Lecture 10: Two-Period Model

Transcription

1 Lecture 10: Two-Period Model Consumer s consumption/savings decision responses of consumer to changes in income and interest rates. Government budget deficits and the Ricardian Equivalence Theorem.

2 Budget Constraints The consumer s current-period budget constraint: The consumer s future-period budget constraint:

3 Let s combine the budget constraints. First, solve the future-period budget constraint for s:

4 Next, substitute into the current-period budget constraint: c c' y' t' 1 y t r

5 Finally, rearrange to obtain lifetime budget constraint: t y r t y c c 1 ' ' ' r t y t y r c c 1 ' ' 1 ' Lifetime Budget Constraint lifetime wealth (we)

6 Simplified Lifetime Budget Constraint c c' 1 we r c' (1 r) c we(1 r)

7 Consumer s Lifetime Budget Constraint c' (1 r) c we(1 r) The lifetime budget constraint defines the quantities of current and future consumption the consumer can acquire, given current and future and income taxes, through borrowing and lending on the credit market. To the NW of the endowment E, the consumer is a lender with positive savings To the SE of E, the consumer is a borrower with negative savings

8 Indifference Curves between current and future consumption

9 Sara s Desire for Consumption Smoothing Consider the three bundles Sarah prefers the third bundle since the it offers smoother consumption

10 Optimization Marginal condition that holds when the consumer is optimizing: - The marginal rate of substitution between today s and tomorrow s consumption must be equal to the relative price of current consumption in terms of future consumption

11 A Consumer who is a Lender The consumer is endowed with E chooses optimally to consume at A where the marginal rate of substitution is equal to 1+r This consumer is a lender with positive savings

12 A Consumer who is a Borrower The consumer is endowed with E chooses optimally to consume at A where the marginal rate of substitution is equal to 1+r This consumer is a borrower with negative savings

13 An Increase in Current Income for the Consumer What happens when current income increases? (for example winning the lottery) Discussion: what would you do? Spend all or save some?

14 An Increase in Current Income for the Consumer Current and future consumption increase. Saving increases. The consumer acts to smooth consumption over time.

15 An Increase in Current Income for a Lender When current income increases, lifetime wealth increases from we1 to we2 Since the interest rate is unchanged, the slope remains constant The optimal allocation moves from A to B Consumption of both goods increase Current consumption increases by less than the increase of current income Savings increase

16 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. Discussion: why?

17 Deviations from Trend in Durables Consumption and Real GDP Discussion: Is consumption of durables more volatile than real GDP?

18 Deviations from Trend in Consumption of Nondurables/Services and Real GDP Discussion: Is consumption of nondurables/services more volatile than real GDP?

19 An Increase in Future Income for the Consumer What happens when future income increases? (for example getting a job that doesn t start immediately) Discussion: what would you do? Wait until increasing consumption or increase now?

20 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.

21 An Increase in Future Income When future income increases, lifetime wealth increases from we1 to we2 Since the interest rate is unchanged, the slope remains constant The optimal allocation moves from A to B Consumption of both goods increase Future consumption increases by less than the increase of future income Savings decrease, or in this case, becomes a borrower!

22 Temporary and Permanent Increases in Income 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.

23 Temporary Versus Permanent Increases in Income A temporary increase in income is an increase in current income Budget constraint shifts from AB to DE The optimal allocation moves from H to J. Positive saving A permanent increase in income increases both current and future income Budget constraint shifts from AB to FG The optimal allocation moves from H to K. Larger effect on current consumption

24 Next, let s look at how the consumer respond to a change in the real interest rate

25 An Increase in the Real Interest Rate This changes the relative price of future consumption goods in terms of current consumption goods this has income and substitution effects!

26 An Increase in the Real Interest Rate for a Lender Starting point: E Optimal consumption: A with r1 Budget constraint becomes steeper, going through E Optimal consumption: B with r2 A to D is the substitution effect D to B is the income effect As a result, future consumption increases Current consumption and savings may rise or fall

27 An Increase in the Real Interest Rate for a Borrower Starting point: E Optimal consumption: A with r1 Budget constraint becomes steeper, going through E Optimal consumption: B with r2 A to D is the substitution effect D to B is the income effect As a result, current consumption falls savings increases future consumption may rise or fall