Problem 2Suppose that John's preferences over meat (M) and vegetables (V) are represented by thefollowing utility functionU(M,V) = a ln(M) + (1 − a) ln(V)where 0 < a < 1.¹No claim of realism is made for the numbers in this example.1(a) Write down the Lagrangian for John's optimization problem. (Recall that John max-imizes utility given an income, I, and prices på and på for the goods.)(b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income andprices) using the Lagrangian method.=(c) Suppose a = . Suppose also that John has income I=1 and pv2. What is the value of John's optimalhappens if John's income doubles to I = 400?200 and faces prices pconsumption bundle? What=

Utility function : U = a ln (M ) + (1-a) ln (V) V & M are two goods ,0 <a <1Price of M =…

Answered: Suppose that John's preferences over…

Suppose that John's preferences over meat (M) and vegetables (V) are represented by the following utility function where 0 < a < 1. U(M,V) = a ln(M) + (1 − a) ln(V)

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Chapter1: Making Economics Decisions

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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

Problem 2
Suppose that John's preferences over meat (M) and vegetables (V) are represented by the
following utility function
U(M,V) = a ln(M) + (1 − a) ln(V)
where 0 < a < 1.
¹No claim of realism is made for the numbers in this example.
1
(a) Write down the Lagrangian for John's optimization problem. (Recall that John max-
imizes utility given an income, I, and prices på and på for the goods.)
(b) Solve for John's optimal consumption bundle (M*, V*) (as a function of income and
prices) using the Lagrangian method.
=
(c) Suppose a = . Suppose also that John has income I
=
1 and pv
2. What is the value of John's optimal
happens if John's income doubles to I = 400?
200 and faces prices p
consumption bundle? What
=

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