Final Examination
December 18, 1998

Directions: do all work on the exam itself, answering the question in the space provided. If you require extra space, use the back of the exam, indicating that you have done so.

Name:

1-1	1-2	1-3	1-4
1-5	1-6	2-1	2-2
2-3	2-4	2-5	2-6
3-1	3-2	3-3	3-4

First Part (10 point questions)

For each of the following statements, indicate whether they are TRUE or FALSE and explain why.

1 There are times when GDP declines for a year or so. The most prominent example is 1929-1933, the Great Depression. Perhaps there is nothing the government can do about these declines, but it is vital that it keeps national income up during these declines.

This is nonsense. Remember that National Income is the flip side of National Product. If National Product falls, national income must fall and vice versa.

2 I'm not wealthy. I only earn $25,000 a year. It is true that fifteen years from now I will receive an inheritance of $10,000,000. Then, I will be wealthy. But now, I am not wealthy.

Again, nonsense. Wealth is the present value of current and future income. If you are getting $10,000,000 fifteen years from now, you are wealthy. Go out and buy that new sports car.

3 If we cut taxes, people will work harder and the government will collect more revenue.

Disagree. If we cut taxes, people will work harder, but the government may not collect enough revenue from the extra work to offset the revenue loss from the tax cut.

4. If the Federal Reserve System wanted to increase the money supply this month, December 1998, it could do so by simply cutting its reserve requirements. There is no need for open market operations.

Disagree. The reserve requirements that really matter are those set by banks for business reasons. The Fed's reserve requirements are generally avoided.

5. A short run Phillips Curve gives the relation between inflation and unemployment.

Disagree. It gives the relation between unexpected inflation and unemployment.

6. If the government increases spending by $10 for one year and pays for the increased spending with taxes, there will be more of an increase in aggregate demand than if the spending and tax increases were permanent.

I'm slipping. This one is true. The reason is that both the permanent and temporary increases increase government demand by the same amount. But the permanent increase involves a greater reduction in wealth, because there are taxes for years to come, and thus involves a greater reduction in consumption.

Second Part (10 Point Questions)

1. Explain the economy theory that is the basis for purchasing power parity. What assumptions are necessary for the theory to hold up in reality?

The theory is based on assumptions of costless arbitrage, god information about prices and no restrictions on movement of goods and services across borders. If prices are not equal, there is incentive for arbitrage, which will tend to equalize prices.

2. The United States has had a relatively constant rate of growth of real GDP since the end of World War II. European countries initially had high growth rates, but they have recently declined. In other countries, such as Malaysia, growth rates are very high and continue to be high.

(a) Make Sense of this pattern.

(b) What growth rate do you expect for Malaysia in the next few years? What growth rate do you expect 50 years from now? Why?

This is the Catch Up theorem. I expect Malaysia to have high growth in the next few years, but I expect it to decline over time. The nations with low growth rates are those who do not meet the prerequisites for growth.

3. Draw and label carefully a graph showing a short run and a long run aggregate supply curve. Explain carefully why they have different slopes. If the price level was 100 last year and the expected inflation rate as 5%, what can you say about the point at which the two curves intersect? Why?

Put the price level on the vertical axis and the level of output on the horizontal axis. The long run aggregate supply curve is a vertical line. The short run aggregate supply curve is an upward sloping line. The reason why the price level can have an impact on the supply is that people get fooled. References to imperfect information, etc, are called for. The two curves intersect at the expected price level, in this case 105.

4. Explain what is meant by the Natural Rate of Unemployment. Explain why it might be higher in one country than another.

The Natural Rate of Unemployment measures the unemployment rate when we are along the long run aggregate supply curve. It might be higher in one country because of differences in government incentives to search, differences in the safety net, etc.

5. In 1981, Paul Volker, then Chairman of the Federal Reserve System, cut the rate of growth of the money supply, bringing inflation under control but also triggering a major recession. Explain why cutting the rate of growth of the money supply will cut the inflation rate and why the recession could have been avoided if people had believed Volker was serious.

