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Macroeconomics Exam Problems: Demand for Money

(The attached PDF file has better formatting.)

Take heed: Several homework assignments analyze the demand for money. The practiceproblems here are simple; they are basic relations you should know. Some final examproblems are patterned after the homework assignments.

! Know how each macroeconomic variable (real interest rate, inflation rate, consumption,transaction costs) affects the real demand for money.

! Know how the demand for money and the money supply determine the price level.! Know the effects of business cycles and seasonality on the real demand for money and

the price level.! Given a scenario and a change, trace the effects on each macroeconomic variable.

Review the homework assignments for complete exam preparation.

! The four scenarios in the homework assignment for Module 24 are not tested on thefinal exam, since they are not explicitly discussed in the textbook.

! The other homework assignments use scenarios explicitly discussed in the textbook.If you do not understand the macroeconomic relations after reviewing the textbookchapter, post a question on the discussion forum for any item that is unclear to you.

*Question 1.1: Nominal Demand for Money

People demand money to buy goods, but currency and checking deposits earn no interest.Which of the following increases the nominal demand for money?

A. A one time only decrease in the price level.B. A one time only decrease in the money supply.C. A decrease in the nominal interest rate.D. A decrease in the amount of consumption expenditures.E. A decrease in the transaction costs of exchanging bonds for money.

Answer 1.1: C

Statements A and B: A one time only decrease in the price level or the money supply hasno effect on inflation or nominal interest rates. The change in the price level decreases thenominal demand for money.

Statement C: A decrease in the nominal interest rate makes consumers less concernedabout investing their cash and more concerned about avoiding transaction costs. Theyexchange bonds for money less frequently and hold larger average money balances.

Statement D: A decrease in consumption causes a decrease in the demand for money.

Statement E: A decrease in transaction costs causes consumers to exchange bonds formoney more frequently, leading to a decrease in average money balances.

*Question 1.2: Demand for Money

Suppose the government bans on-line banking and ATM machines to reduce identify theft. Consumers must do their banking at bank branch offices with live tellers, raising thetransaction costs of bank visits. If money is neutral, the government action causes

A. The real interest rate to decline.B. The real interest rate to rise.C. The price level to decline.D. The price level to rise.E. Neither the real interest rate nor the nominal interest rate to change.

Answer 1.2: C

The demand for money increases, since consumers want to avoid bank visits. For themoney market to remain in equilibrium, the real money supply must increase, so the pricelevel must decline. Money is neutral so it has no effect on real interest rates.

Macroeconomics Final Exam Practice Problems: Indifference Curves


Indifference curves are used in both the microeconomics and macroeconomics courses.

! The microeconomics course uses indifference curves for two commodities (bread andwine) to illustrate free market pricing.

! The macroeconomics course uses indifference curves for leisure and wage income toexplain the labor market.

The concepts are the same. Material from one course is valid for the other course as well.

Indifference curves are downward sloping and convex (decreasing marginal utility). Thepractice problems focus on these two properties. Given a set of points on one indifferencecurve, determine if another point might be on the same curve.

If you have not taken the microeconomics on-line course, see the discussion forum for thatcourse for additional practice problems.

*Question 1.1: Indifference Curves

Leisure (time not working) is on the horizontal axis and consumption is on the vertical axis. An indifference curve is the locus of points among which the consumer is indifferent.

Three combinations of leisure and consumption on one indifference curve are

1. 20 hours of leisure per day + $80,000 of consumption per year2. 18 hours of leisure per day + $84,000 of consumption per year3. 16 hours of leisure per day + $92,000 of consumption per year

Which of the following combinations might be on the same indifference curve? (Four ofthese points can not be on the same indifference curve; one might be on the same curve.)

A. 22 hours of leisure per day + $75,000 of consumption per yearB. 14 hours of leisure per day + $99,000 of consumption per yearC. 19 hours of leisure per day + $89,000 of consumption per yearD. 21 hours of leisure per day + $83,000 of consumption per yearE. 12 hours of leisure per day + $121,000 of consumption per year

Answer 1.1: E

Leisure and consumption are economic goods with positive utility. If one point has moreleisure and more consumption than a second point, that point has greater utility.

Indifference curves show decreasing marginal utility along each axis. If the two axes areGoods Y and Z, as we reduce Good Y, we need increasing amounts of Good Z to retainthe same utility.

! As we reduce Good Y, its marginal utility increases.! As we increase Good Z, its marginal utility decreases.

1 1 2 2 3 3Illustration: Three points lie on the same indifference curve: (L , C ), (L , C ), and (L , C ),

1 2 3with L < L < L . (L is leisure; C is consumption.)

1 2 3Both goods are valuable, so C > C > C . As leisure increases along an indifferencecurve, consumption decreases (and vice versa).

2 3 3 2 1 2 2 1By decreasing marginal utility, (C C ) / (L L ) > (C C ) / (L L ). As leisureincreases, its marginal value decreases, so we need more consumption per unit of leisureto have the same total utility.

Consider Points 1, 2, and 3.

! Point #1 has the highest leisure and the lowest consumption.! Point #3 has the lowest leisure and the highest consumption.

2 3 3 2 1 2 2 1We compare the ratios (C C ) / (L L ) and (C C ) / (L L ) in $000 per hour:

2 3 3 2! (C C ) / (L L ): ($84,000 $92,000) / (16 hours 18 hours) = 4.000

1 2 2 1! (C C ) / (L L ). ($80,000 $84,000) / (18 hours 20 hours) = 2.000

Decreasing marginal utility means that indifference curves are convex (concave upwards). These three points on the same indifference curve imply that a consumer who has

~ 16 hours of leisure a day would pay $6,000 a year for two more hours of leisure a day.~ 18 hours of leisure a day would pay $4,000 a year for two more hours of leisure a day.

We infer the following items about this indifference curve:

! The curve is convex between 18 and 20 hours of leisure a day. A consumer who has19 hours of leisure must receive less than (or equal to) ($80,000 + $84,000) =$82,000 to be on the same indifference curve.

! The curve is convex between 16 and 18 hours of leisure a day. A consumer who has17 hours of leisure must receive less than (or equal to) ($84,000 + $92,000) =$88,000 to be on the same indifference curve.

! The curve is convex between 14 and 16 hours of leisure a day. A consumer who has14 hours of leisure must receive more than (or equal to) $92,000 + ($92,000 $84,000)= $100,000 to be on the same indifference curve.

! The curve is convex between 20 and 22 hours of leisure a day. A consumer who has22 hours of leisure must receive more than (or equal to) $80,000 ($84,000 $80,000)= $76,000 to be on the same indifference curve.

The principle of economic goods eliminates Choices C and D.

! Point C has more leisure and more consumption than point #2, so it has higher utility.! Point D has more leisure and more consumption than point #1, so it has higher utility.

The principle of decreasing marginal utility eliminates Choices A and B.

! Statement A: Points #1 and #2 imply that leisure is worth $2,000 an hour. As leisureincreases, it is worth less per hour. But Points A and #1 imply that leisure is worth$2,500 an hour at a higher amount of leisure.

! Statement B: Points #2 and #3 imply that leisure is worth $4,000 an hour. As leisuredecreases, it is worth more per hour. But Points B and #3 imply that leisure is worth$3,500 an hour at a lower amount of leisure.

Only point E can be on the same indifference curve as Points 1, 2, and 3.

This solution reviews more the concepts of indifference curves. Economics is a science ofchoices: why consumers choose one situation over another. Much of this course deals withpreferences: do people work, consume, save, and invest more in one scenario or another?

*Question 1.2: Indifference Curves

An indifference curve for leisure and consumption is the locus of points (combinations ofleisure and consumption) among which the consumer is indifferent. Each consumer hasan infinite number of indifference curves that cover the plane.

Joseph has two job offers.

! Job k requires 7 hours of work a day and pays $49,000 a year! Job j requires 6 hours of work a day and pays $44,000 a year

For the indifference curve analysis, we express this as

! Job k is 17 hours of leisure a day and $49,000 of consumption a year! Job j is 18 hours of leisure a day and $44,000 of consumption a year

On July 1, Joseph is just graduated from college and has no savings. On July 2, Josephwins a $2 million lottery.

A. If Joseph is indifferent between jobs j and k on July 1, he prefers job k on July 3.B. If Joseph is indifferent between jobs j and k on July 3, he prefers job j on July 1.C. If Joseph prefers job k on July 1, he prefers job k on July 3.D. If Joseph prefers job j on July 1, he prefers job k on July 3.E. If Joseph prefers job k on July 3, he prefers job k on July 1.

