1. If a consumer has a utility function u (x1, x2)spend on good 2?= x1x, what fraction of her income will2. For what kind of preferences (or utility) will the consumer be just as well-off facing aquantity tax as an income tax that raises the same money for the government?3. When prices are (P1, P2) = (1,2) a consumer demands (x1, x2) = (1,2), and when prices are(P1, P2) (2,1) the consumer demands (x1, x2) = (2,1). Is this behavior consistent with=the model of utility maximization?4. When prices are (P1, P2) = (2,1) a consumer demands (x1, x2) = (1,2), and when prices are=(P1, P2) (1,2) the consumer demands (x1, x2) = (2,1). Is this behavior consistent withthe model of utility maximization?

The first question is asking about the fraction of income a consumer will spend on good 2 given a…

Answered: 1. If a consumer has a 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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Suppose that a consumer perceives X and AOG (all other goods) to be perfect (one-for-one) substitutes. The consumer has an income of $100 and the price of x is 80 cents. If the price of x rises to 1.20, what is the resulting change in consumer surplus? Show work and explain
Suppose a consumer’s preferences over two goods x_1 and x_2 are given by u = Square root (X_1,X_2). Her income is M and the two goods cost p1 and p2 per unit respectively. a) Derive her utility at the optimal consumption point as a function of prices and income. b) Now suppose the government imposes a proportional tax t on the value of the good x_1 (such as VAT). If the consumer approaches the government for income compensation to remain as well off as before the tax (i.e. compensating variation in income), how much money would she ask for? c) If instead, the government decides to maintain consumer’s utility level not through lump-sum transfer but by introducing a proportional subsidy S on the price of good 2, then what should be the size of the subsidy? d) Based on your answer in part c) discuss how much would it cost for the government to introduce both a tax and a subsidy at the same time? Can you think of any situation when this policy would make sense?
Let the consumer have the utility function a. Show that the utility maximizing demands are and b. Letting p1 = p2 = 1, use the inverse elasticity rule to show that the optimal tax rates are related by c. Setting w = 100, r1 = 0:75, and r2 = 0:5, find the tax rates required to achieve revenue of R = 0:5 and R = 10. d. Calculate the proportional reduction in demand for the two goods comparing the no-tax position with the position after imposition of the optimal taxes for both revenue levels. Comment on the results.
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3.00 0.10 q 20 Figure 9.6 shows an individual's demand curve for time per month spent telecommunicating while driving (talking on the car phone.) A car phone is useless except for talking with somebody who is not in the car. If calls are priced at ten cents per minute, what is the consumer surplus derived from talking? What is the most this person would pay for the car phone? Explain.
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