please teach explain step by step A consumer has utilityu(x₁, x₂) = x₁ + x1x2.Suppose that, because of a shortage of good 1, the government imposes a strict upper limitof ₁ on the quantity of good 1 that the consumer can consume. Assume throughout thefollowing that w > p2.(a) Show that the consumer's preferences are strictly convex.Since preferences are monotone, this implies strict convexity.(b) Find the consumer's Marshallian demand if the consumer cannot violate the governmentlimit.(c) Find the consumer's expenditure function.(d) Suppose that p₁ = P2, w = 3p₁, and ₁ = 1. If the government removes the restrictionon consumption of good 1, the price of good 1 will rise from p₁ to p₁, and p2 and w willremain the same. For what values of p₁ and p₁ does the consumer prefer that the limitremain in place?(e) Suppose that, with the limit in place, the price of good 1 increases. If the consumerchooses ₁ = ₁ both before and after the price change, how does the compensatingvariation compare to the equivalent variation of this price change?£1(f) Consider a different consumer (i.e. one who may not be maximizing the given utilityfunction). Suppose that, when facing the same limit of ₁ on good 1, the consumerchooses ₁ <₁. If this consumer's choices satisfy the weak axiom of revealed preference,is it possible that she will choose ₁ > ₁ after the restriction is removed if, at the sametime, the price of good 1 increases (and the price of good 2 remains the same)? Youmay assume that p₁₁

Utility function : u(x1 , x2 ) = x1 + x1x2 Price of good 1 : P1 , Price of good 2 : P2 Income =…

A consumer has utility u(x₁, x₂) = x₁ + x1x2. Suppose that, because of a shortage of good 1, the government imposes a strict upper limit of ₁ on the quantity of good 1 that the consumer can consume. Assume throughout the following that w > p2. (a) Show that the consumer's preferences are strictly convex. Since preferences are monotone, this implies strict convexity. (b) Find the consumer's Marshallian demand if the consumer cannot violate the government limit. (c) Find the consumer's expenditure function.

A consumer has utility u(x₁, x₂) = x₁ + x1x2. Suppose that, because of a shortage of good 1, the government imposes a strict upper limit of ₁ on the quantity of good 1 that the consumer can consume. Assume throughout the following that w > p2. (a) Show that the consumer's preferences are strictly convex. Since preferences are monotone, this implies strict convexity. (b) Find the consumer's Marshallian demand if the consumer cannot violate the government limit. (c) Find the consumer's expenditure function.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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