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The economics of consumption

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From: President Ella EliTo: Yale StudentsRe: 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

Importance of consumption in macro1. 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 + NXb. AS: What is not consumed is saved and influences national investment and economic growth

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Personal income 12,947 Compensation of employees, received 8,295 64% Proprietors' income 1,157 9% Rental income of persons 410 3% Personal income receipts on assets 1,685 13% Personal current transfer receipts 2,319 18% Less: Contributions for government social insurance, domestic 919Less: Personal current taxes 1,398Equals: Disposable personal income 11,549Less: Personal outlays 11,060Equals: Personal saving 489 Personal saving as a percentage of disposable personal income 4.2

Table 2.1. Personal Income and Its Disposition[Billions of dollars]Bureau of Economic AnalysisLast Revised on: August 29, 2012

Item 2011 Percent of income

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Personal consumption expenditures 10,729 Goods 3,625 33.8% Durable goods 1,146 10.7% Motor vehicles and parts 374 3.5% Furnishings and durable household equipment 252 2.3% Recreational goods and vehicles 340 3.2% Other durable goods 181 1.7% Nondurable goods 2,478 23.1% Food and beverages purchased, off-premises 810 7.6% Clothing and footwear 349 3.3% Gasoline and other energy goods 428 4.0% Other nondurable goods 891 8.3%Services 7,104 66.2% Housing and utilities 1,930 18.0% Health care 1,752 16.3% Transportation services 302 2.8% Recreation services 395 3.7% Food services and accommodations 671 6.3% Financial services and insurance 807 7.5% Other services 956 8.9% Higher education 168 1.6%

by Type of ProductTable 2.4.5. Personal Consumption Expenditures

[Billions of dollars]Bureau of Economic AnalysisLast Revised on: August 02, 2012

  2011

Growth in C and GDP (quarterly)

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-.03

-.02

-.01

.00

.01

.02

00 01 02 03 04 05 06 07 08 09 10 11

ConsumptionGDP

Chicken or egg: - ΔC causes

recession?- Recession causes

ΔC?

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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.

Consumption and Disposable Income

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0

2,000

4,000

6,000

8,000

10,000

12,000

0 2,000 4,000 6,000 8,000 10,000 12,000

Real disposable income

Rea

l co

nsu

mp

tion

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:

Budget constraint:

We will do graphical case now and calculus later.

2 21 1

C YC + = Y +

(1+r) (1+r)

1 2

21{C ,C }

U(C )max U(C ) +

(1+δ)

C1

C2

Budget constraint:C1+C2/(1+r)=Y1

[no income in retirement]

Y1

Indifference curve between current and future consumption

E*

S1*

*1C

*2C

C1

C2

Key result: consumption independent of timing of income!!!

Called “consumption smoothing”

Y1

E*

S1*

*1C

*2C

Summary to hereIncome 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:

Budget constraint:

Discount rate on utility (δ) = real interest rate (r) = 0 (for simplicity)

D D-z -z

z zz 1 z 1

(1 ) C (1 ) Y r r

1 21

max (1 ) ( ), for ages z 1 to D.D

zD z

z

V(C , C , ..., C ) U C

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Techniques for Finding Solution

1. Two periods:

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):

Maximizing implies that U’(C1)=U’(C2)=-λ. This implies that

which again is consumption smoothing independent of Y.

z

D D D-z -z -z

1 D z z z{C } z = 1 z = 1 z = 1

max L C ,...,C = (1+δ) U(C ) + λ (1+r) C - (1+r) Y

1 2 1 1 2 1maxz{C }

U(C ) U(C ) U(C ) U(Y Y - C )

tC C

C1

U

C

( )U C

'( )U C

Since U’(C1)=U’(C2)=… = -λ, C is constant over time.

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age

C, Y, S

Income, Y

R D| |

Consumption, C

0

Saving, S

Diagram of Life Cycle Model Showing Consumption Smoothing

Initial Solution

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age

C, Y, S

Income, Y

R D| |

Consumption, C’=C

0

Saving, S’

Anticipated change in timing of income

Income “splash” (Y’) with no W increase

Anticipated income change of ΔY.

Because it is anticipated, no change in lifetime income, so no change in (smoothed) consumption. MPC = 0; MPS = 1.

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age

C, Y, S

Income, Y

R D| |

No C change!

0

Saving, S’

What about anticipated taxes?

Income “splash” from tax cut

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age

C, Y, S

Y

R D| |

C

0

Unanticipated change in permanent income

Y’ =unanticipated increase; W increases.

C’

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