Answer 1.2: E

Work is less important and leisure is more valuable to Joseph on July 3 than on July 1,since he is richer on July 3.

~ If Joseph prefers leisure to work in some scenario on July 1, he surely prefers leisureto work in that scenario on July 3.

~ If Joseph prefers work to leisure in some scenario on July 3, he surely prefers work toleisure in that scenario on July 1.

Statement A says that Joseph is indifferent between an extra hour of work and an extra$5,000 a year on July 1. We infer that Joseph might prefer the extra hour of leisure on July3, which is Job j, not Job k.

Statement B is the inverse of Statement A; Joseph might prefer Job k, not Job j, on July 1.

Statement C: Joseph might prefer Job k on July 1 because he needs income. On July 3,when he has less need f or income, he might prefer Job j.

Statement D: If Joseph prefers Job j on July 1, he surely prefers Job j on July 3.

Statement E is correct. Even when Joseph is wealthy (on July 3) he prefers the extra$5,000 of income to the extra hour of leisure. When he is poor (on July 1), he surelyprefers the extra income to the extra leisure.

Jacob: Can we say that Joseph prefers Job k on July 1 and Job j on July 3?

Rachel: No. We dont know Josephs preference for leisure vs income.

! Perhaps Joseph has no use for leisure, and prefers Job k on both July 1 and July 3.! Perhaps Joseph has great use for leisure, and prefers Job j on both July 1 and July 3.

If Josephs tastes are the same on July 1 and July 3 except for the effects of greater wealthon July 3, we infer Statement E.

Macroeconomic final exam practice problems: comparative advantage


*Question 1.1: Corn and Mushrooms

Corn and mushrooms are grown in the U.S. and Mexico.

! Mushrooms grow in the wild and are harvested by hand (with no machines). ! Corn is grown on large farms using tractors and harvesters.

The capital per worker is higher in the U.S. than in Mexico. In all other respects, the twocountries are the same: the quality of the work force and investment risks do not differ.

! U.S. farms have all the tractors and harvesters they can use.! Mexican farms have no tractors or harvesters and must rely on hand labor.

All but which of the following is true?

A. The U.S. has a comparative advantage in growing corn.B. Investors prefer to invest in the U.S. rather than in Mexico.C. Farmers trade U.S. corn for Mexican mushrooms.D. The U.S. runs a current-account surplus.E. Mexico runs a current-account deficit.

Answer 1.1: B

Growing corn requires much capital to buy tractors and harvesters. Capital does not helpgrowing mushrooms, since all work is done by hand.

The U.S. has more capital per worker, so it has a comparative advantage in growing corn.U.S. farmers grow corn and exchange it for Mexican mushrooms.

Mexico has less capital per worker, so it has a comparative advantage in growingmushrooms. Mexican farmers grow mushrooms and exchange them for U.S. corn.

U.S. farms already have all the capital they can use and more investment wont help. Butsome Mexican farms may want to grow crops that require much capital. They are willingto pay higher interest rates for the capital, so investors prefer to invest in Mexican farms.

The current-account deficit reflects national savings minus domestic investment.

! U.S. citizens save money and invest in Mexico. " U.S. national savings exceeds domestic investment, so the U.S. runs a current-

account surplus.

! Mexican farmers borrow money from U.S. investors." Mexican national savings is less than domestic investment, so Mexico runs a

current-account deficit.

Jacob: This seems counter-intuitive. If Mexico is the better place to invest, why does theU.S. have so much more capital? People invest in developed countries with much capital,not in developing countries with little capital.

Rachel: This exercise stipulates that all else is equal in the two countries. People invest indeveloped countries because the labor force is better educated, the economies are moreopen, the governments are more stable, and business contracts are subject to law, not tothe personal interests of bureaucrats.

Macroeconomics Final Exam Practice Problems: Government


*Question 1.1: Permanent Increase in Government Expenditures

Government spending may affect private consumption, investment, and interest rates.

Suppose government spending is now $500 billion. If the government permanently raisesspending to $600 billion to finance national health insurance, which of the following is true?

Private Consumption Private Investment Interest Rates

A rise rise fall

B fall fall rise

C no change fall rise

D fall no change no change

E rise rise no change

Answer 1.1: D

Increased government spending makes it harder for private firms to borrow and causespeople to consume and invest less.

If the government finances its spending with debt, interest rates rise, and private firmsinvest less. Consumers expect to pay higher taxes in later years, so they spend less.

If the government finances its spending with higher taxes, consumers spend less and saveless. Interest rates rise, and private firms invest less.

*Question 1.2: Permanent Increase in Government Expenditures


Suppose government spending is now $500 billion. If the government permanently raisesspending to $600 billion to finance national health insurance, which of the following is true?

Real GDP Private Consumption Private Investment Interest Rates

A fall rise rise fall

B rise fall fall rise

C fall no change fall rise

D no change fall no change no change

E rise rise rise no change

Answer 1.2: D




*Question 1.3: Cyclicality

The correlation of consumption, investment, and government expenditures with real GDPaffects our interpretation of business cycles.

! Pro-cyclical a correlation significantly greater than zero.! Counter-cyclical a correlation significantly less than zero.! Independent a correlation not significantly different from zero.

What is the correlation of private consumption, gross domestic investment, and permanent(non-wartime) government expenditures with real GDP?

Private Consumption Gross Domestic

Investment

Permanent Government

Expenditures

A pro-cyclical pro-cyclical counter-cyclical

B counter-cyclical counter-cyclical pro-cyclical

C independent counter-cyclical pro-cyclical

D counter-cyclical independent independent

E pro-cyclical pro-cyclical independent

Answer 1.3: E

*Question 1.4: Temporary Increase in Government Expenditures


Suppose government spending is now $500 bi llion. If the government temporarily raisesits consumption to $600 billion to finance a short-term war, which of the following is true?

Private Consumption Private Investment Interest Rates

A rise slightly rise fall

B fall slightly fall rise

C rise slightly fall rise

D fall slightly rise fall

E rise slightly rise no change

Answer 1.4: B




Macroeconomics Final Exam Practice Problems: Labor


This set of practice problems on labor supply has topics from several modules. Changesin several variables change the labor supply curve, the quantity of labor supplied, the realwage rate, or the marginal product of labor. Focus on the following items:

A change in the tax law that changes the marginal tax rate changes (by the substitutioneffect) the supply curve for labor as a function of the pre-tax real wage rate. Similar effectscome from technology, capital per worker ratios, and human capital (education, health).

A change in workers wealth (from taxes, government services, or supply shocks) changesthe labor supply curve by the income effect.

Changes in one industry (such as higher wages in factory work) change the labor supplycurve for other industries (such as farm work).

The macroeconomics course covers the supply and demand curves for labor. Given anyscenario, know how the supply and demand curves move. When one or both of the curvesmove, the equilibrium quantity of labor and real wage rate change.

The equilibrium real wage rate and quantity of labor change, affecting both the employmentrate and the hours worked. The hours of leisure change, so the marginal value of leisurechanges. The marginal product of labor changes, both pre-tax and after-tax. The changein the labor supply changes the capital per worker and the marginal product of capital.

The final exam problems test the mathematics of the natural unemployment rate. From thejob finding and separation rates, calculate the natural unemployment rate. The homeworkassignment reviews the relations, and two exhibits in the textbook show the computations.

These quantitative problems may be asked various ways, such as

! From the natural unemployment rate and job finding rate, compute the job separationrate.

! From specified changes in job finding and separation rates, compute the percentagechange in the natural unemployment rate.

Some exam problems test the quali tative influences on the natural unemployment rate. Aqualitative influence may have two or more stages. For example, a higher minimum wagemay raise unemployment among unskilled workers and lower unemployment among skilledworkers. We show practice problems with several stages.

Some exam problems test relations among the real wage rate, marginal product of labor,nominal wage rate, price level, real demand for money, and nominal money supply. Thesequestions combined several course modules. Focus on

! the equilibrium relations, such as real demand for money equals the real money supply,or the real wage rate equals the marginal product of labor

! the conversion of real values (real wage rate, real interest rate, real GDP) to nominalvalues (nominal wage rate, nominal interest rate, nominal GDP)

*Question 1.1: Technology level

Workers in Bangladesh sew clothes for sale as exports to Western Europe. Bangladeshis a small country, and its exports are a tiny portion of the world clothes market.

The workers are paid an hourly wage, which reflects the marginal product of labor. A newsewing machine enables workers to sew clothes twice as efficiently.

