Consider a consumer with wealth w who consumes two goods, which we shall call goods A and B. Let the amount of good that the consumer consumes be xe and the price of good l be pe. Suppose that the consumer's preferences are described by the utility function: u(XA,XB) = ailog xA+ a²log XB where the at are some fixed strictly positive parameters and all logs are natural logs. a. Set up the utility maximisation problem and write down the Lagrangian. b. Write down the first order necessary conditions for an interior maximum. c. Solve the first order conditions to obtain the Marshallian demand functions

Consider a consumer with wealth w who consumes two goods, which we shall call goods A and B. Let the amount of good that the consumer consumes be xe and the price of good l be pe. Suppose that the consumer's preferences are described by the utility function: u(XA,XB) = ailog xA+ a²log XB where the at are some fixed strictly positive parameters and all logs are natural logs. a. Set up the utility maximisation problem and write down the Lagrangian. b. Write down the first order necessary conditions for an interior maximum. c. Solve the first order conditions to obtain the Marshallian demand functions

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Problem 1 Consider a consumer with wealth w who consumes two goods, which we shall call goods 1 and 2. Let the amount of good that the consumer consumes be x and the price of good be pr. Suppose that the consumer's preferences are described by the utility function: a. Set up the utility maximization problem and write down the Lagrangian. b. Write down the first order necessary conditions for an interior maximum. c. Solve the first order conditions to obtain the Marshallian demand functions.