4. (b) There are three people and two goods in an economy. The utility functions and initialbundles are given below:U1 = X11X12U2 = 2x21 + X22U3 = X31X32 + X32W1 = (0,8)W2 = (2, 2)W3 = (8,0)%3DSuppose it is suggested that the three traders move to the allocation x given by:X1 = (1,2), x2 = (8,4), x3 = (1,4).%3D%3Diii) Show that x is not in the core.

Utility function can be defined as the measure for a group of goods and services preferred by…

(b) There are three people and two goods in an economy. The utility functions and initial bundles are given below: U₁ = X11X12 W₁ = (0,8) U₂ = 2x21 + x22 W₂=(2, 2) U3 = X31X32 + x32 W3 = (8,0) Suppose it is suggested that the three traders move to the allocation x given by: x₁ = (1,2), x₂ = (8,4), x3 = (1,4). iii) Show that x is not in the core.

(b) There are three people and two goods in an economy. The utility functions and initial bundles are given below: U₁ = X11X12 W₁ = (0,8) U₂ = 2x21 + x22 W₂=(2, 2) U3 = X31X32 + x32 W3 = (8,0) Suppose it is suggested that the three traders move to the allocation x given by: x₁ = (1,2), x₂ = (8,4), x3 = (1,4). iii) Show that x is not in the core.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2) Which of the following utility functions represent the same preferences? Explain. a) U (x₁, x₂) = X₁ X₂ b) W (x₁, x₂) = 5lnx₁ +5lnx₂ c) V (x₁, x₂) = x₁¹/3x₂ ¹/3 - 0.8 d) Z(x₁, x₂) = 0.5x₁ + 0.5x₂
3(b)Consider the following social choice problem in the setting of consumption of two goods by two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2. Consumer 1 has utility function U; (t,g) =6+.4 In(t) + .6 In(q) (where t is the amount of tillip 1 consumes and q is the amount of quillip). Consumer 2 has utility function U; (t,q) = 8 + In (t) + In(q). The social endowment consists of 15 units of tillip and 20 units of quillip. a. Suppose that a social dictator has social welfare functional of the following form: social welfare, as afunction of (u",u") is a weighted sum with weight 2 on the lesser of u' and u' and weight 1 on the greater of the two. What will be the welfare optimum plan chosen by this social planner? b. What is the set of all feasible, Pareto efficient allocations of the consumption good for this society? %3D
1. Consider the consumer problem with two goods, apples and oranges. Let x be the amount of apples and y be the amount of oranges, and let u(x, y) = 2√x + y be the utility function of the consumer. Let på be the price of apples, py be price of oranges, and I be the income of the consumer. (a) Using the condition that the MRS is equal to the relative prices, that is, Px ди/дх ди/ду Py 2 derive the demand functions of apples and oranges. (b) Even though the demand function of apples does not explicitly contain I, it is assumed that I cannot be too small. Explain why this assumption is necessary. = (c) Let I 90 and suppose that py = 6. Consider a price increase of apples from 2 to 3 that leaves the price of oranges unchanged at 6. Calculate the substitution effect and the income effect from this price change regarding the demand for apples.
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CS 11 Economics
1
A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility yielded by their consumption is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. (a) Complete the following table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places. (b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z? Product X Product Y Quantity Utility Marginal Quantity Utility Marginal Utility Utility per$ per$ 1 23 4567 42 82 118 148 170 182 182 1 23 4 5 6 7 14 26 36 44 50 54 56.4 Product Z Quantity Utility Marginal Utility per$ 1 23456 7 32 60 84 100 110 116 120 3..
Question 1. (i) please!
10. Consumer A and B have each been given an allocation of 2 goods x and y (assume each has positive amounts of both goods). At this allocation, consumer A has an MRS of 2, while consumer B has an MRS of 1/2. Could this allocation be Pareto efficient? Explain why or why not.
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