Copyright © 2010 Pearson Education Canada Chapter 8 A Two-Period Model: The Consumption-Savings Decision and Credit Markets Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Chapter 8 Topics Consumer’s consumption/savings decision – responses of consumer to changes in income and interest rates. Government budget deficits and the Ricardian Equivalence Theorem. Social Security. Credit market imperfections. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

A Two-Period Model of the Economy To maintain simplicity and to retain focus on the important ideas in this chapter, our two-period model will leave out production and investment. A consumer’s consumption-savings decision is dynamic decision. Two periods: we will denote the first period as the current period and the second period as the future period.

Consumers Assume, there are m consumers, where we can think of m as being a large number. Each consumer lives for two periods. Consumers do not make a work-leisure decision in either period. Consumers simply receive exogenous income. Let y be a consumer’s real income in the current period and y' be real income in the future period.

Consumers Note that we will use lower-case letters to refer to variables at the individual level, and upper-case letters for aggregate variables. Also note that primes will denote variables in the future period (e.g., y' denotes the consumer’s future income). Each consumer pays lump-sum taxes, t, in the current period and t' in the future period.

Consumers Suppose that incomes can be different for different consumers, but all consumers pay the same taxes. Let s be a consumer’s savings in the current period. We assume that the consumer starts the current period with no assets.

Copyright © 2010 Pearson Education Canada Budget Constraints The consumer’s current-period budget constraint: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Budget Constraints In the consumer’s current period budget constraint, if s > 0 then the consumer will be a lender on the credit market, and if s < 0, the consumer will be a borrower. Assume, the financial asset is a risk-free bond. Bonds can be issued by consumers as well as by the government. Assume that the bonds are directly traded in the credit market. There are no financial intermediaries, such as chartered banks.

Budget Constraints The real interest rate on each bond is r. Since this implies that one unit of current period consumption can be exchanged in the credit market for 1+r units of the future period consumption, the relative price of future consumption in terms of current consumption is 1/(1+r). Assume, the borrowing and lending rates of interest are same.

Copyright © 2010 Pearson Education Canada Budget Constraints The consumer’s future-period budget constraint: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Simplify Solve the future-period budget constraint for s: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Next, Substitute in the current-period budget constraint obtaining lifetime budget constraint: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Consumer’s Lifetime Budget Constraint Substitute in the current-period budget constraint obtaining lifetime budget constraint: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Consumer’s Lifetime Wealth Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Simplified Lifetime Budget Constraint Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Lifetime Budget Constraint: Slope-Intercept Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Consumer’s Lifetime Budget Constraint Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada A Consumer’s Indifference Curves Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Sara’s Desire for Consumption Smoothing Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Optimization Marginal condition that holds when the consumer is optimizing: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada A Consumer Who Is a Lender Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada A Consumer Who Is a Borrower Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada An Increase in Current Income for the Consumer Current and future consumption increase. Saving increases. The consumer acts to smooth consumption over time. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada The Effects of an Increase in Current Income for a Lender Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Observed Consumption-Smoothing Behavior Aggregate consumption of non-durables and services is smooth relative to aggregate income, but the consumption of durables is more volatile than income. This is because durables consumption is economically more like investment than consumption. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Percentage Deviations from Trend in GDP and Consumption Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada An Increase in Future Income for the Consumer Current and future consumption increase. Saving decreases. Again, these results are explained by the consumer’s motive to smooth consumption over time. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada An Increase in Future Income Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Temporary and Permanent Increases in Income As a permanent increase in income will have a larger effect on lifetime wealth than a temporary increase, there will be a larger effect on current consumption. A consumer will tend to save most of a purely temporary income increase. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Temporary Versus Permanent Increases in Income Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Stock Prices and Consumption of Nondurables and Services Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Stock Prices and Consumption of Nondurables and Services Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada An Increase in the Real Interest Rate Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada An Increase in the Market Real Interest Rate An increase in the market real interest rate decreases the relative price of future consumption goods in terms of current consumption goods – this has income and substitution effects for the consumer. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada An Increase in the Real Interest Rate for a Lender Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada An Increase in the Real Interest Rate for a Borrower Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Effects of an Increase in the Real Interest Rate for a Lender Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Effects of an Increase in the Real Interest Rate for a Borrower Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Example with Perfect Complements Preferences Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Aggregate Effects of an Increase in the Real Interest Rate For both lenders and borrowers, there is an intertemporal substitution effect of an increase in the real interest rate which leads to a substitution of future consumption for current consumption. But they have opposing income effects. The population consists of many consumers, some of whom are lenders and some borrowers. For borrowers, the current consumption decreases when the real interest goes up. But the effects on the current consumption of lenders depends on the strength of opposing income and substitution effects.

