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Consider a government that raises money in a two-good economy by taxing good 1 at a rate of t per unit. The government is considering replacing these taxes with a lump-sum tax to the consumer that raises the same revenue. Thus, if the consumer consumes x units of good 1 before the change in taxes, she must pay the government a lump sum of tx after the change. Suppose, moreover, that prices change only by the amount of the tax; i.e., if prices are (p₁ +t, p2) before the change, then they become (P₁, P2) after. Let x = (x₁, x₂) be the consumer's demand before the change, and x' = (x₁, x2) the consumer's demand after. Suppose that x ‡x'. (a) Is one of x or x' revealed preferred to the other (and if so, which)?

Consider a government that raises money in a two-good economy by taxing good 1 at a rate of t per unit. The government is considering replacing these taxes with a lump-sum tax to the consumer that raises the same revenue. Thus, if the consumer consumes x units of good 1 before the change in taxes, she must pay the government a lump sum of tx after the change. Suppose, moreover, that prices change only by the amount of the tax; i.e., if prices are (p₁ +t, p2) before the change, then they become (P₁, P2) after. Let x = (x₁, x₂) be the consumer's demand before the change, and x' = (x₁, x2) the consumer's demand after. Suppose that x ‡x'. (a) Is one of x or x' revealed preferred to the other (and if so, which)?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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. Consider a government that raises money in a two-good economy by taxing good 1 at a rate of t per unit. The government is considering replacing these taxes with a lump-sum tax to the consumer that raises the same revenue. Thus, if the consumer consumes x units of good 1 before the change in taxes, she must pay the government a lump sum of tx after the change. Suppose, moreover, that prices change only by the amount of the tax; i.e., if prices are (p₁ + t, p2) before the change, then they become (P₁, P2) after. Let x = (x1, x2) be the consumer's demand before the change, and x' (x1, x2) the consumer's demand after. Suppose that x = x'. = (a) Is one of x or x' revealed preferred to the other (and if so, which)? Solution: The budget constraint before the change is (p₁+t)ã₁+p2ã2 ≤w and after the change is p₁₁ +p2x2 ≤ w − tx₁. Since x = (x1, x2) satisfies the first budget constraint, it must also satisfy the second one. Hence x is affordable after the change when x' is chosen. Therefore, x' is revealed preferred to x. Depending on the choices, x may or may not be revealed preferred to x'; it is impossible to determine.
Transcribed Image Text:. Consider a government that raises money in a two-good economy by taxing good 1 at a rate of t per unit. The government is considering replacing these taxes with a lump-sum tax to the consumer that raises the same revenue. Thus, if the consumer consumes x units of good 1 before the change in taxes, she must pay the government a lump sum of tx after the change. Suppose, moreover, that prices change only by the amount of the tax; i.e., if prices are (p₁ + t, p2) before the change, then they become (P₁, P2) after. Let x = (x1, x2) be the consumer's demand before the change, and x' (x1, x2) the consumer's demand after. Suppose that x = x'. = (a) Is one of x or x' revealed preferred to the other (and if so, which)? Solution: The budget constraint before the change is (p₁+t)ã₁+p2ã2 ≤w and after the change is p₁₁ +p2x2 ≤ w − tx₁. Since x = (x1, x2) satisfies the first budget constraint, it must also satisfy the second one. Hence x is affordable after the change when x' is chosen. Therefore, x' is revealed preferred to x. Depending on the choices, x may or may not be revealed preferred to x'; it is impossible to determine.
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According to the revealed preference theory, which was first put out by American economist Paul Samuelson in 1938, customers' preferences may be inferred from the things they buy when faced with various situations, especially those involving varying levels of income and price. 

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