Consider a household with the following utility function representing their preferencesover consumption:U = u(Ct) + Bu(C++1)with=-u(C) = exp(-aC), BE (0,1), a > 0where C and C++1 represent consumption in the current and future periods, respectively.The household faces a two-period decision problem. They receive endowments of Y, andYt+1 in the current and future periods, respectively. The real interest rate is denoted byrt.Notice: The utility function u(C) takes on negative values for all positive consumptionlevels. However, in economic models, the absolute value of utility is less important thanhow utility changes with consumption. A higher level of utility represents a morepreferred outcome for the household.Question:Formulate the household's budget constraints for the current and future periods. Com-bine them to derive the household's intertemporal budget constraint.Write down the household's optimization problem (objective function) that they seek tomaximize.Derive the first-order conditions (Euler Equation) that characterize the optimal con-sumption plan. Provide an economic interpretation of these conditions (hint: you needto take logs at some point to make the expressions linear

Utility function : U = u(Ct) + Bu (Ct+1)Where , u(C) = -exp (-aC) In period t -Consumption : Ct…

Consider a household with the following utility function representing their preferences over consumption: U = u(Ct) + Bu(C++1) with u(C) = − exp(−aC), BE (0,1), a > 0 where C+ and C++1 represent consumption in the current and future periods, respectively.

Consider a household with the following utility function representing their preferences over consumption: U = u(Ct) + Bu(C++1) with u(C) = − exp(−aC), BE (0,1), a > 0 where C+ and C++1 represent consumption in the current and future periods, respectively.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider a household with the following utility function representing their preferences
over consumption:
U = u(Ct) + Bu(C++1)
with
=-
u(C) = exp(-aC), BE (0,1), a > 0
where C and C++1 represent consumption in the current and future periods, respectively.
The household faces a two-period decision problem. They receive endowments of Y, and
Yt+1 in the current and future periods, respectively. The real interest rate is denoted by
rt.
Notice: The utility function u(C) takes on negative values for all positive consumption
levels. However, in economic models, the absolute value of utility is less important than
how utility changes with consumption. A higher level of utility represents a more
preferred outcome for the household.
Question:
Formulate the household's budget constraints for the current and future periods. Com-
bine them to derive the household's intertemporal budget constraint.
Write down the household's optimization problem (objective function) that they seek to
maximize.
Derive the first-order conditions (Euler Equation) that characterize the optimal con-
sumption plan. Provide an economic interpretation of these conditions (hint: you need
to take logs at some point to make the expressions linear

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