Suppose that an individual with income I cares about two goods, X and Y. The prices of the two goods are px and py. The individual has the utility function U(X, Y) = 5 ln X + 3 ln Y. (a) Derive the Marshallian demands for the two goods. (b) Find the indirect utility function.

Suppose that an individual with income I cares about two goods, X and Y. The prices of the two goods are px and py. The individual has the utility function U(X, Y) = 5 ln X + 3 ln Y. (a) Derive the Marshallian demands for the two goods. (b) Find the indirect utility function.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.11P

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

Suppose that an individual with income I cares about two goods, X and Y. The prices of
the two goods are px and py. The individual has the utility function
U(X,Y)= 5 ln X + 3 ln Y.
(a) Derive the Marshallian demands for the two goods.
(b) Find the indirect utility function.

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Step 1: Define Marshallian demand

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Step 2: Find the Marshallian demand.

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Step 3: Find the IUF:

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