2. Constructing an EquilibriumHouseholds live two periods and have preferencesU(ci) + 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'%3Dwhere consumption for the type i agent in period j is denoted c. The type 2 agentfaces budget cOnstraintsY2 +rs2 =The resource constraints areN1c + N2cNịc+ 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) Solve the social planning problem. Compare the solution of the social planningproblem with the competitive equilibrium. Demonstrate that the decentralizedsolution solves the social planning problem for a particular set of Pareto weights.Explain how this is an example of the First Welfare Theorem.

An intertemporal budget constraint is a concept in economics that represents the balance between…

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 y₁ 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

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 y₁ 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

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