Exam 6: A: Revealed Preference

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 4 doggerels per unit and the price of y was 4 doggerels per unit. Paasche price index of prices in 2000 relative to prices in 1850 is

Let us reconsider the case of Ronald in Problem 4. 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 $3, and his current consumptions of good 1 and good 2 are 25 and 20 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 10 doggerels per unit and the price of y was 4 doggerels per unit. Paasche price index of prices in 2000 relative to prices in 1850 is

In Problem 1, if the only information we had about Goldie were that she chooses the bundle (6, 6) when prices are (6, 7) and she chooses the bundle (10, 0) when prices are (2, 5), then we could conclude that

In Problem 3, Pierre's friend Henri lives in a town where he has to pay 3 francs per glass of wine and 2 francs per loaf of bread. Henri consumes 10 glasses of wine and 4 loaves of bread per day. Recall that 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 the consumption of bread and wine,

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 84 fragels. In 2000, the price of good 1 was 3 fragels and the price of good 2 was 4 fragels. The Laspeyres price index for the price level in 2000 relative to the price level in 1900 is