The inflation rate is given by the quantity theory, which states that the inflation rate equals the rate of growth of the money supply less the rate of growth of real output. Thus the Quantity Theory directly prescribes a cut in the rate of growth of the money supply as a way of cutting the inflation rate. The recession came about because of a lack of credibility. The cut in the money supply also cut aggregate demand, and thus caused a movement along the short run aggregate supply curve. If people had believed Volker, the short run aggregate supply curve would have shifted and the recession would have been avoided.

6. Explain how an open market operation works. Give an example of how the Federal Reserve System might use open market operations if it wanted to push the aggregate demand curve to the right. Show why the open market operation you suggest would have the effect on aggregate demand.

An open market operation occurs when the Federal Reserve System buys or sells government bonds in the open market. When it buys bonds, it pays for them with newly printed money. When it sells bonds, it retires the money it receives from the money supply. Recall the equation of exchange, MV = PY. If it wants to increase Y, aggregate demand, it must increase M, and it can do that by buying bonds in the open market.

Third Part (20 Point Questions)

1. In answering these questions, be sure to show your work.

a. If the M2 multiplier is 70, M2 is $14,000, the price level is 1.4, real GDP is $5000, and M1 velocity is 5, what is the M1 multiplier?

If M2 is $14,000 and the M2 multiplier is 7, then the monetary base is $200. We also know that MV = PY, if Y = $5000, V = 5, the price level equals 1.4, then M2 = $1400. The M2 multiplier must then be 7

b. If real GDP rises from $5,000 to $6,000 and M and the price level are unchanged, how much (in percent) must velocity change?

Recall the equation MV = PY. If Y goes up by 20% and M and P are unchanged, then V must go up by 20%

c. The kingdom of Bratwurst expects that factor productivity will grow by 2% next year. Both population and the labor force are expected to grow by 1%, and the capital stock is expected to grow by 4%. What will be the rate of growth of total output?

From our basic growth equation, we know that the rate of growth of output is equals the rate of growth of factor productivity (2%) plus the rate of population growth (1%) plus 1/3 of the difference between the rate of capital growth (4%) and the rate of growth of the labor force. That difference is 3%, so we know this contributes another 1% to GDP growth. Thus GDP is growing at 4%.

d. If M2 is growing at 5% a year, and real GDP is growing at 6%, and prices are stable, then what can you say about the rate of growth of velocity?

It must be growing at 1% a year.

2. Suppose that, when you go home after this exam, you get some news. For each of these events, predict what effect it will have on your wealth and hence your consumption. Note: assume that these stories are true. Don't worry about whether the check is good, whether the newspaper stories are accurate, or that you might change your major, etc. Further, show what effect it will have on the real interest rate and the level of investment. Show the logic by which you arrive at your answer. I expect clear well-labeled graphs in these answers.

· Your Uncle Frank has written, surprisingly enclosing a check for $500.

Your budget line shifts out, thus leading to an increase in wealth and consumption now. Your saving goes up, leading to an increased supply of loans and hence a lower interest rate and an increase in the level of investment.

· You read a newspaper story that salaries for persons with your major are expected to rise.

Your budget line shifts out, leading to an increase in wealth and consumption. But, you have no more income this year. Thus your saving goes down or borrowing goes up. The increase in consumption leads to a decreased supply of loans and hence a high interest rate and an decrease in the level of investment

· You read of a new law requiring an additional year of study for persons in your major.

Your budget line shifts in, leading to a decrease in wealth and consumption. The decrease in consumption leads to an increased supply of loans and hence a lower interest rate and an increase in the level of investment

3. The theory of real business cycles argues that an increase in factor productivity explains some key factors about real business cycles:

· The cyclical nature of employment

· The cyclical nature of wage rates

· The cyclical nature of corporate profits

To illustrate these concepts, suppose that some new virus hits the United States, making all workers lethargic. Thus all workers are less productive. However it is expected that in a year, the population will acquire immunity to this new viral disease. Using the real business cycle model, trace the impact of this disease on employment, wage rates, and corporate profits, both in the coming year and two years from now.