What are the effects on the supply and demand curves for workers who sew clothes?

Demand curve Supply curve

A moves right (increases) moves right (increases)

B moves right (increases) no change

C moves right (increases) moves left (decreases)

D no change moves left (decreases)

E no change moves right (increases)

Answer 1.1: B

Suppose a worker could sew five shirts in an hour without the new sewing machine, andfirms would hire 1,000 workers at the going rate of $2 an hour. With the new sewingmachine, workers sew 10 shirts an hour, and firms want to hire more workers at the rateof $2 an hour, so the demand curve shifts to the right.

The supply curve is the same workers as before. At a rate of $2 an hour, the same numberof people want to work. If the real wage rate increases, more of these people take jobssewing shirts. That is a shift in the quantity supplied, not a shift in the supply curve.

*Question 1.2: Technology level

Workers in Bangladesh sew clothes for sale as exports to Western Europe. Bangladeshis a small country, and its exports are a tiny portion of the world clothes market.

The workers are paid an hourly wage, which reflects the marginal product of labor. A newsewing machine enables workers to sew clothes twice as efficiently.

What are the effects on the real wage rate and the number of textile workers?

Real Wage Rate Number of Work ers

A increases increases

B increases no change

C increases decreases

D no change decreases

E no change increases

Answer 1.2: A

The previous question says the demand curve moves to the right (increases) and thesupply curve does not change.

! The intersection of the supply and demand curves occurs further to the right.! The supply curve is upward sloping, so a point further to the right is higher.

Farther to the right mean a higher quantity of workers. A higher point means a higher realwage rate.

*Question 1.3: Labor Force

Unskilled men in parts of the Congo work as farm laborers, tilling crops by hand, or searchfor diamonds by hand. Neither task requires much skill, and all workers can do either task.

! People do not search for diamonds on their own. They are hired by diamond searchfirms, which pay an hourly wage.

! The Congo is a small portion of the diamond market. The price of diamonds is notaffected by the number of diamond workers in the Congo.

! The Congo has a limited amount of land on which to search for diamonds. If moreworkers search for diamonds, each worker expects to find fewer diamonds.

In 20X8, a drought ruins the harvest, and the demand for farm laborers falls. What are theeffects on the labor market for diamond workers? For this problem, assume that

Supply ofDiamond Work ers

Demand forDiamond Work ers

Number ofDiamond Work ers

Real Wage Rate ofDiamond Work ers

A Decreases Decreases No change Decreases

B Increases Increases Increases No change

C Increases No change Increases Decreases

D No change No change Decreases Increases

E Increases Decreases Decreases No change

Answer 1.3: C

The supply of diamond workers is the number of workers who want to search for diamondsat a given real wage rate. At a wage rate of $2 an hour for diamond workers

! When the harvest is bountiful, landowners pay more than $2 an hour for farm laborers.Most workers find jobs on farms, and only 10,000 want to hunt for diamonds.

! When the harvest is poor, landowners pay less than $2 an hour for farm laborers. Fewworkers find jobs on farms, and 50,000 workers want to hunt for diamonds.

Take heed: The demand for farm workers has changed, which affects the reservation wagefor diamond workers and the supply of diamond workers.

The demand for diamond workers has not changed. The owners of diamond search firmspay a real wage rate based on the marginal product of labor. The market for diamonds hasnot changed and the quality of diamond workers has not changed, so the demand curvedoes not change.

The greater supply of diamond workers means the supply curve shifts to the right (shiftsdown). The intersection of the supply and demand curves is at a higher quantity of laborand a lower price for labor (real wage rate).

*Question 1.4: Real Wage Rate

Chicago raises the minimum wage from $5.50 to $8.50 an hour so that all employees earna living wage. Chicago has many pizza shops and restaurants that hire teen-age workersand small shops that hire part-time sales clerks at the minimum wage. The change in theminimum wage does all but which of the following?

A. Lowers the quantity demanded of unskilled laborB. Raises the quantity supplied of unskilled laborC. Encourages firms to substitute capital for unskilled laborD. Lowers unemployment of teen-age workersE. Hurts workers whose marginal product of labor is less than the new real wage rate

Answer 1.4: D

Statement A: Unskilled labor costs more after the increase in the minimum wage, so lessis demanded. A pizza shop may pay a teen-ager $6.00 an hour because the hours workis worth $6.00. If the pizza shop must pay $8.50 an hour, it prefers to hire an older workerwith a higher marginal product of labor.

Statement C: Unskilled labor costs more, so firms look for substi tutes. Instead of hiringcheck-out clerks, supermarkets may install self-checkout lanes with machines (capital) forreading the prices of goods.

Illustration: Many factories in France are highly automated: machines do the work, with fewhuman workers. The French say they are more intelligent that other nations, so they moreeasily automate their factories. Economists say that restrictions on labor in France, suchas the 35 hour work week, the difficulty of firing unneeded workers, and the high benefits,reduce the relative value of labor. Firms substitute capital for the high-priced labor.

Statement D: Many teenagers work at the minimum wage, since their marginal product oflabor is low.

! If demand for teen-age labor falls, the unemployment rate increases.! If the minimum wage rises, more teen-agers leave school and seek jobs, further raising

the unemployment rate. Teen-agers who leave school suffer later on.

Statement E: The equilibrium real wage rate is the marginal product of labor. In a freelabor market, workers with a marginal product of labor of $7.00 an hour receive $7.00 anhour in wages. If the minimum wage is $10.00 an hour, firms do not hire these workers.

The effects of minimum wage laws are grasped by a comparison with consumer products.Suppose beef costs $5.00 a pound on free markets, and 40 farms produce 10,000 poundsof beef apiece. Legislators fear that beef producers are not earning a living wage, so theymandate that beef be sold for not less than $10.00 a pound.

Consumers substitute cheaper foods for beef. They eat more fowl and fish and less beef. The quantity of beef demanded declines from 400,000 pounds to 100,000 pounds.

At the higher price, farmers are more willing to sell their cattle for beef. At $5.00 a pound,farmers supply 400,000 pounds of beef. At $10.00 a pound, farmers are willing to supply1,000,000 pounds of beef.

Of the 1,000,000 pounds that farmers supply, only 100,000 are bought. The other 900,000pounds that farmers supply but can not sell are like unemployed labor: people who wantto work but no firm wants to hire them.

The real world is worse. Farm price supports in the U.S. and Western Europe give farmersextra income through the tax system and transfer payments. Consumers pay more forfood and farmers produce too much, which is sold to third world countries. Farmers in thirdworld countries can not compete with government subsidized crops. Everyone loses except the farmers in the U.S. and Western Europe.

Take heed: The terms differ among economists. The natural unemployment rate reflectsthe time needed to search for jobs and workers. Some economists say the higher minimumwage raises the unemployment rate above its natural level. Other economists (like Barro)do not distinguish among causes of unemployment. The higher minimum wage reducesthe job finding rate and raises the natural unemployment rate.

*Question 1.5: Minimum Wage

A city has pizza shops and restaurants that employ waiters, busboys, and cooks.

! Pizza shops cater to blue collar consumers and hire teen-age staff earning $6 an hour.! Restaurants cater to white collar consumers and hire skilled staff earning $12 an hour.

The city has 50 pizza shops and 50 restaurants, with each store serving 1,000 consumersa week.

The mayor believes that income inequality causes unhappiness. To reduce incomeinequality, the city raises the minimum wage from $6 an hour to $12 an hour.

If the wage of pizza shop workers rises to $12 an hour, with no change in the type ofworkers of the work requirements, what are the effects on the quantity of labor suppliedand the quantity of labor demanded?

A. The quantity supplied increases and the quantity demanded decreases.B. The quantity supplied decreases and the quantity demanded increases.C. The quantity supplied and demanded decrease.D. The quantity supplied and demanded increase.E. The quantity supplied decreases and the quantity demanded does not change.

Answer 1.5: A


After the change to a $12 minimum wage, the pizza shops move to other cities. Someconsumers who previously ate pizza now eat at the restaurants.

! In the long-run, more restaurants are opened.! In the short run, the current restaurants serve more consumers, and prices adjust.

Teen-age waiters, busboys, and cooks do not have the skills for high-income restaurants.The current restaurant staff will work more hours, i f needed. Their indifference curverelating income and leisure is convex; that is, they have an upward sloping supply curve.

