Consumption Notes

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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