Expert answer:Discussion on Households: Consumption-Saving Decis
Expert answer:For this discussion highlight how relevant are intertemporal choices as they pertain to prices (interest rates), postponing consumption (patience), credit availability, income shocks, and individuals’ foresight for your company/industry.Text book: chpt 3Davis, Morris, Macroeconomics for MBAs and Masters of Finance, Cambridge University PressISBN-13: 978-0521762472ISBN-10: 052176247
econ562_module5.pptx
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ECON 562
Macroeconomic Analysis & Public Policy
Module 5: Households’ ConsumptionSaving Decision
Copyright 2017 Montclair State University
Introduction
A two-period
model of a
household
Optimal allocation
of consumption
and savings
Choices under
uncertainty
Introduction
As individuals, once we have chosen our hours of work, then
we have to decide between consuming or saving our income.
How can we model this economic decision?
ECON 562
Macroeconomic Analysis & Public Policy
Module 5a: A Two-Period Model
A Two-Period Model
In this module, we develop a theory of households who live for
two days — that’s progress!
So we model how a “representative” household chooses:
• how much to consume and
• how much to save
A Two-Period Model
So, let’s talk about optimal savings decisions.
We will consider a model where people do not have preferences
over leisure, but do have preferences over items consumed at
different points in time:
• Today vs tomorrow
A Two-Period Model
In this model
world:
People live
two periods
People get
utility from
consumption
in each
period.
People prefer
consumption
this period
relative to
consumption
next period.
A Two-Period Model
The utility function from consumption in period t and period t+1
would look like:
+ +
< < is a preference parameter that weights utility from
consumption in t+1 (next period) relative to utility from
consumption in t (this period).
A Two-Period Model
In this dynamic model, savings links the two periods in the budget
constraint.
+ + = + + .
Higher next period assets + means lower on (left hand side).
Thus, savings affect current and future utility.
The right hand side represents the household’s capital and labor income at
time t.
In the model people are time-consistent, forward-looking, and rational.
A Two-Period Model
Formally, the household’s problem is given by:
The utility function
+ +
and the budget constraints:
+ + = + + .
+ + + = + + + + + .
Where the choice variables are: , + , and + .
A Two-Period Model
The optimization conditions to this problem yield the (Euler) equation:
= + +
+
This result means that households:
• balance (the marginal utility of) consumption across periods,
• like to smooth consumption, in other words.
For a low + and close to 1, people prefer a steady consumption pattern
–just like in the data!
ECON 562
Macroeconomic Analysis & Public Policy
Module 5b: Choice Under Uncertainty
Choice Under Uncertainty
What about uncertainty? We have assumed the
household knows future interest rates and
consumption with certainty.
To allow for uncertainty we let the household
maximize expected utility.
The expectation is over a probability distribution
of possible states of the world (imagine, a good
state and a bad state).
Choice Under Uncertainty
The utility function becomes
+
+ ,
=
Where is the probability of state i.
And the utility maximization condition is given by
=
+ +
+
It is the same decision equation except for the expectations operator.
...
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