In the short run, what are the effects on supply of and demand for experienced labor byrestaurants? Assume that no teen-age staff have the experience to work in restaurants,and no experienced workers switch to restaurants from other industries. (The questionasks about the effects on the supply and demand curves, not the quantity supplied and thequantity demanded.)

A. Supply increases and demand decreases.B. Supply decreases and demand increases.C. Supply and demand increase.D. Supply and demand decrease.E. Supply does not change and demand increases.

Answer 1.6: E

! The demand curve increases because more customers want to eat in restaurants.! The supply curve does not change because no workers switch from other industries.


After the change to a $12 minimum wage, the pizza shops close and their owners moveto other states. Some consumers who previously ate pizza now eat at the restaurants.



In the short run, what are the effects on the cost of restaurant meals and the real wage ratefor restaurant workers?

A. Restaurant meals cost more, and the real wage rate rises.B. Restaurant meals cost more, and the real wage rate stays the same.C. Restaurant meals cost the same, and the real wage rate rises.D. Restaurant meals cost the same, and the real wage rate stays the same.E. Restaurant meals cost more, and the real wage rate declines.

Answer 1.7: A

The supply curve is upward sloping. To induce employees to work more, owners must paythem a higher real wage rate. The variable costs of restaurant meals increases, so theprice of the meals increases.

*Question 1.8: Gains and Losses

After the change to a $12 minimum wage, the pizza shops close and their owners moveto other states. Some consumers who previously ate pizza now eat at the restaurants.



Who gains from the minimum wage law?

A. Teen-age waiters gain from the higher real wage rate.B. Restaurant staff gain from the higher demand for their labor.C. Consumers gain from the reduced competition between restaurants and pizza shops.D. Pizza shop owners gain from the higher quality of labor.E. Society gains by the reduced income inequality.

Answer 1.8: B

Statement A: Teen-age workers are now unemployed; they lose.

Statement B: Restaurant workers are paid more and work more. If they want, they couldwork the same hours and be paid more, so they surely gain.

Statement C: Reduced competition hurts consumers.

Statement D: Pizza shop owners have to close and move to other cities; they lose.

Statement E: Income inequality has increased, since teen-age workers are unemployedand restaurant workers earn more.

*Question 1.9: Job Separation

In 20X7, the job separation rate for disabled persons is 0.5% a month, meaning that 0.5%of disabled persons leave their jobs each month, and the job finding rate is 4.5% a month,meaning that 4.5% of unemployed disabled persons find new jobs each month.

To prevent disabled persons from being laid off, Congress adjusts the Americans withDisabilities Act in 20X8, making it harder to fire disabled persons.

! The job separation rate declines to 0.25% a month.! Employers now are more reluctant to hire disabled workers, so the job finding rate

declines to 1.75% a month.

What is the natural unemployment rate for disabled persons, at which workers finding newjobs equals workers leaving their jobs in 20X7 and 20X8?

20X7 20X8

A 0.50% 0.25%

B 4.50% 1.75%

C 5.00% 2.00%

D 9.00% 10.00%

E 10.00% 12.50%

Answer 1.9: E

Use the following reasoning: Let

Z be the natural unemployment rateF be the monthly job finding rate S be the monthly job separation rate

! Workers finding jobs each month are F Z.! Workers leaving jobs each month are S (1 Z).

In equilibrium, workers finding jobs just offset workers leaving jobs.

We solve for the natural unemployment rate before and after the new legislation:

! Before: 4.5 Z = 0.5 (1 Z) A 5Z = 0.5 A Z = 10%! After: 1.75 Z = 0.25 (1 Z) A 2Z = 0.25 A Z = 12.5%

People sometimes speak of a law of unintended consequences. Free markets are efficient,in that they often maximize social welfare. Legislation that interferes with free markets to

help one party generally reduces total social welfare. All parties respond to the legislationto maximize their own self-interests. Since the total pie is smaller, all parties may be worseoff, including the party that the legislation was designed to help.

*Question 1.10: Marginal Product of Labor

! In 20X8, real GDP = $400, price level = 100, and the nominal wage rate = $20 / hour! In 20X9, real GDP = $500, price level = 120, and the nominal wage rate = $30 / hour

The real interest rate, inflation rate, and bank transaction costs do not change.

Which of the following is true?

A. The money supply increased 50%, and the marginal product of labor increased 25%B. The money supply increased 25%, and the marginal product of labor increased 50%C. The money supply decreased 50%, and the marginal product of labor decreased 25%D. The money supply decreased 25%, and the marginal product of labor decreased 50%E. The money supply increased 50%, and the marginal product of labor decreased 25%

Answer 1.10: A

Real GDP increases 25%, so the real demand for money increases 25% and the realmoney supply increases 25%. The price level increases 20%, so the nominal moneysupply increases 1.25 1.20 1 = 50.00%.

The nominal wage rate increases 50% and the price level increases 20%, so the real wagerate increases 1.500 / 1.200 1 = 25.00%

The change in the price level reflects real GDP growth and money growth.

! 1% rise in money supply with no change in real GDP 1% rise in the price level! 1% rise in real GDP with no change in money supply 1% rise in the price level

From the changes in real GDP and the price level, determine the change in the moneysupply. The changes are large, so use a multiplicative model, not an additive model.

The real wage rate is the nominal wage rate divided by the price level. From the changesin the nominal wage rate and the price level, determine the change in the real wage rate.

If the labor market is in equilibrium, the real wage rate equals the marginal product of labor.

Alternative problems:

give change in money supply; determine the change in the price level and then the changein the real wage rate and the marginal product of labor.

308 *Question 1.11: Marginal Product of Labor

! In 20X8, real GDP = $600, price level = 150, and the nominal wage rate = $30 / hour! In 20X9, real GDP = $750, price level = 180, and the nominal wage rate = $45 / hour



A. The money supply increased 50%, and the marginal product of labor increased 25%B. The money supply increased 25%, and the marginal product of labor increased 50%C. The money supply decreased 50%, and the marginal product of labor decreased 25%D. The money supply decreased 25%, and the marginal product of labor decreased 50%E. The money supply increased 50%, and the marginal product of labor decreased 25%

Answer 1.11: A

Real GDP increases 25%, so the real demand for money increases 25% and the realmoney supply increases 25%. The price level increases 20%, so the nominal moneysupply increases 1.25 1.20 1 = 50.00%.


The change in the price level reflects real GDP growth and money growth.

! 1% rise in money supply with no change in real GDP 1% rise in the price level! 1% rise in real GDP with no change in money supply 1% rise in the price level

From the changes in real GDP and the price level, determine the change in the moneysupply. The changes are large, so use a multiplicative model, not an additive model.

The real wage rate is the nominal wage rate divided by the price level. From the changesin the nominal wage rate and the price level, determine the change in the real wage rate.

If the labor market is in equilibrium, the real wage rate equals the marginal product of labor.

Alternative problems:

give change in money supply; determine the change in the price level and then the changein the real wage rate and the marginal product of labor.

*Question 1.12: Real Wage Rate

! 20X8: nominal money supply = $400, price level = 100, nominal wage rate = $20 / hour! 20X9: nominal money supply = $500, price level = 120, nominal wage rate = $30 / hour



A. Real GDP decreases 25%, and the marginal product of labor increases 25%B. Real GDP decreases 20%, and the marginal product of labor increases 20%C. Real GDP decreases 5%, and the marginal product of labor decreases 25%D. Real GDP does not change, and the marginal product of labor increases 5%E. Real GDP increases 4%, and the marginal product of labor increases 25%

Answer 1.12: E

The real demand for money equals the real money supply. The nominal money supplyincreases 25% and the price level increases 20%, so the real money supply increases1.250 / 1.200 1 = 4.17%.

The real money supply equals the real demand for money, so the real demand for moneyincreases 4.17%.

The real demand for money is proportional to real GDP, so real GDP increases 4.17%.


*Question 1.13: Capital Deepening

In 2001, a developing country has many laborers and few machines. All laborers areidentical and all machines are identical. The real interest rate is 5% per annum, themarginal product of labor is $10 per hour, and the marginal product of a machine (capital)is $20 per hour.

From 2002 to 2048, the country invests in new capital. A strong birth control program plusgreater education for women reduces the fertility rate and the population.

In 2049, the country has many machines and few workers. The technology level has notchanged.

Which of the following is the most likely for 2049? (Dollar figures are in real terms.)

Real Interest Rate Marginal Product ofa Work er

Marginal Product ofa Machine

A 7% $14 $16

B 3% $14 $16

C 7% $8 $22

D 3% $8 $22

E 5% $8 $22

Answer 1.13: B

The country has more machines (more capital) in 2049. Think of labor as farm workers andmachines as tractors.