Aggregate Effects of an Increase in the Real Interest Rate There is a tendency for the income effects on the consumption of borrowers (decrease in current and future consumption) to offset the income effects on the consumption of lenders (increase in current and future consumption), leaving us with only the substitution effects. However, there is no theoretical guarantee that aggregate consumption will fall when the real interest rises.

Copyright © 2010 Pearson Education Canada Perfect Complements Example With perfect complements, the ratio of future consumption to current consumption is constant. The consumer’s budget constraint must hold. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Perfect Complements Example With perfect complements we can solve explicitly for current and future consumption: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Perfect Complements Example Substituting for lifetime wealth gives: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Government Government purchases an exogenously fixed G amount of consumption goods in the current period and G’ units in the future period. The aggregate quantity of taxes collected by the government in the current period is T. Recall that there are m consumers who each pay a current tax of t, so that T = mt. Similarly, in the future period total taxes are equal to T’, and we have T’ = mt’.

Government The government can borrow by issuing bonds. Recall that government bonds and private bonds are indistinguishable, with these bonds all bearing the same interest rate, r. Let B denote the quantity of government bonds issued in the current period.

Copyright © 2010 Pearson Education Canada Government Budget Constraints The government’s current-period budget constaint: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Government Budget Constraints The government’s current period budget constraint shows that government spending is financed through taxes and issue of bonds. In other words, the current-period government deficit, G - T, is financed by issuing bonds.

Copyright © 2010 Pearson Education Canada Government Budget Constraints The government’s future-period budget constraint: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Government Budget Constraints The government’s future period budget constraint shows that the government’s future outlays are financed through future taxes. The government’s future outlays consists of future government purchases and the principal and interest on the government bonds issued in the current period. Note that B can greater or less than 0. If B < 0, this would imply that the government was lender to the private sector, rather than a borrower from it.

Copyright © 2010 Pearson Education Canada Government Budget Constraints The government’s present-value budget constraint: Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Government Budget Constraints The government’s present-value budget constraint states that the present value of government purchases must equal the present value of taxes. This is similar to the consumer’s lifetime budget constraint, which states that the present value of consumption is equal to the present value of lifetime disposable income. An interpretation of the government present-value constraint is that the government must eventually pay off all of its debt by taxing its citizens.

Competitive Equilibrium The market in which the m consumers in this economy and the government interact is the credit market where consumers and the government can borrow and lend. In trading in the credit market, consumers and the government are effectively trading future consumption goods for current consumption goods. Recall that the relative price at which future consumption goods trade for current consumption goods is (1/1+r), which is determined by real interest rate, r.

Competitive Equilibrium In a competitive equilibrium for this two period economy, three conditions must hold: Each consumer chooses first- and second-period consumption and saving optimally given the real interest rate, r and exogenously fixed disposable income in the current and future periods. The government present-value budget constraint holds. The credit market clears.

Copyright © 2010 Pearson Education Canada Credit Market Equilibrium Condition Total private savings is equal to the quantity of government bonds issued in the current period. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Income-Expenditure Identity Credit market equilibrium implies that the income-expenditure identity holds. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Ricardian Equivalence Theorem The Ricardian Equivalence Theorem states that if current and future government spending are held constant, a change in current taxes with an equal and opposite change in the present value of future taxes leaves the equilibrium real interest rate and the consumptions of individuals unchanged.

