consumer lecture

7/25/2019 Consumer Lecture

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Consumer Theory

Motivation: The key limitation of Solow growth theory is thatit abstracts from optimizing consumers. Economists widely be-

lieve that consumers and firms respond to incentives. Absent

optimizing consumers, the theory offers little in the way of

(1) an understanding of how the economy will react to shocks

due to war, immigration, technological booms or important changes

in tax policy

(2) a welfare analysis of different policies

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Review of Static Consumer Theory:

Assume:

1. Preferences over goods: U(c1, c2)

2. Budget set: p1c1+p2c2 I

Prices: (p1, p2)

Income: I2


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Consumer maximization implies:

(1) M RS(c1, c2) = p1p2

(2) p1

c1

+p2

c2

=I

Notation: M RS(c1, c2) denotes the marginal rate of

substitution between good 1 and good 2 at the allo-

cation (c1, c2). Basic Micro: M RS(c1, c2) = U1(c1,c2)U2(c1,c2)

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Cobb-Douglas Preferences:

U(c1, c2) =c1c

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U(c1, c2) = log c1+ (1 )log c2

M RS(c1, c2) = U1(c1,c2)U2(c1,c2) = c2(1)c1

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Solve (1)-(2) w/ Cobb-Douglas Preferences:

(1) M RS(c1

, c2

) = c2(1)c1

= p1p2

(2) p1c1+p2c2=I

Result (Marshallian Demand Functions) :

c1= Ip1

c2= (1)I

p2

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Q: Is the consumer theory we have just reviewed ap-

plicable to decision making over time which is key in

Macro?

A: With some reinterpretation of income and priceconcepts, standard vanilla consumer theory is a theory

of optimal decision making over time.

Key Assumptions: perfect foresight and lifetime plans

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History of Economic Thought:

Irving Fisher - early 1900s he applies stardard con-

sumer theory to decision making over time

Modigliani and Brumberg - 1950s pursue this idea

over the life cycle

Friedman - 1950s pursues this idea but adds risky

labor income

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Dynamic Consumer Theory:

Maximize U(c1, c2) subject to

(1) c1+ a2 w1

(2) c2 w2+ a2(1 + r)

(w1, w2) - wages in period 1 and 2

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r - real interest rate


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Algebra:

1) c1+ a2 w1

(2) c2 w

2+ a

2(1 + r)

imply the present value budget constraint:

c1+ c21+r w1+

w21+r

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Equivalence of present value and standard

budget constraint:

c1+ c21+r w1+

w21+r

p1c1 +p2c2 I

Equivalent when

p1= 1, p2= 1/(1 + r) and I=w1 + w21+r

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Cobb-Douglas Preferences - Again!:

[Use: p1= 1, p2= 1/(1 + r) and I=w1+ w21+r ]

c1=

I

p1 =[w1 +

w2

1+r]

c2= (1)I

p2=

(1)[w1+ w21+r ]

1

1+r

a2=w1 c1

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Multi-Period Models:

Many applications require many time periods to inter-pret data

Utility - Generalized Cobb Douglas:

U(c1, c2,...,cJ) =1 log c1 + 2 log c2+ ... + Jlog cJ

Assume: weights add up to 1 (i.e.

jj = 1)

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c1+ c2

(1 + r)+

c3(1 + r)2

+ ... + cJ

(1 + r)J1

P V w1+ w2

(1 + r)+

w3(1 + r)2

+ ... + wJ

(1 + r)J1


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Solution:

Consumption: cj = jP V

( 11+r)j1,j

Asset Holding: aj+1=wj+ aj(1 + r) cj

Asset holding is determined as a residual

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Stylized Numerical Example:

0. Lifetime - J= 60

1. Utility - as specified and j = 1/J at all ages

2. Interest rate: r = 0

3. Labor Income: constant (wj = 10 j=1 -40) then

zero for j >40

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Empirically Motivated Questions:

1. Why is (mean) consumption profile hump shapedover the life cycle?

2. Why do high income households save a higher

fraction of income than low income households?

3. Why are consumption responses to permanent and

temporary income changes quite different?

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Why is Consumption Hump Shaped?

Possible Story: Income is hump shaped ... and some-

how this implies the same for consumption.

Use Dynamic Consumer Theory: cj = jP V

( 11+r )j1

,j

Does this work??????

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Two Famous Savings Rate Facts:

1. The aggregate savings rate in the US is withouttrend

2. In any year, high income households in the US

save a greater fraction of income than low income

households.

What type of theory explains these facts?

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g1410161048021009204836448125957727.gif (GIF Image, 545 290 pixels)

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Keynesian Story:

Households follow a simple rule of thumb:

The fundamental psychological law, upon which we

are entitled to depend with great confidence both a

priori from our knowledge of human nature and from

the detailed facts of experience, is that men are dis-

posed, as a rule and on average, to increase theirconsumption as their income increases, but not by as

much as the increase in their income. - JM Keynes

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Modigliani-Brumberg Story:

1. Labor Income is Hump Shaped

2. Preferences lead to consumption smoothing mo-tivated by retirement

3. Low income are largely young + old, whereas high

income are largely middle age

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Responses to Permanent and Temporary Income

Changes

1. Keynesian Story: response should be the same!

2. Modigliani-Brumberg Story: response should de-

pend on how it impacts the present value of lifetime

labor income

[numerical example ... connection to tax cuts and

stimulus debate]

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Theory: cj = jP V

( 11+r)j1

,j and J= 60

Temporary Shock: compare two situations

1. wj = 10 in all periods

2. w1= 70 and wj = 10 in all other periods

Consumption change: cj = jP V

( 11+r)j1

,j

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Theory: cj = jP V

( 11+r)j1

,j and J= 60

Permanent Shock: compare two situations



Consumption change: cj = jP V

( 11+r)j1

,j

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Overview:

1. Dynamic Consumer Theory highlights rational de-

cision making over the lifetime and a forward looking

view of individuals. The main reason for saving is to

smooth consumption over the lifetime.

2. Theory Omits: Savings for (1) precautionary rea-

sons, (2) for purchases of a house and (3) bequests

among other possibilities.

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3. Precautionary motives are easy to add to our

model. Precautionary motives are a popular response

in consumer surveys. Connection to Expected Utility

Theory.

4. The evidence on the differential savings response

to temporary vs permanent shocks presents difficulties

to theories that do not allow for some foresight on the

part of consumers.


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consumer lecture

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