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Chapter 8

Chapter 8. A Two-Period Model: The Consumption-Savings Decision and Ricardian Equivalence. In this chapter we will introduce the intertemporal choice . More specifically, consumption-saving decision over time. Solow model has done it in an arbitrary way.

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Chapter 8

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  1. Chapter 8 A Two-Period Model: The Consumption-Savings Decision and Ricardian Equivalence

  2. In this chapter we will introduce the intertemporal choice. More specifically, consumption-saving decision over time. • Solow model has done it in an arbitrary way. • While we will solve it as an optimization results.

  3. We will also talk about an important implication of this model—Ricardian Equivalence Theorem. • We start from the simplest framework: a two-period model

  4. The Two-period Model • First period: current • Second period: future • No production and investment ( no K )

  5. Consumer Behavior • N consumers • Receive y in the current period, y’ in the future period. Paid tax t and t’ in two periods respectively.

  6. Budget Constraint • Current period budget constraint c+s=y-t c>0, s can >, or < 0

  7. Second period budget constraint c’=y’-t’+(1+r)s • The life time budget constraint

  8. It says present value of lifetime consumption = present value of lifetime income – present value of lifetime tax • Call the RHS the lifetime wealth we

  9. Figure 8.1 Consumer's Lifetime Budget Constraint

  10. Preferences • Still keep the same properties as before, in stead that now is a trade-off b/w current and future consumption. • More is Preferred to Less (increasing) • Consumers Value Diversity (concave) • Current and Future Consumption are Normal Goods

  11. Figure 8.2 A Consumer's Indifference Curves

  12. Concavity of utility function (or convexity of the indifference curve) determines consumer’s desire to smooth consumption over time

  13. Table 8.1 Sara’s Desire for Consumption Smoothing

  14. Consumer Optimization • The optimization condition

  15. Figure 8.3 A Consumer Who Is a Lender

  16. Figure 8.4 A Consumer Who Is a Borrower

  17. An Increase in y • The effect of y ↑ on c, c’ and s • Current consumption c increases • Future consumption c’ increases • Saving s increases

  18. Why s↑? • Consumer wants to smooth the consumption over time • The theory predicts aggregate consumption is less volatile than aggregate output. • Recall the business cycle facts, it is true.

  19. Figure 8.5 The Effects of an Increase in Current Income for a Lender

  20. Figure 8.6 Percentage Deviations from Trend in GDP and Consumption, 1947–2003

  21. An Increase in y’ • The effect of y’ ↑ on c, c’ and s • Current consumption c increases • Future consumption c’ increases • Saving s decreases

  22. Figure 8.7 An Increase in Future Income

  23. Permanent Income Hypothesis • Consumer’s response will be different when they face temporary or permanent changes in income. • Think about the example. You win lottery $1000 only this year, or you win lottery $1000 every year. Does this make difference in your consumption behavior?

  24. Milton Friedman claims a primary determinant of a consumer’s current consumption is his or her permanent income (we in our model). Temporary changes in income yield small changes in permanent income, hence will have small effects on current consumption. While permanent changes in come will have large effects on we and current consumption.

  25. Figure 8.8 Temporary Versus Permanent Increases in Income

  26. In our two-period setting, permanent increases in income will have a larger effect on current consumption. • If the increase is temporary, we see saving increases; while if the increase is permanent, there need not be an increase in saving.

  27. Permanent tax decrease • Graphical analysis • How does the saving change?

  28. An Increase in r • Budget constraint pivots around the endowment point. • Income effects vs. substitution effects

  29. r↑ for lender • Substitution effect: c↓, c’ ↑ (recall the relative price of future consumption is 1/(1+r)) • Income effect: c↑, c’ ↑ • Total effect: c?, c’ ↑, s?

  30. Figure 8.11 An Increase in the Real Interest Rate

  31. Figure 8.12 An Increase in the Real Interest Rate for a Lender

  32. r↑ for borrower • Substitution effect: c ↓, c’ ↑ (recall the relative price of future consumption is 1/(1+r)) • Income effect: c ↓, c’ ↓ • Total effect: c ↓, c’?, s ↑

  33. Figure 8.13 An Increase in the Real Interest Rate for a Borrower

  34. An Example: Perfect Complements

  35. Figure 8.14 Example with Perfect Complements Preferences

  36. Add in Government • Government collect current taxes T=Nt • Futuretaxes T’=Nt’ • Government can also issue bonds B, bearing the interest rate r

  37. Government current period budget constraint G=T+B • Future period budget constraint G’+(1+r)B=T’

  38. Hence government has present-value budget constraint

  39. Competitive Equilibrium In this two-period economy, an CE isan consumption allocation (c,c’), an saving decision s for N consumers, and a real interest rate r such that • Each consumer chooses c, c’ and s optimally given r

  40. The government present-value BC holds. • The credit market clears.

  41. National income identity

  42. The Ricardian Equivalence Theorem • If current and future government spending are held constant, then a change in current taxes with an equal and opposite change in the present value of future taxes leaves the equilibrium real interest rate r and the consumption of individuals unchanged.

  43. Put in this way: a change in the timing of taxes by the government is neutral. • It is a very strong result! • Why? Because a tax cut is not a free lunch.

  44. Proof Gov’s present-value BC

  45. Substitute into the consumer’s life-time BC

  46. Now consider the experiment as following • There is no change in Gov’s BC, so does the consumer’s life-time BC.

  47. Hence c,c’ and r stay the same. • But private saving s increases. • Consumers anticipate the increases in future taxes, so they increases their savings by the amount of the tax cut.

  48. Figure 8.17 Ricardian Equivalence with a Cut in Current Taxes for a Borrower

  49. But in the reality, the government deficits (tax cut) do matter because • The Distribution of Taxes across Different Individuals • The Distribution of Taxes across Different Generations • Distorting Taxes • Credit-market Imperfections

  50. What Happens When RET Does Not Hold? • We will relax the assumptions of RET, especially focus on intergenerational redistribution (Social Security System) and the credit market imperfections.

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