Suppose there are two consumers, Az B. The utility functions of each consumer are given by kem xong U₂XX-X²² Therefore For consumer A: MU-2XY; MU, -X² For consumer B: MU-Y²: MU, -2XY The initial endowments are A:X-60: Y-150 B.X-45; Y-75 Suppose the price of Y, Py-1. Calculate the price of X, P, that will lead to a competitive equilibrium How much of each good does each consumer demand in equilibrium? Consumer A's demand for X: Consumer A's demand for Y Consumer 8's demand for X Consumer B's demand for Y ts) What is the marginal rate of substitution for consumer A at the competitive equilibrium

Suppose there are two consumers, Az B. The utility functions of each consumer are given by kem xong U₂XX-X²² Therefore For consumer A: MU-2XY; MU, -X² For consumer B: MU-Y²: MU, -2XY The initial endowments are A:X-60: Y-150 B.X-45; Y-75 Suppose the price of Y, Py-1. Calculate the price of X, P, that will lead to a competitive equilibrium How much of each good does each consumer demand in equilibrium? Consumer A's demand for X: Consumer A's demand for Y Consumer 8's demand for X Consumer B's demand for Y ts) What is the marginal rate of substitution for consumer A at the competitive equilibrium

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

1. This question will let you examine/explore a more interesting utility func- tion than the simple example discussed in class as there will be both cross-price elas- ticity and an inferior good. Suppose you are told a consumer has the following utility function: U (9219₂) = 9z+√9z+ 9₂ You should assume income is Y, the price of good r is P2, and the price of good z is P₂. This question will ask about several concepts discussed in lecture. (a) What is the Marshallian demand for goods x and z? I.e. find (qq) for both interior solutions and corner solutions. Note: the outcome is "ugly" for the interior section and both corner should include constraints, i.e. limits using Y relative to f(P, P₂). Hint: if solving using MRS = MRT, can use this information again in part (d). (b) Suppose you are told P₂ = $8 and P₂ = $1. Create a graph showing the Income Consumption Curve (ICC) for Y = {$12.25, $35, $49, $70, $98). Be sure to clearly label the graph. Based on the ICC, which of the goods is…
nments: 2022-SU-ECO2023 x apter 7 Problems 1 eBook https://ezto.mheducation.com/ext/map/index.html?_con=con&external_browser=0&launchUrl=https%253A%252F%252Flms.mheduca Question 1 - Chapter 7 Problem: X Mc Graw Hill Type here to search Suppose that at three units purchased, marginal utility is $8 and total utility is $30. If the marginal utility of the fourth unit purchased is $6, how much is the total utility of four units? Marginal ultility: $ im o Et Soved Prey 1 of 5 Nex
Alex's utility is U (xA, YA) = min {TA, YA}, where zA, and y, are his consumptions of %3D goods a and y respectively. Becky's utility function is U (zB, YB ) = TBYB where ap and yp are her consumptions of goods a and y. Alex's initial endowment is 20 units of x and 12 units of y. Becky's initial endowment is 12 units of x and 20 units of y. At the Walrasian equilibrium, a) Both of them consume 16 units of good y each. b) Alex consumes 8 units of good y and Becky consumes 16 units of y. c) Both of them consumes 12 units of good x each. d) Alex consumes 12 units of good x and Becky consumes 20 units of x. e) None of the above
4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.
741 Ny 7:0 Mond Content X + ultra/courses/_99030_1/cl/outline manipic cempo me manipic accompis. INIU Force Completion. This test can be saved and resumed later. BILLETTE Your answers are saved automatically. * Question Completion Status: QUESTION 1 The goal of the consumer is to maximize the total utility or satisfaction derived from their purchase choices, given the unique budget constraint. To calculate total utility of a given combination of T-shirts and movies, one would use the following approach: O a. For a given combination of T-shirts and movies, survey a group of individuals to determine an average for utils to be assigned to the number of T-shirts and movies. O b. For a given combination of T-shirts and movies, use Google to identify the number of utils associated with the number of T-shirts and movies and thenlum them. O c. For a given combination of T-shirts and movies, assign a number of utils to that combination. O d. Use utils as a measure of utility, assigning a…
. Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.
6. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and d Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution. and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo).
The figure below show the initial optimal point of a family who has to decide how much kids (K) to have in 5 years and at the same time how much of all other goods to consumer (measured as composite good in dollars). Now assuming that kids are inferior goods/services, show the new optimal point as e2 if the income of the family increases. IC₁ to K
Given: Assume a consumer is attempting to maximize utility subject to the budget constraint by choosing units of consumption between two goods: good 1 and good 2. Utility maximizing choices are provided in the following table for a baseline scenario and new scenario. Item Baseline New Price of Good 1 $10 $10 Price of Good 2 $10 $6 Income $20,000 $20,000 Units Consumed, Good 1 1000 1250 Units Consumed, Good 2 1000 1250 Utility 4000 5000 Using the table, how did the new event affect good 2? It caused demand for good 2 to decrease. O It caused demand for good 2 to incrcase. OIt caused quantity demanded for good 2 to increase. O It caused no change in quantity demanded for good 2. It cause quantity demanded for good 2 to decrease. It caused no change in demand for good 2.
2. Consider a society with only two people one rich and one poor-who have the same util- ity functions. These utility functions exhibit diminishing marginal utility. Suppose that taxes are set such that the total amount of utility that each person loses is the same. Does it follow that the tax will be progressive? Explain.
6. Sarah and Clare have identical utility functions U = 5 In(x)+y: Sarah starts out with 16 units of x and 5 units of y and Claire starts out with 4 units of x and 15 units of y. a. Draw the Edgeworth box, label the endowment point and sketch some "normal" indifference curves through the endowment point. Shade the region where trades are possible. b. Find Sarah and Claire's Marshallian demands as a function of the price of x, price of y and their endowments. c. Find the market clearing price and how much x and y the two consumer after trading. d. Who is happier after trading?
Zach's preferences are representable by the utility function u = 90.3927, where 9₁ and 92 denote his consumption of goods 1 and 2. (Answers to each of these questions are rounded, where required, to two decimal places.) Still assuming endowments of e₁ = 5 and e₂ = 9 and market prices p₁ = 20 and p2 = 30, what is the maximised value of Zach's utility? O Au= 6.74 O B. u = 5.39 O Cu = 5.65 O D.u = 7.56 O E. None of the above