If the country has only a few tractors, each one is used on productive land, so its marginalproduct is high.

If the country has many tractors, all farms have tractors. The marginal product is the valueadded by an additional tractor. Adding another tractor doesnt do as much as the firsttractors, so the marginal product of a machine declines.

The real interest rate is the marginal value of capital. If farms dont need more tractors, noone buys more machines, so no one has incentive to produce more machines. Firms dontborrow money to produce machines, so the interest rate falls.

*Question 1.14: Labor and Capital

In 20X1-20X3, an insurrection in Country W destroys all factories and equipment. Peoplelive on farms, food is planted and harvested by hand, and capital per worker decreases.

In 20X4, a coup restores democracy. In 20X4 through 20X9, Country W adopts industrialand agricultural technology from other countries, and capital per worker increases.

For the period 20X4 through 20X9, which of the following is true?

(This exam problem deals with 20X4 20X9, when capital per worker increases, not 20X1 20X3, when capital per worker decreases.)

MarginalProduct of

Capital

Real RentalPrice

MarginalProduct of

Labor

Real WageRate

A

B

C

D

E

Key:

! = the variable increases! = the variable decreases

Use the following reasoning:

! What is the relation of the capital per worker ratio to the marginal product of capital andthe marginal product of labor?

! What is the relation of the real rental price to the marginal product of capital? The realrental price equals the real interest rate.

! What is the relation of the real wage rate to the marginal product of labor?

Answer 1.14: B

The capital per worker increases, so the marginal product of labor and the real wage rateincrease and the marginal product of capital and the real rental price decrease/

Macroeconomics Final Exam Practice Problems: Convergence


Background: Convergence is a malleable concept. In the nineteenth century, the WesternEuropean nations were more successful than Asian or African countries. Most Europeanspresumed they were innately superior to Asians or Africans.

In later decades, as third world countries developed, fewer people believed in the innatesuperiority of Europeans. Instead, they presumed that natural advantages of Europe madethese nations successful: accessible coasts for shipping, fertile agricultural land, or evenreligious (Protestant) systems that fit well with capitalism.

By the second half of the twentieth century, European civilization had produced two worldwars. Numerous countries in Asia, Europe, the Americas, and the Middle East seemedeconomically capable. Differences were ascribed to historical happen-stance. Low incomecountries would grow quickly by imitating the economies of advanced countries.

Some economists adopted a theory of absolute convergence. Countries were inherentlysimilar, and eventually all would achieve the same economic level. The emergence ofAfrican nations after WW2 and the rapid rise of Asian economies in the 1960s and 1970sseemed to support this theory. Japans ability to duplicate or exceed the characteristics ofWestern economies seemed proof of the theory.

In recent years, some parts of the world (such as Asia) have moved closer or caught upto developed countries and some parts (such as Africa and the Middle East) are fallingfurther behind. Barro presumes that each country has a steady state level, but countriesmay differ. He suggests that political, legal, and cultural attributes affect the steady stateincome of the economy. For example, a culture that does not allow women to work maynever reach the per capital income of Western economies.

Exam problems test absolute convergence, conditional convergence, and their attributeswith scenarios. Focus on the following items:

! When absolute convergence occurs and when only conditional convergence occurs.! How convergence relates to income inequality.! What attributes cause faster or slower growth rates.

*Question 1.1: Conditional Convergence

Conditional convergence presumes a countrys long-term expected economic growth rate(g) is a function of its steady state economic level (y*) and its current economic level (y).Which of the following correctly expresses the signs of the correlation of g with y and y*?

! D(g, y) = correlation of g with y, holding y* fixed; same sign as Mg/My! D(g, y*) = correlation of g with y*, holding y fixed; same sign as Mg/My

D(g, y) D(g, y*)

A > 0 > 0

B < 0 < 0

C > 0 0

D > 0 < 0

E < 0 > 0

You may think of the question as: If y increases with no change in y* (or vice versa) doesg increase or decrease?

Answer 1.1: E

Take heed: The text uses plus and minus signs to show the sign of the partial derivative.Exam problems may use partial derivatives, correlations, or plus/minus signs.

*Question 1.2: Conditional Convergence

Suppose the rate of conditional convergence is 10% per annum for all countries.

Illustration: If steady state output is $20,000 per capita and current output is $16,000 percapita, the expected growth rate is 10% ($20,000 $16,000) / $16,000 = 2.50%.

Countries W, Y, and Z have the following current and steady state output at 1/1/20X6.

Country Current Output Steady State Output

W 20,000 28,000

Y 30,000 40,000

Z 30,500 31,000

Which country has the highest growth rate in 20X6 and which has the greatest output levelat 12/31/20X6?

Highest Growth Rate

in 20X6

Highest Economic Output

at 12/31/20X6

A W W

B Y Y

C Y Z

D W Y

E W Z

Answer 1.2: D

We compute the growth rates in 20X6 and the output level at 12/31/20X6.

Country Current Output Steady State

Output

Growth rate 12/31/20X6

Output Level

W 20,000 28,000 4.00% 20,800

Y 30,000 40,000 3.33% 31,000

Z 30,500 31,000 0.16% 30,550

*Question 1.3: Convergence and Fertility Rates

An economist examining convergence among a group of developing countries finds thateconomic growth stimulates greater education of women and lower birth rates: a 10%increase in GDP per capital leads to a 10% decline in the fertility rate.

! Developing countries start with fertility rates of 5 to 6 live births per woman.! As countries develop, fertility rates decline to between 2 and 3 live births per woman.

All countries benefit from modern medicine. Infant mortality, infectious diseases, andmortality rates rapidly decline in all the countries, whether or not the fertility rate declines.

What type of convergence do we expect over the next generation?

A. Fertility rates do not affect long-term economic growth. The economist examines onlydeveloping countries, so we expect absolute convergence.

B. Fertility rates do not affect long-term economic growth. Developing countries may differ,so we expect conditional convergence, not absolute convergence.

C. High fertility rates promote economic growth. Countries with low fertility rates have lowfuture growth. We expect absolute convergence with especially rapid mean reversion.

D. High fertility rates are important for economic growth. Countries with lower fertility rateshave lower future growth, but other conditions may preclude absolute convergence. Weexpect conditional convergence with especially rapid mean reversion.

E. High fertility with low mortality prevents consumers from saving money. New capitalmust support new workers, and the capital per worker ratio may decline. If developmentleads to lower fertility rates, convergence may not be evident, since countries that growrapidly and have lower birth rates may grow even more rapidly in later years.

Answer 1.3: E

Barro explains why convergence has not been evident in Africa and the Middle East overthe past forty years. One explanation relies on endogenous population growth.

Economic development often leads to better education and equal opportunity for womenand lower fertility rates, which leads to faster development.

Take heed: Neither Barro nor NEAS advocate lower fertility or take any position regardingbirth control, family planning, or abortion. The textbook summarizes a common perspectiveon economic growth. Economists argue about the effects of low fertility on the social andeconomic future of Western Europe, Russia, Japan, China, and other low growth countries.

*Question 1.4: Convergence

An economist examines convergence in two places:

! Among the states of the U.S. ! Among the countries of Africa.

The economist finds convergence in the U.S. but not among the countries of Africa.

The likely reasons for this difference include all but which of the following?

A. Labor moves easily across U.S. states but not between African countries.B. U.S. states have similar legal and court systems; African countries do not.C. U.S. states have the same currency and federal taxes; African countries do not.D. U.S. states have similar public education systems; African countries do not.E. U.S. states have never had large economic differences; African wars caused large

differences that convergence could not overcome.

Answer 1.4: E

The civil war in the U.S. was as severe (for its time) as most African wars. Europe has alsohad absolute convergence, though its world wars were more severe than African wars.

*Question 1.5: International Trade and Convergence

Since the mid-1980s, the removal of trade barriers, reduction in transportation costs, andbetter education enable skilled workers in developing countries, such as China and India,to perform jobs formerly done in North America and Western Europe. Western countriesnow out-source both skilled and unskilled jobs to China, India, and other Asian nations.Countries focus on industries and professions where they have comparative advantages.

China and India were among the worlds most advanced nations in the fifteenth throughseventeenth centuries. They have highly intelligent populations, strong support for civil law,economic freedoms, and widespread education. Their steady state income per worker isthe same as that of the U.S. and Europe.

Which of the following is most likely to be true?

