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 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.

In economics, an intertemporal budget constraint is an idea that symbolizes the equilibrium between…

Answered: (a) State the maximization problem…

(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.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

2. Constructing an Equilibrium
Households live two periods and have preferences
U(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 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
in the first period and
in the second, where
Ñ = N1 + N2.
Households have access to a credit market where they can borrow (s < 0) or save
s > 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.

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