Exam 6: Revealed Preference-Part A

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.

It follows from the weak axiom of revealed preference that if a consumer chooses x when he could afford y and chooses y when he could afford x, then his income must have changed between the two observations.

Twenty years ago, Dmitri consumed bread which cost him 10 kopeks a loaf and potatoes which cost him 20 kopeks a sack.With his income of 330 kopeks, he bought 9 loaves of bread and 12 sacks of potatoes.Today he has an income of 452 kopeks.Bread now costs him 22 kopeks a loaf and potatoes cost him 17 kopeks a sack.Assuming his preferences haven't changed (and the sizes of loaves and sacks haven't changed), when was he better off?

When prices are ($6, $3), Holly chooses the bundle (9, 18), and when prices are ($1, $2), she chooses the bundle (8, 14).

When prices are ($4, $2), Tomoko chooses the bundle (9, 18), and when prices are ($1, $2), she chooses the bundle (8, 14).

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 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

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 $4, and Ronald's current consumptions of good 1 and good 2 are 25 and 5 respectively, what is the Laspeyres price index of current prices relative to base year prices? (Pick the most nearly correct answer.)

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 $60, Hillary sees the doctor 2 times.After health care reform, a visit to the doctor will cost $10 but her taxes will rise by $100. 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?

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

At prices (p₁, p₂)= ($4, $2), Ivan buys the bundle (x₁, x₂)= (8, 20).At prices (p'₁, p'₂)= ($2, $4), he buys the bundle (x'₁, x'₂)= (10, 13).At prices (p''₁, p''₂), he buys the bundle (x''₁, x''₂)= (14, 11).If his preferences satisfy the strong axiom of revealed preferences, then it must be that

If Goldie chooses the bundle (6, 6)when prices are ($6, $2)and the bundle (10, 0)when prices are ($2, $5),

When prices are ($2, $4), Ms.Consumer chooses the bundle (7, 9), and when prices are ($15, $3), she chooses the bundle (10, 3).Is her behavior consistent with the weak axiom of revealed preference?

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

If all prices increase by 20%,

Remember that the Laspeyres price index uses the old quantities for the weights.In 1991, good x cost $2 and good y cost $1.The current price of good x is $6 and the current price of good y is $2.In 1971 the consumption bundle was (x, y)= (3, 6).The current consumption bundle is (x, y)= (6, 4).The Laspeyres index of current prices relative to 1991 prices is closest to which of the following numbers?

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 ($5, $1), Vanessa chose the bundle (x, y)= (6, 3).Now at the new prices, (p_x, p_y), she chooses the bundle (x, y)= (5, 7).For Vanessa's behavior to be consistent with the weak axiom of revealed preference, it must be that