A. GDP falls in Europe and the U.S. and it rises in China and India.B. Employment falls in Europe and the U.S. and it rises in China and India.C. GDP rises everywhere, but more in Europe and the U.S. than in China and India.D. GDP rises everywhere, but less in Europe and the U.S. than in China and India.E. Employment rises everywhere, but more in Europe and the U.S. than China and India.

Answer 1.5: D

The steady state income per worker of China and India is the same as that of the U.S. andEurope, so they show absolute convergence. They have lower current income per worker,so their income per worker rises faster than that of the U.S. and Europe.

International trade helps all parties, as countries make the goods and services for whichthey have comparative advantages.

Macroeconomics Final Exam Practice Problems: Income Taxes


The final exam problems compare various tax systems. Each tax has two effects:

! The income effect causes people to work more.! The substitution effect causes people to work less.

The income effect is difficult to measure. Taxes pay for government programs, which payfor peoples needs.

Illustration: A person earns $50,000 of pre-tax income. The government imposes a $5,000head tax (lump-sum tax), which has no substitution effect. The person receives $45,000after-tax, and has an incentive to work more.

Suppose the tax funds a national health insurance system. For the same private insurance,the person might pay $10,000. After adjusting for the value of health insurance, thepersons wealth increases after the tax, and the person works less.

Some exam problems compare two tax systems with the same total tax revenue. Thegovernment services are the same under both programs, but the income and substitutioneffects differ for each worker.

Take heed: If the exam problem does not mention the value of the government programsto the taxpayer, assume the tax is used for foreign aid (such as helping residents of Sudan)or foreign wars that have no effect on the taxpayers work effort.

Taxes on labor income are of several forms:

! Flat tax on all income. The marginal tax rate is the statutory tax rate. ! Progressive tax on all income. The tax rate is generally linear from Y% to Z%. Know

how to compute the marginal tax rate from the statutory tax rate. The mathematics isstraight-forward: differentiate the tax liability with respect to pre-tax income. If the taxrate increases with income, the marginal tax rate exceeds the statutory tax rate.

! A tax credit for low income workers makes the tax more progressive.! A two-tiered flat tax (Y% on one range and Z% on another range) has different marginal

tax rates in each range.

Take heed: Taxes are a critical part of the macroeconomic model. The textbook does notshow the mathematics, since many college students can not handle differentiation andintegration. The final exam problems give simple tax systems and ask for the income andsubstitution effects.

*Question 1.1: Marginal Tax Rates

Workers pre-tax wages in Country W are a uniform distribution from $0 to $100,000.

The labor force has 10,000 persons with an average of 2,000 work-hours a year.

In 20X7, Country W has a flat tax rate of 20%.

To reduce income inequality, the government changes the tax code for 20X8 so that

! Workers earning $0 receive a $10,000 tax refund (a negative tax liability). ! The tax refund declines linearly to zero as the workers earnings increase to $100,000.! Income is taxed at a flat rate of 40%.

Illustration: Esther earns $25,000 pre-tax.

! 20X7: Esther pays $25,000 20% = $5,000 and keeps $20,000 after-tax.! 20X8: Esther keeps (1 $25,000 / $100,000) = 75% of the $10,000 tax refund and

pays tax of $25,000 40% = $10,000. Her net tax is $10,000 75% $10,000 =$2,500. Her after-tax income is $25,000 $2,500 = $22,500.

What are the marginal tax rates in 20X7 and 20X8?

20X7 20X8

A 20% 40%

B 40% 50%

C 20% 50%

D 40% 40%

E 20% 60%

Answer 1.1: C

20X7: For a flat tax of 20%, the marginal tax rate is the tax rate of 20%.

20X8: For a flat tax of 40%, the marginal tax rate is the tax rate of 40%. Workers alsoreturn the tax refund of $10,000 linearly as 10% of their income. The combination is a 50%flat tax rate.

The marginal tax rate is the slope of the graph, where the horizontal axis is pre-tax incomeand the vertical axis is the tax liability. In 20X8, the tax liability is

$10,000 Y / $100,000 + Y 40% = 50% Y

Intuition: A person earning $0 gets a tax credit of $10,000, and a person earning $100,000get no tax credit. The tax credit has a 10% tax for all taxpayers.

! Pre-tax income is a uniform distribution from $10,000 to $110,000.! The tax rate is 50%, not 40%.

*Question 1.2: Marginal Tax Rate

People earn $100 million in 20X7 and pay a flat tax rate of 20%. Each person earnsbetween $20,000 and $60,000 a year (pre-tax), with an average of $40,000 per person.

To make the income tax more progressive in 20X8, the government makes the tax rate 0%for the first $20,000 of income and 40% for the next $40,000 of income.

! Joseph earns $35,000 a year (pre-tax) before the change in the tax rate.! Benjamin earns $40,000 a year (pre-tax) before the change in the tax rate.! Ephraim earns $45,000 a year (pre-tax) before the change in the tax rate.

The marginal tax rate affects peoples incentives to work. The amount they work affectsthe total tax they pay.

For this question, ignore wealth effects on labor supply. Assume only the substitution effect(the relative benefit of work vs leisure) affects hours worked.

Who works more hours, who works fewer hours, and who works the same hours?

Joseph Benjamin Ephraim

A more more more

B more same fewer

C more fewer fewer

D fewer same more

E fewer fewer fewer

Answer 1.2: E

For all three workers, the marginal tax rate increases, so each one works fewer hours.

*Question 1.3: Marginal Tax Rate

People earn $100 million in 20X7 and pay a flat tax rate of 20%. Each person earnsbetween $20,000 and $60,000 a year (pre-tax), with an average of $40,000 per person.

To make the income tax more progressive in 20X8, the government makes the tax rate 0%for the first $20,000 of income and 40% for the next $40,000 of income.

! Jacob earns $35,000 a year (pre-tax) before the change in the tax rate.! Rachel earns $45,000 a year (pre-tax) before the change in the tax rate.

The marginal tax rate affects peoples incentives to work by the substitution effect. Theirnet after-tax income affects their need for cash (the income effects). The amount they workaffects the total tax they pay.


A. Jacob pays less tax in 20X7; Rachel may pay more or lessB. Rachel pays more tax in 20X7; Jacob may pay more or lessC. Both Jacob and Rachel pay less tax in 20X7D. Jacob pays less tax in 20X7; Rachel pays more taxE. Both Jacob and Rachel may pay more or less tax in 20X7

Answer 1.3: A

Jacob pays less tax in 20X7; Rachel may pay more or less

To solve this problem, we determine

! The total tax each person would pay if he/she worked the same amount.! Whether each person works more or less in 20X8 than in 20X7.

We reason through each scenario.

! If the same work leads to less tax and the person works less in 20X8, he/she surelypays less tax.

! If the same work leads to more tax and the person works less in 20X8, he/she may paymore or less tax.

! If the same work leads to more tax and the person works more in 20X8, he/she surelypays more tax.

! If the same work leads to less tax and the person works more in 20X8, he/she may paymore or less tax.

A higher marginal tax rates induces a person to work less, though we dont know howmuch less. Raising the marginal tax rate from 20% to 40% may induce a person to workone hour less or not to work at all at the 40% marginal tax rate. For example,

! Raising the tax rate from 1% to 2% has a small effect on the hours worked.! Raising the tax rate from 50% to 100% causes the person to stop working.

The marginal tax rate increases for both Jacob and Rachel, so both work less in 20X7. The decrease in work lowers pre-tax income. One is tempted to reason that:

! If the marginal value of leisure is small, the decrease in work is small, and the pre-taxincome declines little.

! If the marginal value of leisure is large, the decrease in work effort is large, and the pre-tax income declines much.

This reasoning is a good way to start, but it is not well worded. At equilibrium, the marginalvalue of leisure equals the marginal variance of the work income. Raising the marginal taxrate reduces the marginal variance of work income. To determine how much less theperson works, we examine the slopes of the value of leisure and work income.

! If the value of leisure and of work are relatively flat (the marginal value varies little byamount of work or leisure), a decrease in the after-tax wage causes a large decreasein work effort.

! If the value of leisure and of work are relatively steep (the marginal value varies greatlyby amount of work or leisure), a decrease in the after-tax wage causes a smalldecrease in work effort.

Take heed: For the final exam, focus on the intuition. The exam problems do not computethe exact amount by which work effort increases or declines.

We also consider the income effect.

If Jacobs work hours do not change, his after-tax income is

! 20X7: $35,000 (1 20%) = $28,000! 20X8: $35,000 40% ($35,000 $20,000) = $29,000

Jacob has more income in 20X8, so the income effect induces him to work less.

