# Discussion on Households: Consumption-Saving Decision

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
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ECON 562
Macroeconomic Analysis & Public Policy
Module 5: Households ConsumptionSaving Decision
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. ... Purchase answer to see full attachment

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