2. General Equilibrium.consumers, each with the same Cobb-Douglas preferences except with differ-ent parameters. Consumer 1 has utility function u(x, x)= (x})"(x})!-«, whileConsumer 2 has utility function u(x, x;) = (xP(x)-P. The endowment ofgood j owned by consumer i is denoted w. The price of good 1 is p, and theprice of good 2 is 1. In the superscript, we denoted the consumer i = 1,2; in thesubscript, we denote the good j= 1,2.Consider an exchange economy with twoWrite the maximisation problem faced by each consumer i =(a)1,2, taking care to define the objective function and the budget constraint.Set up the Lagrangian and find the first order conditions.(b)For each consumer i = 1,2 , use the first-order conditions todetermine the demand functions for each consumer i = 1,2 and for eachgood j = 1,2, in terms of the price p.(c)Find the aggregate demand for each good j = 1,2 and clear themarkets for each good. Hence, show that the equilibrium price pi is givenby the expressionaw; +Bw;[(1-a)w} +(1-B)w}]Define Walras' here and show that this holds here.

The two consumers are i = 1 and 2For consumer 1, the utility function is : For consumer 2, the…

2. General Equilibrium. Consider an exchange economy with two consumers, each with the same Cobb-Douglas preferences except with differ- ent parameters. Consumer 1 has utility function u(x,x) = (x¹)(x₂)¹", while Consumer 2 has utility function u(x², x2) = (x3)(x2). The endowment of good j owned by consumer i is denoted w. The price of good 1 is p, and the price of good 2 is 1. In the superscript, we denoted the consumer i = 1,2; in the subscript, we denote the good j = 1,2. (a) Write the maximisation problem faced by each consumer i = 1,2, taking care to define the objective function and the budget constraint. Set up the Lagrangian and find the first order conditions. (b). (c) For each consumer i = 1,2, use the first-order conditions to determine the demand functions for each consumer i = 1,2 and for each good j = 1,2, in terms of the price p₁. Find the aggregate demand for each good j = 1,2 and clear the markets for each good. Hence, show that the equilibrium price p, is given by the expression aw+Bw²₂ P₁ [(1-a)w+(1-B)w²] Define Walras' here and show that this holds here.

2. General Equilibrium. Consider an exchange economy with two consumers, each with the same Cobb-Douglas preferences except with differ- ent parameters. Consumer 1 has utility function u(x,x) = (x¹)(x₂)¹", while Consumer 2 has utility function u(x², x2) = (x3)(x2). The endowment of good j owned by consumer i is denoted w. The price of good 1 is p, and the price of good 2 is 1. In the superscript, we denoted the consumer i = 1,2; in the subscript, we denote the good j = 1,2. (a) Write the maximisation problem faced by each consumer i = 1,2, taking care to define the objective function and the budget constraint. Set up the Lagrangian and find the first order conditions. (b). (c) For each consumer i = 1,2, use the first-order conditions to determine the demand functions for each consumer i = 1,2 and for each good j = 1,2, in terms of the price p₁. Find the aggregate demand for each good j = 1,2 and clear the markets for each good. Hence, show that the equilibrium price p, is given by the expression aw+Bw²₂ P₁ [(1-a)w+(1-B)w²] Define Walras' here and show that this holds here.

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

Part 1: Illustrate general equilibrium and the Laffer curve in the context of a repre- sentative consumer with a utility function: U(C.I) = In(C) + In() that he or she maximises subject to a constraint: C= w(1 – t)(h – 1) + * where w, h,1, C,t and a are wages, hours of time available, leisure, consumption, tax rate, and dividend income. The production function for this economy is given by Y = C+G = A(h - 1)/2 Assume that h = 1, A =1 and that the government has a balanced budget. (a) Find the equilibrium by matching the Marginal Rate of Substitution to the Marginal Rate of Transformation and then substitute into the constraint. Also take into account that profits are non-zero for this setup. (b) Plot the government tax revenue for 0
9
Consider an economy with 2 goods and 2 agents. The Örst agent has the utilityfunction, u (x1; x2) = ln x1 + 2 ln x2, and the other one has u (y1; y2) = 2 ln y1 + ln y2.The aggregate endowments of the 2 goods are given by (50; 100). Suppose there is asocial planner who cares about agents equally.(a) Set up the plannerís problem b) Calculate the first-best outcome (i.e., the social plannerís solution).
(5) A has utility function u4(x4) = x4 + x and initial endowment w4 = (3,6). Consumer B has utility function uB (xB) = xf · x% and initial endowment wB = (3,6). Consider an exchange economy with two consumers and two goods. Consumer (a) Is the initial endowment a Pareto efficient allocation? Justify your answer. (b) Find a competitive equilibrium (p, xª, x³) for the economy. (c) Construct the contract curve. A picture here is not a complete answer; you need to specify analytically the set of points that are in the contract curve.
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
!
In a two-good market, a consumer starts with an initial endowment of (x₁, x2) = (15.00, 5.00), while the market prices for these goods are given by (P1, P2) = (7.00, 3.00). The consumer has the following utility function: U 0.52 0.48 - Given this information, what will this consumer's final choice of quantity for each good be? x1 = x2 =
Ma1. Please give only typed answer.
B4
Suppose that consumer has the following utility function: U(X,Y) - X1/2y1/4. Suppose also that P 2, P -3 and 1=144. What would be the optimal consumption of X and Y at the equilibrium. respectively? 36, 24 12,40 24,32 48.16
A small exchange economy is comprised of two of individuals, A and B, and two types of goods, x, ,x,. The individuals' preferences over two goods are can be represented by the following utility functions: U*(x;,.x; ) = min (2.x,x; ) and U* (x;,x;) = min(x;.2x, ). Initial endowments are 10 x, (individual A), and 10 x, (individual B). Calculate the price ratio which yields an equilibrium in the exchange market.
!