two goods, x and y. Between 2000 and 2001, the price of good x rose by 8% and the price of good y rose by 8%. In 2001, Bruce bought the same amount of x as he bought in 2000, but he bought more of good y than he had bought in 2000.

The compensated demand function refers to the demand function of someone who is adequately paid for what he or she sells.

Charlie's utility function is x_Ax_B. The price of apples used to be $1 per unit and the price of bananas was $2 per unit. His income was $40 per day. If the price of apples increased to $1.50 and the price of bananas fell to $1.75, then in order to be able to just afford his old bundle, Charlie would have to have a daily income of

Cindy consumes goods x and y. Her demand for x is given by x(p_x, m) = 0.04m -4.24p_x. Now her income is $322, the price of x is $2, and the price of y is $1. If the price of x rises to $3 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS, then

Neville from your workbook has a friend named Peregrine. Peregrine has the same demand function for claret as Neville, namely q = .02m - 2p, where m is income and p is price. Peregrine's income is $6,500 and he initially had to pay a price of $50 per bottle of claret. The price of claret rose to $60. The substitution effect of the price change