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Consumption Notes

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Consumption 15 November 2010


* Consumption

* The Keynesian Consumption Function

* Two-Period Model - Graphical Analysis

* Two-Period Model - Mathematical Analysis



* 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







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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