If Rachels work hours do not change, her after-tax income is

! 20X7: $45,000 (1 20%) = $36,000! 20X8: $45,000 40% ($45,000 $20,000) = $35,000

Rachel has less income in 20X8, so the income effect induces her to work more.

The substitution effect causes Rachel to work less. We dont know which effect is stronger,so we dont know if she works more or less.

Take heed: Some exam problems separate the income effect from the substitution effect,giving easier problems. For your exam preparation, first examine each effect separately.The exam problems are not intricate, and they do not test mathematical ability. If youunderstand the concepts and review the practice problems, you can solve exam problems.

*Question 1.4: Marginal Tax Rates

A country has a flat income tax, so the total tax revenue is the pre-tax income times the taxrate. The government wants to maximize the total tax revenue. An increase in the tax rate

A. Raises total tax revenue.B. Lowers total tax revenue.C. Lowers total tax revenue at low tax rates and raises total tax revenue at high tax rates.D. Raises total tax revenue at low tax rates and lowers total tax revenue at high tax rates.E. Has little or no effect on total tax revenue.

For this exam problem, interpret low tax rates as a tax rate that approaches zero and hightax rates as a tax rate that approaches one. The actual demarcation point depends onother characteristics of the economy and the workers. Barro believes the dividing point issomewhere between 50% and 75%

Answer 1.4: D

We use the following reasoning:

! At a zero tax rate, the total tax revenue is zero, so an increase in the tax rate increasesthe total tax revenue.

! At a 100% tax rate, people dont work, since they keep none of their earnings, and totaltax revenue is zero. A decrease in the tax rate induces some people to work, so totaltax revenue increases.

Illustration: Suppose workers earn $10 an hour. If the tax rate is zero, people work 2,000hours a year. If the tax rate is Z%, people work (1 Z%) 2,000 hours a year.

~ If the tax rate is 10%, people work 90% 2,000 = 1,800 hours a year. Total taxrevenue is 10% $10 1,800 = $1,800.00 per worker.

~ If the tax rate is 11%, people work 89% 2,000 = 1,780 hours a year. Total taxrevenue is 11% $10 1,780 = $1,958.00 per worker.

At low tax rates, total tax revenue increases as the tax rate increases.

~ If the tax rate is 90%, people work 10% 2,000 = 200 hours a year. Total tax revenueis 90% $10 200 = $180.00 per worker.

~ If the tax rate is 91%, people work 9% 2,000 = 180 hours a year. Total tax revenueis 91% $10 180 = $162.00 per worker.

At low tax rates, total tax revenue decreases as the tax rate increases.

Intuition: At a 0% tax rate, total tax revenue is zero. At a 100% tax rate, people do nowork, since they keep nothing of what they earn, and total tax revenue is again zero. At

rates between 0% and 100%, people do some work, so total tax revenue is positive. Weinfer that at low tax rates, total tax revenue increases from zero to a positive amount, andat high tax rates, total tax revenue decreases from a positive amount to zero.

Algebra: In the example here, people work 2,000 (1 Z) hours, where Z is the tax rate. The total tax revenue is 2,000 (1 Z) Z. The partial derivative with respect to Z is2,000 (1 2Z).

~ If Z < 50%, the partial derivative is positive and total tax revenue increases.~ If Z = 50%, the partial derivative is zero and total tax revenue stays the same.~ If Z < 50%, the partial derivative is negative and total tax revenue decreases.

The incentive effects are stronger when the tax rate is progressive. This illustration usesflat tax rates, with weaker but still evident effects.

In countries with high marginal tax rates, such as Switzerland, total tax revenue decreases,because people have less incentive to work. If the tax rate were lower, the governmentwould have more tax revenue and the workers would have more after-tax income.

Jacob: If reducing the tax rate causes people to work more and raises total tax revenue,the government has more money for social programs. Why would anyone oppose a taxreduction?

! Conservatives want to reduce the tax rate.! Progressives want more total tax revenue for social programs.

Rachel: Progressive tax rates reduce income inequality. Many people dont like inequality. They would like everyone to be wealthy. But if not everyone can be wealthy, they prefereveryone to be poorer if it reduces economic differences.

*Question 1.5: Income and Substitution Effects

In 20X7, Country W has a flat tax rate of 20%.

To reduce income inequality, the government changes the tax code for 20X8 so that

! Workers earning $0 receive a $10,000 tax refund (a negative tax liability). ! The tax refund declines linearly to zero as the workers earnings increase to $100,000.! Income is taxed at a flat rate of 40%.

Abigail earns pre-tax income of $33,333 in 20X7. What are the income and substitutioneffects on her labor hours if each is considered separately.

Illustration: Choice A says:

! If the substitution effect is zero, the income effect causes her work hours to decrease.! If the income effect is zero, the substitution effect causes her work hours to increase.

Income Effect Substitution Effect

A Fewer Hours More Hours

B More Hours Fewer Hours

C Fewer Hours Fewer Hours

D More Hours More Hours

E No Change Fewer Hours

Answer 1.5: E

Abigail has pre-tax income of $33,333 in 20X7.

! 20X7: The tax liability is 20% $33,333 = $6,667! 20X8: The net tax liability is 50% $33,333 $10,000 = $6,667

As worked out above, a tax refund that decline from $10,000 to $0 is like a tax refund of$10,000 and an extra 10% tax rate.

If Abigail works the same hours in 20X8, her net tax liability is the same as in 20X7, so theincome effect is zero.

If the substitution effect is zero, the income effect by worker is

! A worker who earns less than $33,333 pays less tax and works fewer hours.! A worker who earns more than $33,333 pays more tax and works more hours.

The marginal tax rate is higher in 20X8 than in 20X7 for all workers. The substitution effectcauses all workers to work fewer hours.

*Question 1.6: Income and Substitution Effects

Abigail earns pre-tax income of $33,333 in 20X8. What are the income and substitutioneffects on her labor hours if each is considered after the other has its effect.

Illustration: Choice A says:

! After the substitution effect, the income effect causes her work hours to decrease.! After the income effect, the substitution effect causes her work hours to increase.

Income Effect Substitution Effect

A Fewer Hours More Hours

B More Hours Fewer Hours

C Fewer Hours Fewer Hours

D More Hours More Hours

E No Change Fewer Hours

Answer 1.6: B

Abigail has pre-tax income of $33,333 in 20X7.

! 20X7: The tax liability is 20% $33,333 = $6,667! 20X8: The net tax liability is 50% $33,333 $10,000 = $6,667

The marginal tax rate is higher in 20X8 than in 20X7 for all workers. The substitution effectcauses all workers to work fewer hours.

Because of the substitution effect, Abigail works fewer hours in 20X8. Her net tax liabilityis smaller than in 20X7, so her after-tax income is lower and the income effect makes herwork more hours.

*Question 1.7: Income Effect

In 20X7, Sarah, Rebecca, and Leah earn pre-tax income of $30,000, $40,000, and$50,000, respectively.

From the income effect alone (not the substitution effect), will they work more or fewerhours in 20X8?

Sarah Rebecca Leah

A Fewer Fewer Fewer

B More More Fewer

C Fewer More More

D Fewer No Change More

E More No Change Fewer

Answer 1.7: C

Consider Rebecca, who earns $40,000 in 20X7.

! In 20X7, she pays tax of 20% $40,000 = $8,000.! In 20X8, she keeps 1 40% = 60% of the tax refund. She pays tax of 40% $40,000

= $16,000. Her net tax liability is $16,000 $6,000 = $10,000.! She has less after-tax income in 20X8. By the income effect, she works more hours.

Similar analysis for Sarah and Leah give Choice C for the answer.

*Question 1.8: Substitution effect

In 20X6, Sarah, Rebecca, and Leah earn pre-tax income of $30,000, $40,000, and$50,000, respectively.

From the substitution effect alone (not the income effect), will they work more or fewerhours?

Sarah Rebecca Leah

A Fewer Fewer Fewer

B More More Fewer

C Fewer More More

D Fewer No Change More

E More No Change Fewer

Answer 1.8: A

The marginal tax rate increases from 20% to 50% for all workers, so all workers work fewerhours by the substitution effect.

*Question 1.9: Marginal tax rates

Country W and Country Z have identical labor forces, with workers earning pre-tax incomesin a uniform distribution from $0 to $100,000. Neither country yet has an income tax.

To finance the costs of reversing global warming, both countries levy an income tax.

