The economics of consumption
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From: President Ella Eli
To: Yale Students
Re: Generous Gift
My dear students,
I am delighted to report that a generous alumna has made a
gift of $1000 per Yale student, available immediately. You can come
by the office and pick up your check any time.
Professor Nordhaus has requested that you detail how you
would spend the funds. Would you please write this down in your
notebooks in class today. You will find it instructive as you discuss
Consumption in class this week.
With best wishes,
President Ella Eli
P.S. Professor Nordhaus has told me about “elevator quizzes,” which
are a great idea. This is not an elevator quiz, but you should hold on
to your answers for later reference. EE
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Importance of consumption in macro
1. Consumption is two-thirds of GDP –
understanding its determinants is major part of
the ball game.
2. Consumption is the entire point of the economy:
3. Consumption plays two roles in microeconomics:
a. AD: It is a major part of AD in the short run:
recall IS curve in which
Y = C(Yd) + I + G + NX
b. AS: What is not consumed is saved and
influences national investment and economic
growth
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Table 2.1. Personal Income and Its Disposition
[Billions of dollars]
Bureau of Economic Analysis
Last Revised on: August 29, 2012
Item
Personal income
Compensation of employees, received
Proprietors' income
Rental income of persons
Personal income receipts on assets
Personal current transfer receipts
Less: Contributions for government social insurance, domestic
Less: Personal current taxes
Equals: Disposable personal income
Less: Personal outlays
Equals: Personal saving
Personal saving as a percentage of disposable personal income
2011
Percent of income
12,947
8,295
64%
1,157
9%
410
3%
1,685
13%
2,319
18%
919
1,398
11,549
11,060
489
4.2
4
Table 2.4.5. Personal Consumption Expenditures
by Type of Product
[Billions of dollars]
Bureau of Economic Analysis
Last Revised on: August 02, 2012
Personal consumption expenditures
Goods
Durable goods
Motor vehicles and parts
Furnishings and durable household equipment
Recreational goods and vehicles
Other durable goods
Nondurable goods
Food and beverages purchased, off-premises
Clothing and footwear
Gasoline and other energy goods
Other nondurable goods
Services
Housing and utilities
Health care
Transportation services
Recreation services
Food services and accommodations
Financial services and insurance
Other services
Higher education
2011
10,729
3,625
1,146
374
252
340
181
2,478
810
349
428
891
7,104
1,930
1,752
302
395
671
807
956
168
33.8%
10.7%
3.5%
2.3%
3.2%
1.7%
23.1%
7.6%
3.3%
4.0%
8.3%
66.2%
18.0%
16.3%
2.8%
3.7%
6.3%
7.5%
8.9%
1.6%
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Growth in C and GDP (quarterly)
Chicken or egg:
- ΔC causes recession?
- Recession causes ΔC?
.02
.01
.00
-.01
-.02
Consumption
GDP
-.03
00
01
02
03
04
05
06
07
08
09
10
11
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Alternative Theories of Consumption
The basic Keynesian insight is that consumption depends
fundamentally on personal income (“consumption function”)
This enters into the Keynesian models as C = α + βYd
On a closer look, a major puzzle: the short-run and cross-sectional
consumption functions looked very different from the long-term
consumption function.
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Consumption and Disposable Income
12,000
Real consumption
10,000
8,000
6,000
4,000
2,000
0
0
2,000
4,000
6,000
8,000 10,000 12,000
Real disposable income
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Short-run v. Long-run Consumption Function
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Alternative Theories of Consumption
The basic Keynesian insight is that consumption depends
fundamentally on personal income (“consumption function”)
This enters into the Keynesian models as C = α + βYd
On a closer look, a major puzzle: the short-run and cross-sectional
consumption functions looked very different from the long-term
consumption function.
There are four major approaches in macroeconomics:
*1. Fisher's approach: sometimes called the neoclassical model
2. Keynes original approach of the consumption function
*3. Life-cycle or permanent income approaches (Modigliani,
Friedman)
4.Rational expectations (Euler equation) approaches (in Jones)
*We will do in class, but more Fisher in section.
