Exam 6: Revealed Preference

Hillary has an initial endowment of $500 and is interested in two things: how many visits she can make to the doctor and how much money will be left over to spend on other things. When a trip to the doctor costs $50, Hillary sees the doctor 7 times. After health care reform, a visit to the doctor will cost $10 but her taxes will rise by $360.

On the planet Homogenia, every consumer who has ever lived consumes only two goods, x and y, and has the utility function U(x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900, the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 72 fragels. In 2000, the price of good 1 was 5 fragels and the price of good 2 was 2 fragels. The Laspeyres price index for the price level in 2000 relative to the price level in 1900 is

Let A stand for the bundle (7, 9), B stand for the bundle (10, 5), and C stand for the bundle (6, 6). When prices are (2, 4), Betty chooses C. When prices are (12, 3) she chooses A.

Twenty years ago, Amanda consumed cans of motor oil which cost her 6 pesos each and gallons of gasoline which cost her 14 pesos each. With her income of 112 pesos, she bought 7 cans of motor oil and 5 gallons of gasoline. Today she has an income of 230 pesos. Cans of motor oil now cost 10 pesos each and gallons of gasoline now cost 32 pesos each. Assuming her preferences haven't changed, she

Tonal is a traveling substitute orchestra conductor. Each year, he starts in Ann Arbor, moves to Brownsville, then to Carson City, and so on until he reaches Zilvania, Ohio, after which he returns to Ann Arbor. He gets a salary according to the following simple rule. In Brownsville he is paid what his Ann Arbor consumption bundle would cost in Brownsville. In Carson City he is paid what his Brownsville bundle would cost in Carson City, and so on. After 26 two-week stints, he returns to Ann Arbor, where he is paid the cost in Ann Arbor of his Zilvania bundle. At each stop, he spends his entire salary on apples (A) and paperback books (B), so as to maximize the utility U = AB. Over the course of the year, his utility will

When the prices were ($4, $1), Maria chose the bundle (x, y) = (8, 6). Now at the new prices, (p_x, p_y), she chooses the bundle (x, y) = (7, 9). For Maria's behavior to be consistent with the weak axiom of revealed preference, it must be that

Prudence was maximizing her utility subject to her budget constraint. Then prices changed. After the change, she is better off. Therefore the new bundle costs more at the old prices than the old bundle did.

The Laspeyres index of prices in period 2 relative to period 1 tells us the ratio of the cost of buying the period 1 bundle at period 2 prices to the cost of buying the period 1 bundle at period 1 prices.

Pierre's friend Henri lives in a town where he has to pay 3 francs per glass of wine and 5 francs per loaf of bread. Henri consumes 5 glasses of wine and 4 loaves of bread per day. Bob has an income of $15 per day and pays $.50 per loaf of bread and $2 per glass of wine. If Bob has the same tastes as Henri and if the only thing that either of them cares about is consumption of bread and wine,

An increase in the price of an inferior good makes the people who consume that good better off.

Hillary has an initial endowment of $500 and is interested in two things: how many visits she can make to the doctor and how much money will be left over to spend on other things. When a trip to the doctor costs $40, Hillary sees the doctor 4 times. After health care reform, a visit to the doctor will cost $10 but her taxes will rise by $160. a. Explain what conditions are necessary for Hillary to be made better off by health care reform. b. Is it possible to tell whether Hillary has been made better off with the given information? c. Explain what conditions are necessary for Hillary to be made worse off by health care reform. d. Is it possible to tell whether Hillary has been made worse off with the given information?

The strong axiom of revealed preference requires that if a consumer chooses x when he can afford y and chooses y when he can afford z, then he will not choose z when he can afford x.

Desmond has lived in Australia, Belgium, and Canada. His tastes never changed but his income and prices did. In Australia his commodity bundle was (x₁, x₂) = (7, 8), in Belgium it was (9, 4), and in Canada it was (7, 5). Prices in Canada were (p₁, p₂) = (3, 3), and prices in Australia were (p₁, p₂) = (3, 3), and prices in Australia were (p_1, p ₂) = (16, 4).

Consider the case of Ronald. Let the prices and consumptions in the base year be as in situation D, where p₁ = 3, p₂ = 1, x₁ = 5, and x₂ = 15. If in the current year, the price of good 1 is $1 and the price of good 2 is $2, and Ronald's current consumptions of good 1 and good 2 are 25 and 25 respectively, what is the Laspeyres price index of current prices relative to base year prices? (Pick the most nearly correct answer.)

On the planet Hyperion, every consumer who has ever lived has a utility function U(x, y) = min{x, 2y}. The currency of Hyperion is the doggerel. In 1850 the price of x was 1 doggerel per unit and the price of y was 2 doggerels per unit. In 2000 the price of x was 11 doggerels per unit and the price of y was 4 doggerels per unit. The Paasche price index of prices in 2000 relative to prices in 1850 is

Recall that the Laspeyres price index (P.I.) uses the old bundle as weights and the Paasche price index uses the new bundle as weights. If the prices of all goods double and your income triples,

There are two goods, bananas and potatoes. The price of bananas increases and the price of potatoes decreases. If after the price change a consumer (whose preferences satisfy WARP) can still exactly afford her old consumption bundle, then she will consume at least as many potatoes as before, even if potatoes are a Giffen good.

On the planet Hyperion, every consumer who has ever lived has a utility function U(x, y) = min{x, 2y}. The currency of Hyperion is the doggerel. In 1850 the price of x was 1 doggerel per unit and the price of y was 2 doggerels per unit. In 2000 the price of x was 8 doggerels per unit and the price of y was 4 doggerels per unit. The Paasche price index of prices in 2000 relative to prices in 1850 is

If a consumer maximizes a utility function subject to a budget constraint and has strictly convex preferences, then his behavior will necessarily satisfy the weak axiom of revealed preference and the strong axiom of revealed preference.

On the planet Homogenia, every consumer who has ever lived consumes only two goods, x and y, and has the utility function U (x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900, the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 96 fragels. In 2000, the price of good 1 was 4 fragels and the price of good 2 was 5 fragels. The Laspeyres price index for the price level in 2000 relative to the price level in 1900 is