Remember the old proverb: well-labeled and explained graphs are worth a thousand words.

See the lecture notes

4. The following table gives data on the assets of three individuals: John Smith, Will Jones, and Sally Brown, as well as some basic financial data on the U.S. and Canada. (You may assume that all financial data are correct, though some of it has been adjusted to make for easier computation.).

Warning: this may look like the same problem as one I gave last year, but all the numbers and facts have been revised.

John Smith	Will Jones	Sally Brown
Income this period of $40,000, and expects to earn $63,000 next period. Smith has assets of $10,000.	Working in Toronto this period, earning $160,000 Canadian. Will not work after this period, in part because he will receive $88,000 Canadian next period from the estate of his Aunt Helen. No other assets	Now works in San Francisco. Is earning $100,000 this period. Plans to take a job in Canada next period that will pay $220,000 in Canadian Dollars.

Series	Value
US Nominal Interest Rate	5%
Price of Gold in San Francisco	$200 an ounce
Price of Sourdough Bread in San Francisco	$2.00 a loaf
Price of a 2 bedroom apartment in San Francisco	$500 a month
US Unemployment Rate	4.4%
Canadian Unemployment Rate	7.2%
Canadian Nominal Interest Rate	10%
Price of Gold in Vancouver	$400 (Canadian) an ounce
Price of Sourdough Bread in Vancouver	$3.00 (Canadian) a loaf
Price of a 2 bedroom apartment in Vancouver	$800 (Canadian) a month

· Using these data, compute John Smith's wealth in US dollars. Show your work.

This is simple. Wealth consists of income this period ($40,000) plus the value of assets ($10,000), plus the present value next year's income, equal to $63,000/1.05 or $60,000. Thus wealth is $110,000.

· Using these data, compute Will Jones's wealth in US dollars. Show your work.

There are two ways to do this problem. First, Will's income this year is $160,000 Canadian. From the relative price of gold in the US and Canada, we know the current exchange rate is $1 C = $0.50 US. Thus his current income is worth $80,000 US. There are two ways you can account for next period's inheritance. First, you can look at the difference in interest rates, which indicates a 5% appreciation for the US dollar against the Canadian dollar. That is, the Canadian dollar will be worth $0.475 US. Thus his inheritance will be worth ($88,000)(0.475) = $41,800 US. When you discount this at 5% you will get a present value of $39,800, for a total wealth of $119,800. The other way you could do it is to discount the $88,000 at 10%, get a present value of $80,000 in Canadian Dollars. Converting at the current exchange rate, you would get a value of $40,000, with a total wealth of $120,000.

Why don't you get the same answer either way? Round off error. I will accept either answer.

· Using these data, compute Sally Brown's wealth in US dollars. Show your work.

The job this period is worth $100,000. Next period, the job is worth either $100,000 or $99,500 depending on which approach you use. See the answer to Will above. Thus wealth is either $200,000 or $199,500. I will take either one.

· Assuming that they all have the same preferences, whom would you expect to consume the most this year? The least?

Consumption is proportional to wealth. Sally has the highest wealth, while John has the least. Thus Sally has the highest consumption and John has the lowest.

· The US inflation rate is expected to be 3% in the coming year. Because Canada and the US economy are closely linked, with free flow of capital, labor, and goods across the border, there is reason to believe you can tell something about Canadian Inflation Rate. What do you expect the Canadian rate to be?

If the two economies are closely linked, they have the same real interest rate. In the US, the real rate is 2%. Remember Fisher's Law. In Canada, the nominal rate is 10%, so that implies an expected inflation rate of 8%.