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Intertemporal Consumption Choice: Fisher’s model
Basic idea:
People have expectations of lifetime income; they determine their
consumption stream optimally; this leads consumers to “smooth”
consumption over their lifetime.
Assumptions of two period model:
Periods 1 and 2
Income Y1 and Y2
Maximize utility:
U(C 2 )
max U(C1 ) +
{C1 ,C 2 }
(1+ δ)
Budget constraint:
C1 +
C2
Y2
= Y1 +
(1+ r)
(1+ r)
We will do graphical case now and calculus later.
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Budget constraint:
C1+C2/(1+r)=Y1
[no income in retirement]
C2
Indifference curve
between current and
future consumption
C 2*
E*
S1 *
C 1*
Y1
C1
C2
Key result: consumption
independent of timing of
income!!!
Called “consumption
smoothing”
C 2*
E*
S1 *
C 1*
Y1
C1
Summary to here
Income over life cycle is the major determinant of
consumption and saving.
In idealized case, have consumption smoothing over
lifetime.
Now move from two-period (Fisher model) to multi-period
(life cycle model).
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Basic Assumptions of Life Cycle Model
Basic idea:
People have expectations of lifetime income; they determine their
consumption stream optimally; this leads consumers to “smooth”
consumption over their lifetime.
Assumptions:
“Life cycle” for planning from age 1 to D.
Earn Y per year for ages 1 to R.
Retire from R to D.
Maximize utility function:
max V(C 1 , C 2 , ..., C D ) 
D
 (1   ) z U(C z ),
for ages z  1 to D.
z1
Budget constraint:
D
 (1  r )
z 1
-z
Cz 
D
 (1  r )-z Yz
z 1
Discount rate on utility (δ) = real interest rate (r) = 0 (for simplicity)
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Techniques for Finding Solution
1. Two periods:
max U(C1 )  U(C2 )  U(C1 )  U(Y1  Y2 - C1 )
{Cz }
Maximizing this leads to U’(C1)=U’(C2). This implies that C1 = C2 ,
which is consumption smoothing. The Cs are independent of
the Ys.
2. Lagrangean maximization (advanced math econ):
D
 D
-z
max L C1 ,...,CD  =  (1+ δ) U(C z ) + λ   (1+ r ) C z -  (1+ r )-z Yz

{C z }
z=1
z=1
 z=1
D
-z




Maximizing implies that U’(C1)=U’(C2)=-λ. This implies that Ct  C
which again is consumption smoothing independent of Y.
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U
U '(C )
U(C )
Since U’(C1)=U’(C2)=…
= -λ, C is constant over
time.
C
C1
Initial Solution
C, Y, S
Diagram of Life
Cycle Model
Showing
Consumption
Smoothing
Income, Y
Consumption, C
Saving, S
|
0
R
age
|
D
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Anticipated change in timing of income
C, Y, S
Income “splash” (Y’) with no W increase
Income, Y
Anticipated income
change of ΔY.
Consumption, C’=C
Because it is
anticipated, no
change in lifetime
income, so no
change in
(smoothed)
consumption. MPC
= 0; MPS = 1.
Saving, S’
|
R
0
age
|
D
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What about anticipated taxes?
C, Y, S
Income “splash” from tax cut
Income, Y
No C change!
Saving, S’
|
R
0
age
|
D
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Unanticipated change in permanent income
C, Y, S
Y’ =unanticipated increase; W increases.
Unanticipated windfall
of ΔY in period z.
Leads to smoothing
the windfall over
remaining lifetime.
(a) one time splash:
MPC = ΔY/(D-z).
For life expectancy
of 40 years, would
be MPC = .025.
(b) Permanent income
increase: MPC =
ΔY(R-z)/(D-z) = .6
to .8
Y
C’
C
|
R
0
age
|
D
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