Title PageIntroductionConsumption and SavingsOctober 10, 20161 / 51ConsumptionIThe major components:IPurchases of non-durable goods and services: Food,clothing, education, health care, financial services...IPurchases of durable goods: Autos, computers, furniture...IConsumption is between 60 and 70% of GDP in mostcountriesIRelatively stable, except for expenditures on durable goodswhich fluctuate significantly2 / 51GDP vs. Consumption3 / 51IIf you know that your wealth will grow in the future, willyour consumption exceed your income?IIf you cannot borrow?4 / 51Key lessons from the dataIConsumption is not just a constant fraction of incomeIConsumption is strongly correlated with GDP and income,IImplications :IHouseholds must use their savings to smooth consumptionover time.IWe need to understand the link between consumption andsavingsIEvidence for consumption smoothing–throughsavings–across periods5 / 51Saving and BorrowingIWhy save or borrow? (Friedman, Modigliani)ILife-cycle: save for retirementILife-cycle: borrow against future earnings for educationIPrecautionary savings: uncertain income =⇒ save forrelative drops in incomeITime discounting: Preferences for consumption today vs.tomorrowIConsumers optimal choice is to smooth consumptionITrade-off: Interest rate on borrowing/saving vs.preferences for consumption today/tomorrow6 / 51A Simplified ModelIAssume agents live for only two periods: present and future(generalizes to > 2 periods)Iy : Current incomeIyf: Future incomeIc : Current consumptionIcf: Future consumptionIa : Assets at the beginning of current periodIaf: Assets at the beginning of next periodIr : Real interest rate7 / 51Budget Constraintsc + af= y + aIUse wealth and income to consume today, save the restIafsavings save for tomorrow in some assets (e.g. savingsaccount, stocks, etc.)IGrows at rate: 1 + rIConsumption tomorrow:cf= yf+ (1 + r) afIConsume all of interest on savings afand income since lastperiod (not if > 2 periods)8 / 51Intertemporal Budget constraint (IBC)Combine the two budget constraints into an IBC expressed inpresent value terms:c +cf(1 + r)= a + y +yf1 + r≡ P V LRIPresent values discounted by 1 + r:IFor 1$ of future consumption, need to save11+r$ and earninterest 1 + rISimilarly, 1$ of future income is like having11+r$ todayIcf(1+r)is the present value of future consumptionIyf(1+r)is the present value of future incomeIAs before, PVLR is the present value of lifetime resources9 / 51Intertemporal Budget constraint (IBC)IHow do we draw the consumer’s problem?ILet’s have current consumption on the ”x-axis” and futureconsumption on the ”y-axis’IWhat are the ”terminal conditions”?IWhat is the slope of the budget constraint?IWhat are the effects of a change in the interest rate?10 / 51Intertemporal Budget constraint (IBC)IHow do we draw the consumer’s problem?ILet’s have current consumption on the ”x-axis” and futureconsumption on the ”y-axis’IWhat are the ”terminal conditions”?IWhat is the slope of the budget constraint?IWhat are the effects of a change in the interest rate?11 / 51Intertemporal Budget constraint (IBC)IHow do we draw the consumer’s problem?ILet’s have current consumption on the ”x-axis” and futureconsumption on the ”y-axis’IWhat are the ”terminal conditions”?IWhat is the slope of the budget constraint?IWhat are the effects of a change in the interest rate?12 / 51Intertemporal Budget constraint (IBC)IHow do we draw the consumer’s problem?ILet’s have current consumption on the ”x-axis” and futureconsumption on the ”y-axis’IWhat are the ”terminal conditions”?IWhat is the slope of the budget constraint?IWhat are the effects of a change in the interest rate?13 / 51Intertemporal Budget constraint (IBC)IHow do we draw the consumer’s problem?ILet’s have current consumption on the ”x-axis” and futureconsumption on the ”y-axis’IWhat are the ”terminal conditions”?IWhat is the slope of the budget constraint?IWhat are the effects of a change in the interest rate?14 / 51The effect of an increase in theinterest rateISubstitution effect:IRelative price of tomorrow’s consumption increases. Sosubstitute from today?’ consumption to tomorrow’s bysaving more.IIncome effect:IIf saver: Can save less to get same income tomorrow.Therefore it tends to reduce savingsIIf borrower: Need to save more to get same incometomorrow. Therefore it tends to increase SIThe effect of (real) interest rate on aggregate saving istheoretically ambiguous. Empirical research suggests thatsaving increasesIThe (aggregate) Saving Curve will be upward sloping15 / 51Copyright ©2014 Pearson Education, Inc. All rights reserved. 4A-27 The Real Interest Rate and the Consumption-Saving Decision • The real interest rate and the budget line (Fig. 4.A.6) – When the real interest rate rises, one point on the old budget line is also on the new budget line: the no-borrowing, no-lending point – Slope of new budget line is steeperCopyright ©2014 Pearson Education, Inc. All rights reserved. 4A-28 Figure 4.A.6 The effect of an increase in the real interest rate on the budget lineCopyright ©2014 Pearson Education, Inc. All rights reserved. 4A-29 The Real Interest Rate and the Consumption-Saving Decision • The substitution effect – A higher real interest rate makes future consumption cheaper relative to current consumption – Increasing future consumption and reducing current consumption increases saving – Suppose a person is at the no-borrowing, no-lending point when the real interest rate rises (Fig. 4.A.7) • An increase in the real interest rate unambiguously leads the person to increase future consumption and decrease current consumption • The increase in saving, equal to the decrease in current consumption, represents the substitution effectCopyright ©2014 Pearson Education, Inc. All rights reserved. 4A-30 Figure 4.A.7 The substitution effect of an increase in the real interest rateCopyright ©2014 Pearson Education, Inc. All rights reserved. 4A-31 The Real Interest Rate and the Consumption-Saving Decision • The income effect – If a person is planning to consume at the no-borrowing, no-lending point, then a rise in the real interest rate leads just to a substitution effect – But if a person is planning to consume at a different point than the no-borrowing, no-lending point, there is also an income effectCopyright ©2014 Pearson