1. Chapter 9
A Two-Period Model: The Consumption-Savings Decision and Credit Markets
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2. Chapter 9 Topics
Consumer’s consumption/savings decision – responses of consumer to changes in income and interest rates.
Government budget deficits and the Ricardian Equivalence Theorem.
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3. Budget Constraints The consumer’s current-period budget constraint:
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4. Budget Constraints The consumer’s future-period budget constraint:
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5. Solve the future-period budget constraint for s:
Simplify
Solve the future-period budget constraint for s:
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6. Next,
Substitute in the current-period budget constraint obtaining lifetime budget constraint:
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7. Consumer’s Lifetime Budget Constraint
Substitute in the current-period budget constraint obtaining lifetime budget constraint:
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8. Consumer’s Lifetime Wealth
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9. Simplified Lifetime Budget Constraint
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10. Simplified Lifetime Budget Constraint: Slope-Intercept
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11. Figure 9.1 Consumer’s Lifetime Budget Constraint
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12. Figure 9.2 A Consumer’s Indifference Curves
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13. Marginal condition that holds when the consumer is optimizing:
Optimization
Marginal condition that holds when the consumer is optimizing:
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14. Figure 9.3 A Consumer Who Is a Lender
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15. Figure 9.4 A Consumer Who Is a Borrower
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16. An Increase in Current Income for the Consumer
Current and future consumption increase.
Saving increases.
The consumer acts to smooth consumption over time.
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17. Figure 9.5 The Effects of an Increase in Current Income for a Lender
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18. 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.
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19. Figure 9.6 Percentage Deviations from Trend in Consumption of Durables and Real GDP
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20. Figure 9.7 Percentage Deviations from Trend in Consumption of Nondurables and Services and Real GDP
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21. An Increase in Future Income for the Consumer
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.
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22. Figure 9.8 An Increase in Future Income
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23. 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.
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24. Figure 9.9 Temporary Versus Permanent Increases in Income
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25. Figure 9.10 Stock Price Index and the Consumption of Nondurables and Services
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26. Figure 9. 11 Scatter Plot: Consumption of Nondurables and Services vs
Figure 9.11 Scatter Plot: Consumption of Nondurables and Services vs. Stock Price Index
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27. Figure 9.12 An Increase in the Real Interest Rate
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28. 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.
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29. Figure 9.13 An Increase in the Real Interest Rate for a Lender
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30. Figure 9.14 An Increase in the Real Interest Rate for a Borrower
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31. Effects of an Increase in the Real Interest Rate for a Lender
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32. Effects of an Increase in the Real Interest Rate for a Borrower
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33. Perfect Complements Example
With perfect complements, the ratio of future consumption to current consumption is constant.
The consumer’s budget constraint must hold.
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34. Perfect Complements Example
With perfect complements we can solve explicitly for current and future consumption:
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35. Perfect Complements Example
Substituting for lifetime wealth gives:
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36. Figure 9.15 Example with Perfect Complements Preferences
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37. Government Budget Constraints
The government’s current-period budget constraint:
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38. Government Budget Constraints
The government’s future-period budget constraint:
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39. Government Budget Constraints
The government’s present-value budget constraint:
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40. Credit Market Equilibrium Condition
Total private savings is equal to the quantity of government bonds issued in the current period.
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41. Income-Expenditure Identity
Credit market equilibrium implies that the income-expenditure identity holds.
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42. Ricardian Equivalence
The Ricardian Equivalence Theorem is illustrated algebraically, numerically, and in two graphs.
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43. 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.
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44. Ricardian Equivalence
Then, substitute in the consumer’s budget constraint – taxes do not matter in equilibrium for the consumer’s lifetime wealth, just the present value of government spending.
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45. Figure 9.16 Ricardian Equivalence with a Cut in Current Taxes for a Borrower
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46. Figure 9.17 Ricardian Equivalence and Credit Market Equilibrium
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47. Figure 9.18 Perfect Substitutes, MRSl,C <1 + r.
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48. Figure 9.19 Perfect Substitutes, MRSl,C <1 + r.
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49. Figure 9.20 Competitive Equilibrium in the Example
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50. Figure 9.21 Total Government Surplus for the United States
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51. Figure 9.22 Total government Debt (federal, state, and local)
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