2. Constructing an EquilibriumHouseholds live two periods and have preferencesU(c) + BU(c2),where 0 < B < 1 and U is the utility function and satisfies our usual assumptions.There are N households in the economy. N\ of these households have endowment yin the first period and no endowment in the second - these agents are called "Type 1".The remaining N2 have no endowment in the first period and y2 in the second period- these agents are called "Type 2." Hence the resources of the economy arein the first period andin the second, whereÑ = N1 + N2.Households have access to a credit market where they can borrow (s < 0) or saves > 0. The type 1 agent faces budget constraintsY1c+s'rs'where consumption for the type i agent in period j is denoted c. The type 2 agentfaces budget constraintsG + s²Y2 +rs? =The resource constraints areNịc + N2c?Nịc+ N2c(a) State the maximization problem solved by each type of agent and derive the first-order and second-order conditions. Derive the solution using the implicit functiontheorem.(b) Determine the equilibrium conditions for the three markets using the resourceconstraints and the budget constraints. Provide a statement of the equilibrium.(c) Assume logarithmic utility U(c) = In(c) and derive a closed form solution forconsumption in both periods and savings for both types of agents.(d) Sel

2. Constructing an Equilibrium Households live two periods and have preferences U(C₁) + BU (C₂), where 0 < 3 < 1 and U is the utility function and satisfies our usual assumptions. There are Ñ households in the economy. N₁ of these households have endowment y in the first period and no endowment in the second - these agents are called "Type 1". The remaining N₂ have no endowment in the first period and y2 in the second period - these agents are called "Type 2." Hence the resources of the economy are N131 in the first period and N₂92

2. Constructing an Equilibrium Households live two periods and have preferences U(C₁) + BU (C₂), where 0 < 3 < 1 and U is the utility function and satisfies our usual assumptions. There are Ñ households in the economy. N₁ of these households have endowment y in the first period and no endowment in the second - these agents are called "Type 1". The remaining N₂ have no endowment in the first period and y2 in the second period - these agents are called "Type 2." Hence the resources of the economy are N131 in the first period and N₂92

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

3.
Consider an agent who want to maximize her utility function, u (C₁, C₂) = C₁ C₂ subject to the budget constraint, c₁ + pc₂ = w with C₁, C₂ > 0 indicating consumption of commodity 1 and 2, respectively, while p>0 and w>0 are exogenously given parameters, indicating the relative price of good 2 and the relative wealth in term of good 1's price. Decide whether the following claims are true or false. W • The value of the Lagrange multiplier is λ = 2p False True w² • The value function u(w) is equal to u(w) = 4p True False • λ(w) measures the approximate change in utility that can be obtained from an increase/decrease in wealth w. True False
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
2. Constructing an Equilibrium Households live two periods and have preferences U(c) + BU(c2), where 0 0. The type 1 agent faces budget constraints Y1 c+s' rs' where consumption for the type i agent in period j is denoted c. The type 2 agent faces budget constraints G + s² Y2 +rs? = The resource constraints are N1c + N2c Nịc+ N2c (a) State the maximization problem solved by each type of agent and derive the first- order and second-order conditions. Derive the solution using the implicit function theorem.
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 =
B4
3. Answer the problem and provide solutions.
9. Consider an Edgeworth box economy with two consumers, whose utility func- tions and endowments are u'(x},x}) = (x}Xx})} (5,5) In the following, use the normalization p2 = 1. (a) Find the competitive equilibrium price. (b) State the first fundamental theorem of welfare and verify that it holds in this economy. (e) Consider the allocation ĩ = (x',) = (2,3), (8, 7). Show whether this allo- cation can supported as an equilibrium with transfers. (d) State the second fundamental theorem of welfare, and briefly discuss whether the result in part (c) conform with or violate this theorem. 3.