Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of YIS SI per unit. There are two consumers (A and B). The utility functions for the consumersareU A(X,Y) = X0.5 yo.5UB (X,Y) = X 0.8 yo.2%3DConsumer A has an income of $100, and Consumer B has an income of $300.a. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer A.b. Use a Lagrangian to solve the constrained utility-maximization problem for Consumer B.C. Calculate the marginal rate of substitution of Y for X (X is increasing and Y is decreasing;MRSXY) for consumer A at his or her optimal consumption bundles.d. Calculate the marginal rate of substitution of Y for X for consumer B at his or her optimalconsumption bundles.e. Suppose that there is another consumer (let's call her C). You don't know anythingabout her utility function or her income. All you know is that she consumes both goods.What do you know about C's marginal rate of substitution at her optimal consumptionbundle? Why?С.

Given: Px =2Py = 1UA(X, Y) = X0.5Y0.5UB(X, Y)= X0.8Y0.2MA = 100MB = 300 (a) Utility maximization…

Answered: Suppose that there are two goods (X and…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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