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Consumption Notes

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Consumption 15 November 2010

Topics

• Consumption

• The Keynesian Consumption Function

• Two-Period Model - Graphical Analysis

• Two-Period Model - Mathematical Analysis

Reading

Consumption

• Consumption is the biggest component of GDP at about 2/3's

• In the Solow model we forget about utility maximisation because it makes the model simpler

• We assume consumers save a fixed fraction of income

• Saving is for future consumption

• There is a global imbalance based on consumption:

• USA consumes too much

• China consumes too little

• We analyze the optimal consumption-saving decision

• There are two goods:

• Current consumption

• Future consumption

• The Keynesian consumption function is now an out-dated consumption model because it posed a problem known as the consumption puzzle

Key Points

• Consumption

• Keynesian consumption function

• The Kuznet consumption puzzle

• Life-cycle theory of consumption

• Permanent income theory of consumption

• Two period graphical analysis

• Two period mathematical analysis

• Effect of increase in current income

• Effect of increase in future income

• Temporary vs. permanent increase in income

• Consumption smoothing

• Effect of increase in real interest rate

• Linking the two period model to permanent income theory

• Psychology of instant gratification

• Implications of relation between consumption and income

Definitions The Keynesian Consumption Function

• Keynes (1936) posed two ideas:

• C is related to Y

• "The amount of aggregate consumption mainly depends on the amount of aggregate income" and that this relationship "is a fairly stable function" lead, as a rule, to a greater

• "It is also obvious that a higher absolute level of income…
proportion of income being saved"

• Consumption Function:

• Consumption depends on current income


• This the simplest way of stating consumption, however it is now old and out-dated

• Keynes made two claims with his consumption function:

• and are constants

• Average propensity to consume (APC) is falling as income increases
 APC = C/Y = a/Y + b
 Since a>0, when Y increases, APC falls
 Average propensity to save: APS = 1-APC
□ So falling APC implies rising APS

• Beta = how impatient we are

• Life Cycle Theory = Idea of saving for your future

• Life-cycle pattern = Borrow when young (income low), save during middle age (income high), dis-save during old age (retirement)

• The 'pull of instant gratification' = The discount factor between period 1 and 2 is smaller than the discount factor between future period t and t+1

• Transitory Shock = Temporary effects to income, but average income will still be almost the same

Formulae

Consumption Puzzle

• Data on C and Y do not show a consistent and stable relationship

• Across households at a point in time, they found that APC was falling

• i.e. Keynes was correct

• This is microeconomics

• But within a country over time, APC was constant

• So macro disagrees with Keynes

• Both of these cannot occur together
○ This is called Kuznets consumption puzzle Graphical representation of the consumption puzzle

• APC = C/Y = a/Y + b

• At optimal point:

• Average propensity to save: APS = 1-APC

• Current period budget constraint:

• Derive marginal utility:

• Find FOC as:

• Future period budget constraint:

• Lifetime utility for T-period model:

• Y is the current income

• A positive intercept -> Falling APC

• Origin intercept -> Constant APC

• It is important to be able to explain this graph

Solving the Consumption Puzzle

• Two theories developed in the 1950s

• Milton Friedman: Permanent income theory of consumption

• Franco Modigliani: Life-cycle theory of consumption

• Life Cycle Theory = Idea of saving for your future

• Transitory Shock = Temporary effects to income, but average income will still be almost the same

• Saving is for future consumption Life-Cycle Theory of Consumption

• Income varies systematically over the phases of the consumer's "life cycle"

• They plan over entire lifetime to achieve smooth consumption

• Consumption therefore depends on life-time income

• Saving is used to achieve smooth consumption

Course Notes Page 24

• Substitute this into the budget constraint:

• Where lifetime wealth is

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