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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Assume that a person’s utility depends on two products, x and y. The utility function is given by U(x, y) = (x + 2)^2(y + 3)^3. Find the marginal utility of x and marginal utility of y.
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Consider a market with two households (A and B) and two goods (X and Y). Each household holds 12 units of each good. Household A has a utility UA = 5 In LA + In yA when it consumes bundle (*A, YA). Household B hasa utility UB = In aB+5 Inyg when it consumes bundle (гв, ув). The market reaches an equilibrium when the price of each good is $1. Which, of the following sentences, correctly explains what happens in the market? Household A purchases 8 units of good X from household B. Household B purchases 8 units of good Y from household A. Household A purchases 7 units of good Y from household B. Household B purchases 7 units of good X from household A. Household A purchases 9 units of good X from household B. Household B purchases 9 units of good Y from household A. O Household A purchases 7 units of good X from household B. Household B purchases 7 units of good Y from household A. Household A purchases 9 units of good Y from household B. Household B purchases 9 units of good X from…
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Suppose that a consumer has the utility function U(X,Y)= 2X 1/2 y 1/2 for X>0 and Y> 0. Which of the following utility functions would not represent the same preferences? U(X,Y)= 2(X + Y) 1/2 U(X,Y)=2x1/2y 1/2 - 100 O U(X,Y)= In 2 + InX+ In Y O U(X,Y)= X 1/2 y 1/2 O U(X, Y) = 4XY
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Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…
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