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

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