# Macroeconomics: Theory through Applications, v. 1.0

by Russell Cooper and A. Andrew John

## 13.6 End-of-Chapter Material

### In Conclusion

Throughout the world, people contribute to and benefit from social security programs like that in the United States. Yet, owing to demographic changes and other factors, the US Social Security system as we currently know it is unlikely to survive. The challenges faced by the United States are present in many other countries with similar demographics. In much of the developed world, the ratio of workers to retirees will decrease over the next decades. Armed with the tools of this chapter, you are now equipped to understand the implications of proposed changes to Social Security programs, both in the United States and the rest of the world.

Our analysis of Social Security combines two tools often used in macroeconomics. The first is the life-cycle model of consumption/saving, which provides insights into how individuals and households make consumption and saving decisions over long time horizons. We saw that people do not have to match their consumption to their spending each year; instead they can save or borrow to keep their consumption relatively smooth over their lifetimes. However, they must still satisfy a budget constraint over their entire lifetime.

The second is the government budget constraint. We first examined the case where the government kept the Social Security system in balance. In this case, revenues and payments were equal each year. Then we examined the case where the government did not necessarily match revenues and spending. In this case, there is still an accounting of government flows that links surpluses and deficits today with future obligations.

Our discussion illustrates a very important fact about how the economy works: household behavior typically responds to government policy. In the case of Social Security, we saw that households reduce their saving when the government saves on their behalf.

### Exercises

1. Suppose that disposable income is $50,000, working years is 50, retirement years is 20, and the Social Security payment is$20,000. What is the lifetime income for this household?
2. Suppose a household lives for two periods, working and earning disposable income of $10,000 in the first period and obtaining retirement income of$5,000 in the second period. Suppose that the real interest rate is not 0 percent (as in our example of Carlo) but rather is 10 percent. What is the discounted present value of the household’s lifetime income? (Refer to the toolkit if you need a reminder of how to calculate a discounted present value.) How would you write the lifetime budget constraint when the real interest rate is not 0 percent?
3. Some rapidly growing countries, such as China, have a very high saving rate. Everything else being the same, explain why a household in a rapidly growing economy would tend to have a low and not a high saving rate. The social security system in China is not very generous. Explain how this would help you to understand the high saving rate in China.
4. Using the life-cycle model, how would the level of consumption respond to an increase in

1. retirement relative to working years?
2. the annual labor income during working years?
3. payments of Social Security during retirement relative to income earned during working years?
5. The equation for lifetime earnings is key to understanding the effects of Social Security. Explain in your words why the last two terms on the right side of that equation disappear using the government budget constraint.
6. Suppose you expect to live for 50 more years. Suppose also that, because the company you work for had a successful year, you get a $50,000 bonus. If you smooth your consumption perfectly, how much of your bonus will you spend this year, and how much will you save? (You can assume the real interest rate is zero.) 7. Suppose you expect to live for 50 more years. Suppose also that, because you have done an excellent job this year, you get a$2,000 raise. This means you expect that your income will be $2,000 higher every year. If you smooth your consumption perfectly, how much of this raise will you spend this year, and how much will you save? (You can assume the real interest rate is zero.) 8. Suppose you expect to live for 50 more years. Suppose also that, because the company you work for had a successful year, your boss tells you (and you believe her!) that you will get a$50,000 bonus one year from now. If you smooth your consumption perfectly, what will happen to your consumption and saving this year? (You can assume the real interest rate is zero.)
9. Why do you think that the Singaporean government allows people to withdraw funds from the government saving scheme in order to buy a house or apartment but not in order to take a vacation?
10. Suppose a government institutes a pay-as-you-go social security scheme. Explain why the first generation of recipients are clear beneficiaries from the scheme.
11. Give two reasons why households do not smooth their consumption perfectly.

Economics Detective

1. Find the most recent Social Security Administration release. What is the current status of the program? When is it forecasted to go bankrupt?
2. Pick a country other than the United States. What is the social security system like there? What is its current status?
3. Go to http://www.ssa.gov/OACT/COLA/cbb.html#Series. What does the contribution and benefits base mean? Using the correcting for inflation tool, what has happened to the contribution and benefit bases in real terms over the past 20 years?
4. Go to the Social Security Administration (http://www.ssa.gov/pubs/10070.html) to figure out how to calculate the benefits for someone about to retire in your group of family or friends.