please teach explain step by step Consider a government that raises money in a two-good economy by taxing good 1 at a rateof t per unit. The government is considering replacing these taxes with a lump-sum taxto the consumer that raises the same revenue. Thus, if the consumer consumes a units ofgood 1 before the change in taxes, she must pay the government a lump sum of te afterthe change. Suppose, moreover, that prices change only by the amount of the tax; i.e., ifprices are (p₁ +t, p2) before the change, then they become (p₁, p2) after. Let z = = (1, ₂) bethe consumer's demand before the change, and r' = (₁, 2) the consumer's demand after.Suppose that xx¹.(a) Is one of r or a' revealed preferred to the other (and if so, which)?Solution: The budget constraint before the change is (p₁+t)ã₁+p22 ≤ w and after thechange is p₁₁+p2₂Ã2 ≤ w− tx₁. Since x = (x1,x2) satisfies the first budget constraint,it must also satisfy the second one. Hence r is affordable after the change when x' ischosen. Therefore, r' is revealed preferred to 2. Depending on the choices, x may ormay not be revealed preferred to r'; it is impossible to determine.(b) Assuming that the consumer's demand satisfies the Weak Axiom of Revealed Preference,does the change in taxes lead to an increase or decrease in consumption of Good 1, or isit impossible to determine? What about Good 2?Solution: The first coordinate of the point of intersection of the budget lines underthe two regimes is exactly r₁. Therefore, any bundle with less than ₁ of Good 1 that isaffordable under the lump-sum tar is also affordable under the per unit tax. Since (x1, x₂)is chosen under the per unit tax, WARP implies that r₁ > x₁, i.e. the change leads to anincrease in consumption of Good 1. If the choices also lie on the corresponding budgetlines, then this implies a decrease in consumption of Good 2. In general, however, theeffect on consumption of Good 2 is impossible to determine.

According to the Revealed Preference Theory, a consumer's preferences may be deduced from the kinds…

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 2 units of good 1 before the change in taxes, she must pay the government a lump sum of te 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 = (1, ₂) be the consumer's demand before the change, and z' = (₁, ₂) the consumer's demand after. Suppose that x = x¹. (a) Is one of r or a' revealed preferred to the other (and if so, which)? Solution: The budget constraint before the change is (p₁+t)ã1+prỡ2 ≤ w and after the change is piã₁ + P2Ã2 ≤ w− tx₁. Since x = = (1, 2) satisfies the first budget constraint,

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 2 units of good 1 before the change in taxes, she must pay the government a lump sum of te 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 = (1, ₂) be the consumer's demand before the change, and z' = (₁, ₂) the consumer's demand after. Suppose that x = x¹. (a) Is one of r or a' revealed preferred to the other (and if so, which)? Solution: The budget constraint before the change is (p₁+t)ã1+prỡ2 ≤ w and after the change is piã₁ + P2Ã2 ≤ w− tx₁. Since x = = (1, 2) satisfies the first budget constraint,

Principles of Economics, 7th Edition (MindTap Course List)

7th Edition

ISBN:9781285165875

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter6: Supply, Demand And Government Policies

Section: Chapter Questions

Problem 5QR

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