ECON5102 Macroeconomics
Lecture 7
CONSUMPTION
T3 2023
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1 Introduction
• In this lecture, we learn (Jones chapter 16):
The neoclassical consumption model
I Individuals choose the time path of their consumption to max-
imize utility
I How this model leads to a solution in which consumption is
proportional to an individual’s total wealth
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Introduction - 1
• Heterogeneity in consumer behavior at the microeconomic level
Some individuals (rich) tend to follow the permanent-income
hypothesis
Others (poor) respond to changes in current income
• The decline in the personal saving rate and the rise in the debt-
income ratio in recent decades
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Introduction - 2
• Neoclassical consumption model
Individuals choose consumption at each moment in time
Goal: maximize a lifetime utility function
I function depends on current and future consumption
People recognize that income in the future may differ from in-
come today
I such differences influence consumption today
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2 The Neoclassical Consumption Model
• Two time periods: today and the future
People earn income and consume in both periods.
• Key decision to make
How much to consume today versus how much to consume in
the future
• The consumption model is based on two main elements:
An intertemporal budget constraint
A utility function
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The Intertemporal Budget Constraint - 1
• Two budget constraints, each with the form “consumption
equals income less saving”
(1) ctoday = ytoday −
(
ffuture − ftoday
)
(2) cfuture = yfuture = (1 +R)ffuture
where
c = consumption
y = income
f = financial wealth
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The Intertemporal Budget Constraint - 2
• Combine the two, get the intertemporal budget constraint
ctoday +
cfuture
1 +R
= ftoday + ytoday +
yfuture
1 +R
where ytoday =
yfuture
1 +R
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The Intertemporal Budget Constraint - 3
• Human wealth is the present discounted value of labor income
present value of consumption = financial wealth + human wealth︸ ︷︷ ︸
total wealth
• Consumption in a given year can be different from income
• PDV of consumption must equal lifetime resources
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Utility - 1
• Utility depends on consumption today and in the future
• More consumption means more utility
U = u(ctoday) + βu(cfuture)x
Weight placed on future consumption
• Diminishing Marginal Utility
Each additional unit of consumption raises utility by a smaller
amount
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Utility - 2
• If β = 1
Current and future treated equally
• If β < 1
Future consumption is discounted
Today’s consumption is valued more than future consumption
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Flow Utility u(c)
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Choosing Consumption to Maximize Utility - 1
• Maximize utility subject to a budget constraint
maxU
ctoday, cfuture
= u(ctoday) + βu(cfuture)
subject to
ctoday +
cfuture
1 +R
= X¯ ←− total wealth
where
X¯ ≡ ftoday + ytoday + yfuture
1 +R
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Choosing Consumption to Maximize Utility - 2
• Solution requires calculus, but we can walk through the intu-
ition
Want to make ourselves as happy as possible, but we have a
limited income
• Marginal utility of today’s consumption: u′(ctoday)
• Marginal utility of future consumption: u′(cfuture)
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Choosing Consumption to Maximize Utility - 3
• Agents can either:
Consume today
OR
Save and consume 1 +R units in the future
• Utility maximized when agents are:
indifferent between consuming more today or more tomorrow
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Choosing Consumption to Maximize Utility - 4
• Euler Equation:
u′(ctoday) = β(1 +R)u′(cfuture)
MU of consuming 1 more unit today = discounted consumption
of 1 +R units in the future.
• Intuition
Must be indifferent between consuming today and tomorrow
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Solving the Euler Equation - 1
• Log Utility: u(c) = log(c)
• Calculus derivative rule: u′(c) = 1
c
• The Euler equation in this case is then:
1
ctoday
= β(1 +R)
1
cfuture
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Solving the Euler Equation - 2
• Rearranging the Euler equation:
cfuture
ctoday
= β(1 +R)
• Left side is growth rate of consumption (plus 1)
• Consumption is chosen such that:
The growth rate of consumption is a product of the discount
parameter and the interest rate.
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Solving the Euler Equation - 3
• Lower β
Impatient, consumption growth is lower
• Higher β
Patient, consumption growth is faster
• Euler Equation
Explains how interest rates and growth rates are related
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Solving for Ctoday, Cfuture with Log Utility and β = 1 (1)
• To solve for consumption today and in the future (two vari-
ables), we need:
Euler equation
Intertemporal budget constraint
cfuture
ctoday
= β(1 +R)
If β = 1:
ctoday +
cfuture
1 +R
= X¯
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Solving for Ctoday, Cfuture with Log Utility and β = 1 (2)
• If β = 1
• Plug into the budget constraint
ctoday =
1
2
X¯
• Spend half of your wealth today, save the other half
cfuture =
1
2
(1 +R)X¯
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The Effect of a Rise in R on Consumption
• Changes in interest rates often involve a wealth, substitution
and an income effect.
