1. Professor Robert Lucas said in his essay that we can reason by analogy from Kennywood Park to our own, vastly more complicated society. In his analogy (his story), what plays the role of U.S. GDP?

In this essay the value of rides and other goods and services purchased by visitors in the park plays the role of GDP.

2. In his thought experiment, Professor Robert Lucas considered a change in underlying conditions at Kennywood Park. What was that change in underlying conditions? What were its effects?

The change in the conditions was the change in the number of tickets that visitors get per dollar. An important aspect of this change was that it was unannounced (either to the visitors or to the operators of the rides). The result of this change was that the number of rides bought by the visitors went down and that the employment in the ark decreased.

Thinking Exercises

3. Why do you think Professor Robert E. Lucas decided to "make" a depression and "let you watch it unfold" rather than stating his "opinions about the nature and causes of depressions in the United States?" Why would he think this is more valuable to you?

By learning to think logically about an economic issue using a model, like the story of Kennywood Park, you learn how to think about economic issues. If Professor Lucas simply gives you his opinion, you will lack a basis for judging his assertions against other, different, assertions that you might hear from other people.

4. Professor Lucas says that "by increasing the number of tickets per dollar we could as easily have engineered a boom in the park." Explain how that could happen by re-telling Professor Lucas's story with an increase in the number of tickets in the park.

Modify the paragraph that begins, "Yet I want to show you..." so that cashiers begin giving 12 tickets (rather than 8) to the dollar instead of the usual 10. Consider the story as it starts in the next paragraph (beginning, "We can imagine..."). Some customers will buy the same number of tickets as otherwise, spending fewer dollars to do so. Other customers will buy more tickets than usual. Overall, Kennywood Park's money supply (the number of tickets in the park) will have risen. People will use more tickets to buy more rides. Ride operators will see that they are collecting more than the usual number of tickets, and that lines are longer (with people taking less time on "freebies" in between rides). Operators will find that they spend less than the usual amount of time waiting for customers to ride their rides, and that they have fewer empty seats than usual. Some ride operators may take a shorter-than-usual lunch to operate the ride more hours. In other words, the park's real output will have risen -- the park will have experienced a boom.

5. How does Table 1 show diminishing returns to Crusoe’s labor?

As Crusoe increases the number of hours he picks berries, the marginal product of his labor decreases (the last column of Table 1). This decrease means that his labor exhibits diminishing returns.

6. In what way does Crusoe choose his real GDP?

His real GDP is the number of berries he picks. He chooses his real GDP by deciding how many hours to work and how many hours to have for leisure.

Thinking Exercises

7. How would the shape of the production function in Figure 1 change if there were not diminishing returns, so that Crusoe would pick 1,200 berries per hour regardless of how many hours he worked? Draw the production function for that case.

To see that these two figures show the same information it is best to explain how to obtain one of them using the other.

Let's begin with showing that any point on Figure 2 can be deduced from Figure 1. For example, we want to find out what is the largest amount of berries per day Robinson can have given that he chooses x hours of leisure. He has in total 24 a day to divide between work and leisure. So devoting x hours on leisure leaves him with 24-x hours of work. Given the amount of hours worked per day, we can read off Figure 1 the amount of berries. This can be done for any x, so we know how to construct Figure 2 from Figure 1.

Similarly, consider any amount of hours worked on Figure 1. Using Figure 2 we can find out how many berries he will pick a day during that time. Simply deduct from 24 hours the hours worked to obtain the hours devoted to leisure and use this number to find out the corresponding amount of berries on the Production Possibilities Frontier.

9. What determines real GDP in the model with many people specializing and trading? Use graphs to help explain your answer.

The employment in the economy is determined on the labor market:



Firms decide how many people to hire at different wage levels and people decide how much to work. In the equilibrium Demand for labor and Supply of it are equalized.

Given the Equilibrium Employment the real GDP is determined by the Production Function:



 

 

 

10. Explain the equation of exchange and how it relates to the circular flow of economic activity.

The equation of exchange states that the Real GDP multiplied by the GDP price deflator equals the nominal money supply multiplied by the velocity of money.

We know that Real GDP multiplied by the GDP price deflator equals simply the nominal GDP - value of the production of new final goods and services in the economy. The equation of exchange states that all these goods are bought by consumers and paid for with money.

During a year, on average each dollar is used V many times for a purchase of a final good. As there are M dollars available in the economy the total value of transactions made with them equals MV. This gives the equality that MV equals Nominal GDP.

 

11. What is the neutrality of money?

 

Neutrality of money is the implication of an economic model that an increase in the nominal money supply raises nominal prices and wages but leaves real GDP, employment, and relative prices unaffected.

 

Thinking Exercise

12. Suppose the nominal money supply is $4,000, velocity equals 2 per year, and real GDP is 1,000 goods per year. What is the equilibrium price level?

The equilibrium price level is given by equation:



Plugging in the numbers we obtain that the equilibrium price level equals 4000*2/1000=8.

13. Suppose your nominal wage rate rises by 10% and the consumer price index rises by 5%. What happens to your real wage?

 

It increases by a little less than 5%. To see why, denote by w_R the old real wage, by w_N the old nominal wage and by P the old consumer price index. Denote the corresponding new variables by w_R' w_N' and P' respectively. By definition of the real wage we know that:



From the question we know that:



Putting these equations together we obtain:



 

14. Explain why doubling the nominal money supply and all the nominal prices is similar to changing units of measurement from gallons to half-gallons, or miles to half-miles.

