A consumer chooses non-negative consumption levels of two goods x1 and x2 and has a utilityfunction given as:U == 0xfx%where 0 < a <1 and 0 is a constant. Assume that the prices of goods x1 and x2 are respectivelyPiand p2Set up the expenditure minimization problem of the consumer and derive theCompensated (Hicksian) demand function for goods 1 and 2 and investigate whether thetwo goods are complements or substitutes.i.

In consumer theory, the expenditure (EMP) minimization problem is the dual of utility (UMP)…

wo goods X, and X2 and has a function given as: U = 0xfx% where 0 < a<1 and 0 is a constant. Assume that the prices of goods x, and x2 are respecti Pand p2 i. Set up the expenditure minimization problem of the consumer and derive the Compensated (Hicksian) demand function for goods 1 and 2 and investigate whether two go ods are complements or substitutes

wo goods X, and X2 and has a function given as: U = 0xfx% where 0 < a<1 and 0 is a constant. Assume that the prices of goods x, and x2 are respecti Pand p2 i. Set up the expenditure minimization problem of the consumer and derive the Compensated (Hicksian) demand function for goods 1 and 2 and investigate whether two go ods are complements or substitutes

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.13P

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What is the logarithmic transform of the utility function U=xα1xβ2xγ3U=x1αx2βx3γ given the budget constraint px1x1+px2x2+px3x3=Mpx1x1+px2x2+px3x3=M. Select one: a. ln U=ln xα1+ln xβ2+ln xγ3ln U=ln x1α+ln x2β+ln x3γ b. ln U=α ln x1−β ln x2−γ ln x3ln U=α ln x1−β ln x2−γ ln x3 c. ln U=α ln x1+β ln x2+γ ln x3ln U=α ln x1+β ln x2+γ ln x3 d. ln U=ln xγ1+ln xβ2+ln xα3
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A. Consider a consumer whose preferences can be represented by Cobb-Douglas utility function u(x₁, x2) = x³x² where x₁ and ⁄2 are the quantities of good 1 and good 2 she consumes. Let p₁ and p2 be the prices of good 1 and good 2 and let m denote her income. Derive the consumer's Marshallian demand functions. Derive the consumer's Hicksian demand functions. Derive the consumer's expenditure function. Let m = = 120, p₁ = 2, and p2 = 1. Suppose that the price of good 1 drops to p₁ = 1. Find the following Compensating variation (CV) Equivalent variation (EV) Change in consumer surplus (ACS) Compare CV, ACS, and EV. Let m = 120, P₁ P₁ = 2. Find the following = 1, and p2 = 1. Suppose that the price of good 1 increases to Compensating variation (CV) Equivalent variation (EV) Change in consumer surplus (ACS) Compare CV, ACS, and EV.
1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.
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Suppose a consumer purchases food X and clothing Y. The utility function of the consumeris given by: U(X,Y ) = XY + 5Y and the budget /income/ of the consumer is 200 ETB. Andalso the price of food is X P and the price of clothing is Y P . Then drive the equation ofconsumer’s demand function for food and clothing.
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The question is an expenditure minimization question. The answer should be very detailed and clear, THANK YOU!!!