Ricardian Equivalence Theorem This theorem states that a change in the timing of taxes by the government is neutral. By neutral, we mean that in equilibrium a change in current taxes, which is exactly offset in present-value terms by an equal and opposite change in future taxes, has no effect on the real interest rate or on the consumption of individual consumers. This is a very strong result, as it says that there is a sense in which government deficits do not matter, which seems to run counter to standard intuition. A key message: a tax cut is not a free lunch.

Copyright © 2010 Pearson Education Canada Ricardian Equivalence The Ricardian Equivalence Theorem is illustrated algebraically, numerically, and in two graphs. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Ricardian Equivalence Key equation: The consumer’s lifetime tax burden is equal to the consumer’s share of the present value of government spending – the timing of taxation does not matter for the consumer. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Ricardian Equivalence Then, substitute in the consumer’s budget constraint – taxes do not affect the consumer’s lifetime wealth (the present value of government spending influence it). Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Ricardian Equivalence with a Cut in Current Taxes for a Borrower (Figure 8.15) Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Ricardian Equivalence In Figure 8.15, the consumer buys the same consumption bundle before and after the tax cut in the current period. Basically, the consumer is saving all of the tax cut in the current period in order to pay higher taxes that he or she will face in the future period. A tax cut is not a free lunch for the consumer.

Copyright © 2010 Pearson Education Canada Ricardian Equivalence and Credit Market Equilibrium Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Credit Market Imperfections Assume that lenders can lend at a lower interest rate than the one faced by borrowers. The government borrows and lends at the interest rate that lenders face. This implies that Ricardian equivalence does not hold, in general. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada A Consumer Facing Different Lending and Borrowing Rates Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Effects of a Tax Cut for a Consumer with Different Borrowing and Lending Rates Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Effects of a Tax Cut with Credit Market Imperfections Suppose a consumer initially is credit constrained – that is he or she saves zero. For such a consumer, the entire tax cut will be spent on current consumption. This is very different from the case with no credit market imperfections, where the consumer will save the entire tax cut to pay higher future taxes. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Credit Market Imperfections and the Financial Crisis Two key credit market frictions: asymmetric information and limited commitment. Asymmetric information: Would-be borrowers know more about their characteristics than do lenders. Limited Commitment: Borrowers may choose to default – lender can overcome limited commitment with collateral. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Asymmetric Information in Credit Markets Lending carried out through banks. Deposit rate at banks is r1, loan rate is r2. Fraction a of borrowers never defaults, fraction 1-a always defaults – bank cannot tell the good borrowers from the bad ones. All good borrowers identical, borrow L. Bad borrowers mimic the good ones. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Asymmetric Information – Deposit Rate and Loan Rate Zero profits for the bank implies: Therefore, there is a default premium (r2 > r1) when a < 1. The default premium increases as a decreases. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Reduction in Quantity of Creditworthy Borrowers Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Effect of a Decrease in the Fraction of Creditworthy Borrowers Default premium increases – even good borrowers face higher loan rates. Budget constraint shifts in. Consumption falls for all borrowers. Matches observations from the current financial crisis – increase in credit market uncertainty, reduction in lending, decrease in consumption expenditures. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Limited Commitment and Credit Markets Borrowers need incentives not to default on their debts – these incentives typically provided by collateral requirements. Examples: House is collateral for a mortgage loan, car is collateral for a car loan. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Example H=quantity of housing owned by consumer. p=price of housing Assume: Housing is illiquid – can’t be sold in the current period. However, it is possible to borrow against housing wealth, with a collateral constraint. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Consumer’s Constraints Lifetime budget constraint: Collateral constraint: or Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Kinked Budget Constraint – Shifts in When p Falls Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada

Copyright © 2010 Pearson Education Canada Implications of Limited Commitment for the Financial Crisis In the United States, there was a large decrease in housing prices, beginning in 2006. This reduced the value of collateral used in consumer lending (mortgage debt was financing consumer expenditure). Reduction in lending, reduction in current consumption. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Copyright © 2010 Pearson Education Canada