2. David has the utility function u(e,g) = 8,000ln(e) + g, where e represents money spenton education and g represents money spent on other goods. He has M = $50,000 to spend.(i) Suppose that the government gives David a lump-sum subsidy of $L. Find his optimalbundle.(ii) Now suppose that the government gives David a voucher for $V worth of education anda lump-sum subsidy of $(L – V) instead. Find David's optimal bundle. (Assume V < L.)

Given Utility function U=8000lne+g E= education g=Other goods M=$50000 50000=e*Pe+g*Pg

Answered: 2. David has the utility function…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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For an individual the Marginal Rate of Substitution is constant and equal to 1/2 for allcombinations of goods X and Y in his consumption set. The price of good X is $12 per unitand the price of good Y is $8 per unit. The individual has a total budget of $400. Determinethe bundle of goods X and Y that maximize his utility.
1) Alex spends all his income on blueberries and strawberries. His Marginal Utility of blueberries is MUB=100-B. His total utility of strawberries is Us=900+150S-S². Find Alex's income if the price of blueberries is PB=$8/kg, the price of strawberries is Ps=$10/kg, and Alex consumes 30kg of blueberries. 2) A profit-maximizing monopoly faces a demand curve D(P)=1000-P, has variable costs VC(Q)=Q², and fixed costs equal to $30,000. Find this monopoly's profit.
Problem 2 Joan has the following utility function: u(x, y) = 5x + 3y. (a) Find Jane's marshallian demands. (b) Find Jane's hicksian demands. Consider that income is I = $8, and prices are given as p = $4, Py = $2. (c) Does Jane have enough money to attain a utility level of 20? Justify your answer. (d) Assume thè price of y marginally increases. Find the total, income and substitution effect for r due to the change in py.
Number 5 : IV part only. Thank you.
What is Lea's own-price substitution effect of the price increase due to the tax ?
Marvin has a Cobb-Douglas utility function, 0.5 0.5 U= 91 92 his income is Y = $900, and initially he faces prices of p₁ = $1 and p2 = $4. If p₁ increases from $1 to $2, what are his compensating variation (CV), change in consumer surplus (ACS), and equivalent variation (EV)? Marvin's change in consumer surplus (ACS) is $ minus sign if necessary.) Marvin's compensating variation (CV) is $. (Enter your response rounded to two decimal places and include a minus sign if necessary.) (Enter your response rounded to two decimal places and include a Marvin's equivalent variation (EV) is $. (Enter your response rounded to two decimal places and include a minus sign if necessary.)
3.D.3B Suppose that u(x) is differentiable and strictly quasiconcave and that the Walrasian demand function x(p, w) is differentiable. Show the following: (a) If u(x) is homogeneous of degree one, then the Walrasian demand function x(p, w) and the indirect utility function v(p, w) are homogeneous of degree one [and hence can be written in the form x(p, w) = wx(p) and v(p, w) = w(p)] and the wealth expansion path (see Section 2.E) is a straight line through the origin. What does this imply about the wealth elasticities of demand?
True/False? Briefly explain. Assume good x is a normal good. In terms of consumer behavior, a cash grant and a small (relative to the initial consumption of x) limited non-matching grant on good x (with the limit that is equal to the cash grant) are essentially equivalent.
Suppose that an individual has a Utility function represented by a CES function. The utility function of the individual is given as: U(x,y) = x1/2 + y1/2 c. Is the demand more elastic or inelastic than a Cobb-Douglas Utility function? Use the Slutsky matrix to illustrate.
Please answer all the questions below Leonidas has a utility function u(x, y) = x + 3y, an income of 12 and works in Sparta, where the prices of x and y are both 2.(a) What is Leonidas’ current utility?(b) Leonidas’ boss is thinking of sending him to Athens where the price of x is 1 and the price of y is 4. Leonidas says this is as bad as a cut in pay of γ. What is γ equal to?(b) He also says that he wouldn’t mind moving if his pay was increased by δ when he moved. What is δ equal to?

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