• Wealth effect:
Total wealth depends on the interest rate because of PDV of
labor income
Higher interest rate reduces PDV and consumption
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The Effect of a Rise in R on Consumption (cont.)
• Changes in interest rates often involve a wealth, substitution
and an income effect.
• Income effect:
Consumers are now richer - because their current saving leads to
more income in the future - which makes them want to consume
more today.
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The Effect of a Rise in R on Consumption (cont.)
• Changes in interest rates often involve a wealth, substitution
and an income effect.
• Substitution effect:
A higher interest rate, will make consumption more expensive
today
Saving will lead to even more consumption in the future
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The Effect of a Rise in R on Consumption
• Log utility
Substitution and income effects offset
• Other utility forms have a different effect of an increase in R
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3 Lessons from The Neoclassical Model
• The permanent-income hypothesis is an implication of this model
Consumption depends on average income (PDV of income) rather
than current income.
• Recall overall wealth
X¯ = ftoday + ytoday +
yfuture
1 +R
• Last two terms are PDV of income
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Lessons from the Neoclassical Model
• Permanent-income hypothesis
We want to smooth our consumption over time
• What happens if income increases?
We may spend some of the extra income, but not all of it
• Marginal propensity to consume
Portion of additional income that is spent for consumption
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The Desire to Smooth Consumption
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Ricardian Equivalence
• Ricardian Equivalence
Consumption depends on PDV of taxes and is invariant to the
timing of taxes
A tax cut today financed by higher future taxes will not affect
consumption
A change in the timing of taxes
I does not change wealth
I consumption doesn’t change
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Borrowing Constraints - 1
• A key assumption of the model is the ability to freely save or
borrow at the interest rate R
• However, some people may not be able to borrow
Bad credit history
Bad economy
• Thus:
ctoday 6 ytoday
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Borrowing Constraints - 2
• If a consumer is already consuming less than their income,
the no-borrowing constraint will be nonbinding
• If income is low and the borrowing constraint binds, then:
ctoday = ytoday
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Consumption as a Random Walk
• Random walk view of consumption
Changes in consumption should be unpredictable
I due to unpredictable events
I lottery win, job loss
Expected changes are planned for due to permanent-income hy-
pothesis
I due to predictable events
I expected salary raise, new job
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Case Study: Consumption versus Expenditure
• Key prediction of model:
Consumption should not change when an anticipated event oc-
curs
• However, this doesn’t always hold true
Retirement
I Food expenditures decrease
I Calories consumed do not, though
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Precautionary Saving
• Precautionary saving
Saving money just in case of an uncertain and unpredictable
event
I Can lead consumers to behave as if they face borrowing con-
straints even if they don’t
May even save when income is low
I Always a possibility of further income decreases
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4 Empirical Evidence on Consumption
• Does the evidence agree with the following assumptions we’ve
made?
• Individuals with sufficient wealth
Consumption may obey the permanent-income hypothesis
Follow a random walk
• Individuals with low wealth or who cannot borrow
Display much greater sensitivity to current income
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Evidence from Individual Households - 1
• Three main findings:
• The permanent-income hypothesis applies to households with
above-average wealth
The MPC out of a temporary income shock is low
Consumption smoothing is effective
• Low income households
Behave as if borrowing-constrained
Engage in precautionary saving
MPC from income boost is high
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Evidence from Individual Households - 2
• Many departures from the classical model in the data
Are individuals really rational?
• Behavioral economics
Research that blends psychology, neuroscience, and economics
Goal is to better understand how individuals make economic
decisions
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Case Study: Behavioral Economics and Consumption - 1
• Economic Assumption
People are rational
• But:
What if people are bad at math?
They are not irrational, but may make a “wrong” decision
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Case Study: Behavioral Economics and Consumption - 2
• Behavioral considerations from 401(k) plans
Participation is almost 100 percent when the default is opt-in
Participation is less than 50 percent when enrollment is not
automatic
• Enron
Employees did not diversify; the default retirement option was
Enron stock
• The default option is “sticky”
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Aggregate Evidence - 1
• Personal saving rate
Ratio of personal saving to disposable income
• United States household debt-to-GDP
1970s to early 1980s: less than 50 percent
2009: nearly 100 percent
Since 2009: debt-to-GDP has fallen
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Household Debt as a Percent of GDP (USA)
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Household Debt as a Percent of GDP (Australia)
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The Personal Saving Rate
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The Personal Saving Rate
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Household Wealth (as a Ratio to Income)
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Household Wealth (Australia)
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Aggregate Evidence - 2
• Explanation for rise in borrowing and decrease in saving
Households believe they will be richer in the future
Follows the permanent-income hypothesis
• China
Savings rate has been rising
Facts seem to be backward?
I Or is something else missing from our study?
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