When all the nominal prices double, then the relative prices remain unchanged. People get twice as many dollars for their work as before and they pay for the goods and services twice as much as before. As at the same time the nominal money supply doubles, there is enough money to perform all these transactions. No quantities change: people work the same amount of hours and they buy the same goods, firms make the same investment and employment decisions. The only thing that does change is the measure of the value of transactions: each "old dollar" is now worth two "new dollars". This is similar to changing the units to measure volume or distance as suggested in the question: the physical volume or distance does not change but the "measurement value" doubles.

 

15. List some reasons for unemployment.

• Continuing economic changes - job destruction in some industries/regions and job creation in others makes people spend time unemployed to find their new job.
• The costs of matching process - it takes time and resources to match an unemployed worker with a job vacancy. These costs makes the matching process last longer and unemployment persist.

• Recessions - cyclical changes in the economy tend to create cyclical unemployment.

16. Explain why the rate of unemployment tends to move toward its equilibrium level.

If unemployment is below its equilibrium level, the rate of job destruction is higher than the rate of job creation and unemployment rises. If unemployment is above its equilibrium level, the rate of job destruction is lower than the rate of job creation and unemployment decreases. In this way, the rate of unemployment tends to move toward its equilibrium level.

Thinking Exercise

17. Discuss this statement: "Advances in technology that replace workers with machines are likely to raise the rate of unemployment over the next several decades by decreasing the number of jobs available in the economy."

This statement starts with a true assumption -- that many advances in technology over the next several decades will eliminate jobs that people currently do because machines will do them -- and invalidly concludes that unemployment will rise and the total number of jobs will fall. However, a person who has been replaced by a machine is not worthless! That person still has something to contribute to other people, so he and other people can find a mutually-advantageous trade in which that person works to provide goods or services that other people want. In other words, people create new jobs. Jobs are trades. As long as a person has the ability to do something that other people value (as shown by their willingness to pay), they can create new jobs. That is why employment has increased in the past, along with population, despite massive changes in technology in the last two centuries.

18. Consider the Kennywood Park story. (a) Explain how changes in consumer tastes might create unemployment among ride operators in the Park. (b) How would you identify job destruction and job creation in the Park? (c) Explain how the fall in the money supply described by Professor Lucas creates unemployment among ride operators. (d) What could ride operators do to become re-employed in the Park, after a fall in the money supply? (e) How would you estimate equilibrium unemployment in the Park? How would you estimate cyclical unemployment?

(a) If tastes changed, so that people no longer liked roller coasters or any fast rides, and only liked slow, mild rides, then roller-coaster operators would become unemployed.

(b) Job destruction at Kennywood Park would equal the number of roller-coaster operators who lost their jobs. Job creation would occur as the Park built more Merry-Go-Rounds and other slow rides. The park would hire operators for those rides, and job creation would equal the number of new people hired.

(c) The fall in the money supply in Kennywood Park creates unemployment among ride operators in a different way -- each operator has less work to do each day, so each operator spends more time standing around doing nothing, or maybe goes home early.

(d) If Kennywood Park continued to give only 8 tickets to the dollar, ride operators would start charging fewer tickets for their rides. For example, a ride that previously cost 5 tickets might now cost only 4 tickets. Then the number of riders would go back to the original level, and unemployment at the Park would end.

(e) Equilibrium unemployment of ride operators would be the number of hours that they stand around without work to do. Cyclical unemployment would be the extra number of hours they stand around on the Sunday that Professor Lucas describes in his story.

19. (See the story in the textbook.)

20. Why do you think Professor Lucas says that "we could not use monetary manipulation to engineer a permanently higher level of prosperity in the park"? What might happen if the park tried to do that?

If the park tries to do that by increasing the rate of tickets per dollar every Sunday, then the ride operators are going to realize it and adjust their prices accordingly every Sunday. In this way a permanent effect is not possible. If the park tries to do that by changing the rate irregularly, then the operators will try to check the rate every morning to adjust their prices. If this is not possible, they are going to try to somehow insure themselves against the changes - for example by setting high prices every morning and trying to infer current rate from the behavior of visitors. If this happens, the output of the park is going to be lower not higher, so again a permanent prosperity is not feasible.

 

21. In what ways are fluctuations in Robinson Crusoe’s real GDP like recessions and booms in the U.S. economy? In what ways do they differ?

They are similar, because some of them are caused by the same reasons. For example, both in Robinson's and U.S. economy the real GDP is affected by technical change, changes in labor supply, changes in weather.

They are different because there are lots of reasons of variability in U.S. real GDP that are not present in the Robinson's economy. For example, changes in money supply, as explained in the Professor's Lucas story, can cause recessions in real economy, while Robinson is not using money at all.

 

22. Suppose the nominal money supply is $2,000, velocity equals 1 per year, and real GDP is 1,000 goods per year. What happens to the equilibrium price level if real GDP rises to 2,000 goods per year?

The equilibrium price level drops from 2 to 1.

 

23. How large is equilibrium unemployment if the rate of job destruction is 300,000 workers per month, and one-tenth of unemployed workers find jobs each month? Suppose that 10 million people are currently unemployed, and explain why unemployment falls over time toward its equilibrium level.

Denote by U the unemployment. The equilibrium unemployment is defined as unemployment at which the rates of job creation and destruction are equal. This implies that:

300,000 = 0.1*U

Solving for the equilibrium unemployment we obtain that it is equal to 3,000,000.

If at the given month the unemployment is above its equilibrium level, the rate of job destruction is lower than the rate of job creation: one tenth of any number larger than 3 million is more than 300,000. In this way the unemployment decreases toward its equilibrium level.

In the table below we have calculated, how unemployment changes from month to month. Notice, that in the beginning, when the unemployment is much higher than the equilibrium one, the convergence is fast. As the unemployment becomes closer to the equilibrium one, the convergence is much slower. During the first 12 month the unemployment drops by 5 million and during the second 12 months by less than 1.5 million.