Exam 7: Slutsky Equation

Ernest's income elasticity of demand for natural gas is 0.4. His price elasticity of demand for natural gas is -0.3, and he spends 10% of his income on natural gas. What is his substitution price elasticity?

Walt considers x and y to be perfect substitutes. They originally cost $10 and $9 respectively. His income is $720. One day the price of x drops to $8.

What conditions ensure that the quantity of a good demanded increases as its price falls? Explain your answer, using diagrams.

Maude thinks delphiniums and hollyhocks are perfect substitutes, one for one. If delphiniums currently cost $2 per unit and hollyhocks cost $3 per unit and if the price of delphiniums rises to $7 per unit,

Jessica's preferences for peanut butter and jelly are represented by the utility function U(p, j) = min{ 2p, 5j}. If prices and income change, but her old consumption bundle lies somewhere on her new budget line, she will not change her consumption.

The following can be said about the income and substitution effects of a price increase on the demand for a good whose price rose:

Suppose that Agatha has $825 to spend on tickets for her trip. She intends to spend the entire amount $825 on tickets and prefers traveling first class to traveling second class. She needs to travel a total of 1,500 miles. Suppose that the price of first-class tickets is $.60 per mile and the price of second-class tickets is $.30 per mile. How many miles will she travel by second class?

Charlie's utility function is x_Ax_B. The price of apples used to be $1, the price of bananas used to be $2, and his income used to be $40. If the price of apples increased to $6 and the price of bananas stayed constant, the substitution effect on Charlie's apple consumption would reduce his consumption by

Carlos consumes only two goods, apples and bananas. His utility function is given by U(x, y) = a³b². He is endowed with w_a apples and w_b bananas. Unaware that prices are about to change, Carlos buys the quantities of apples and bananas that maximize his utility subject to his budget constraint. After he has made his purchases but before he has eaten them, the relative prices change. Carlos is then free to make further trades at the new relative prices if he wishes.

Suppose that Agatha has $465 to spend on tickets for her trip. She intends to spend the entire amount $465 on tickets and prefers traveling first class to traveling second class. She needs to travel a total of 1,500 miles. Suppose that the price of first-class tickets is $.40 per mile and the price of second-class tickets is $.10 per mile. How many miles will she travel by second class?

A taxpayer says, "Sure I pay a lot of income tax, but I don't mind because I get back just as much money as I pay in." Assuming that his facts are correct, explain why the taxpayer's reasoning is faulty. Use a diagram to show that an income tax can make a person worse off even if he is rebated an amount of money equal to what he paid in.

Draw two different diagrams, one illustrating the Slutsky version of income and substitution effects and the other illustrating the Hicks version of income and substitution effects. How do these two notions differ?

Charlie consumes apples and bananas. His utility function is U(X_A, X_B) = x_Ax²_B. The price of apples is $1 the price of bananas is $2, and his income is $30 per week. If the price of bananas falls to $1

John purchases two goods, x and y. Good x is an inferior good for some range of income. There must be another range of income for which good x is a normal good.

Rob consumes two goods, x and y. He has an allowance of $50 per week and is not endowed with either of the goods. If the price of good x increases and his substitution and income effects change demand in opposite directions,

When the price of a good rises and income remains constant, there is a substitution effect on demand but there cannot be an income effect.

Goods 1 and 2 are perfect complements and a consumer always consumes them in the ratio of 2 units of good 2 to 1 unit of good 1. If a consumer has an income of $300 and if the price of good 2 changes from $5 to $6, while the price of good 1 stays at $1, then the income effect of the price change

Goods 1 and 2 are perfect complements and a consumer always consumes them in the ratio of 2 units of good 2 to 1 unit of good 1. If a consumer has an income of $120 and if the price of good 2 changes from $3 to $4, while the price of good 1 stays at $1, then the income effect of the price change

Waldo consumes only apples and bananas and bananas are an inferior good for him. The price of apples increases, but there is an increase in his income that keeps him on the same indifference curve as before. (Waldo has convex preferences, and he prefers more to less of either good.)

Suppose a consumer has strictly convex preferences and her Engel curve for a good is a vertical line for some range of income. In that same income range, her demand curve for the good slopes down.