! Country W imposes a flat 20% income tax for all workers.! Country Z imposes a progressive income tax that rises linearly from 0% at $0 of pre-tax

income to 30% at $100,000 of pre-tax income.

For a person earning $50,000, what are the marginal tax rates in Countries W and Z?

Country W Country Z

A 20% 15%

B 20% 30%

C 20% 60%

D 40% 30%

E 40% 60%

Answer 1.9: B

Let Y be the pre-tax income.

In Country W:

! The tax is 20% Y. ! The marginal tax rate is M(20% Y)/MY = 20%.

The marginal tax rate equals the tax rate for all workers.

In Country Z:

! The tax rate is 30% Y / $100,000.! The tax is Y 30% Y / $100,000 = 30% Y / $100,000.2

! The marginal tax rate is M(30% Y / $100,000)/MY = 60% Y / $100,000.2

For a person earning $50,000, the marginal tax rate is 60% $50,000 / $100,000 = 30%.

*Question 1.10: Average tax rates





If people do not change their work hours because of the tax, what are the average tax ratesin Country W and Country Z?

Take heed: You must weight the tax rates by the pre-tax income. For persons with incomesof $10,000 and $20,000 and tax rates of 3% and 6%, the average tax rate is ($10,000 3% + $20,000 6%) / $30,000 = 5.00%.

Country W Country Z

A 20% 10%

B 20% 20%

C 20% 30%

D 10% 10%

E 10% 20%

Answer 1.10: B

Country W: The tax rate is 20% for all workers.

Country Z: To simplify the mathematics, we use units of $100,000. The pre-tax income isY, which ranges from 0 ($0) to 1 ($100,000).

! The tax rate is 30% Y.! The tax is Y 30% Y = 30% Y .2

We integrate the tax over the uniform distribution from 0 to 1 to get total tax revenue:

I 30% Y MY = 30% a Y from 0 to 1 = 10%.2 3

The average pre-tax income is $50,000, or 0.5 in units of $100,000.

The average tax rate is 10% / 0.5 = 20%.

*Question 1.11: Average tax rates





A tax affects work effort two ways:

! Substitution effect: The tax reduces the value of each hour of labor compared to anhour of leisure, so people prefer less work and more leisure.

! Income effect: The tax reduces total income, so people have more need for income andwork more.

The income effect and substitution effect depend on the wealth of the worker.

! The income effect is strong as low wage levels. A poor person earning subsistencewages may work an extra hour if the tax rate rises.

! The substitution effect is strong at high wage levels. A rich person may decide to workless if the tax reduces the net income.

If people change their work hours because of the tax, which country raises the greater totaltax revenue and which country has the greater after-tax net income?

Greater Total Tax

Revenue

Greater After-tax Net

Income

A Country W Country W

B Country W Country Z

C Country Z Country W

D Country Z Country Z

E Country W Equal

Answer 1.11: A

If people do not change their work hours because of the tax, the two countries have thesame pre-tax income, the same average tax rate, the same total tax revenue, and thesame after-tax income.

We group workers by pre-tax income:

! Low income workers earn less than $33,333.! Medium income workers earn from $33,333 to $66,667.! High income workers earn more than $66,667.

We compare the tax rates and marginal tax rates in the two countries.

The tax rate and the tax liability in Country Z are lower for people earning < $66,667 andhigher for people earning > $66,666. From the income effect,

! Low income and medium income workers pay less tax in Country Z, so they have moreafter-tax income and they work fewer hours.

! High income workers pay more tax in Country Z, so they have less after-tax income andthey work more hours.

The marginal tax rate in Country Z is lower for people earning < $33,333 and higher forpeople earning > $33,333. From the substitution effect:

! Low income workers have a lower marginal tax rate in Country Z, so they have agreater preference for work over leisure and they work more hours.

! Medium income and high income workers have a higher marginal tax rate in CountryZ, so they have a weaker preference for work over leisure and they work fewer hours.

We combine the two effects by income level.

! The income effect is strong at low incomes, so low income workers work fewer hours.! At medium incomes, both the income effect and the substitution effect causes people

to work fewer hours.! The substitution effect is strong at high incomes, so high income workers work fewer

hours.

Empirical data supports these relations.

Tax rates in the U.S. rose from zero at the beginning of the 20 century to about 30% now.th

Average personal wealth for low income workers doubled or tripled (in real terms). Theprecise change depends on how we measure wealth.

Average work hours per week for low income workers declined from about 55 to about 40.

! In 1900, a poor person worked 55 hours a week to pay for food, clothing, and rent.! In 2000, a person earns enough in 40 hours a week for food, clothing, and rent.

The substitution effect is seen from tax rate changes.

! When tax rates for high income workers rise, they work less and often pay less tax.! When tax rates for high income workers fall, they work more and often pay more tax.

For the average tax per capita, assume one taxpayer. We use units of $100,000The total tax revenue is number of workers times 10,000 in Country W and Country Z.

The marginal tax rates are 20% in Country W and 60% y in Country Z,

MACROECONOMICS FINAL EXAM PRACTICE PROBLEMS ON ECONOMIC GROWTH


The final exam has three types of problems on economic growth

! Qualitative problems on convergence! Qualitative/quantitative problems using the Solow growth model! Quantitative problems using the Cobb-Douglas production function

Take heed: The homework assignments that cover economic growth issues are also testedon the final exam. One homework assignment discusses convergence (mean reversion)and stochasticity. Questions on this topic appear on the final exam.

Know the attributes of the Cobb-Douglas production function. The final exam may test thesteady state income level and capital per worker, the elasticity of income with respect tocapital or labor, the range of ", the profits or capital or labor, and similar items.

Take heed: For the transition path of the Cobb-Douglas production function, the final examasks qualitative (not quantitative) questions. Know how the growth rate along the transitionpath relates to steady state capital per worker, current capital per worker, savings, growthrate of technology, and population growth rate.

Practice problems on convergence are in a separate file.

*Question 1.1: Cobb-Douglas Production Function

An economy has a Cobb-Douglas production function: Y = AK L . (1 )

A is the technology level, K is capital; L is labor; and Y is income.


A. " is the elasticity of income with respect to capital.B. " is the elasticity of income with respect to labor.C. " is the derivative of income with respect to capital.D. " is the derivative of income with respect to laborE. " is the elasticity of income with respect to the marginal product of capital.

Answer 1.1: A

For the Cobb-Douglas production function, the marginal product of capital equals

MPK = MY / MK= " AK L -1 1-

= " AK K L -1 1-

= " AK L (1/K) 1-

= " (Y/ K)

The elasticity of income with respect to capital is MY / MK (K / Y) = (MPK K) / Y

= " (Y/ K) K / Y = " (see equation 3.20 on page 67)

MPK is the effect on Y from a change in K, holding A and L fixed:

Take heed: The elasticity of income with respect to capital is the percentage change inincome from a percentage change in capital. If " = 40%, a 5% increase in capital raisesincome 5% 40% = 2%.

The microeconomics and regression analysis courses have full modules on elasticity. If youhave difficulty with elasticities, review the practice problems from microeconomics.

! The derivative of income with respect to capital is MY / MK.! The elasticity of income with respect to capital is (MY/Y) / (MK/K) = MY / MK (K/Y).

*Question 1.2: Solow Growth Model

In the Solow growth model, an economys growth rate depends on five variables:

! current capital per worker, k ! the depreciation rate of its capital, * ! the population growth rate, n! the savings rate, s! the technology level, A

As each of these parameters increases (holding other parameters constant), does thegrowth rate of capital per worker increase, decrease, or remain the same?

k * n s A

A _ ` _ _ _

B ` ` ` _ _

C ` ` ` ` _

D ` ` ` _ `

E _ _ ` _ _

! _ = the growth rate of capital increases! ` = the growth rate of capital decreases

Answer 1.2: B

Current capital per worker: Economies converge (revert) to their steady state capital perworker and steady state income per worker, by absolute convergence or conditionalconvergence. Mean reversion (convergence) implies that as a random variable increasestoward the mean, its rate of increase slows, and as the variable decreases toward themean, its rate of decrease slows. A lower current capital per worker implies a faster growthof capital per worker during the transition phase.

Depreciation * is a reduction in capital. Higher depreciation means that more capital wearsout and disappears from national income accounts.

Savings provides for three items: replacement of capital that wears out (depreciation);capital for new workers (population growth); and higher capital per worker. A higher savingsrate means that more remains after providing for depreciation and population growth, socapital per worker continues to grow. Conversely, a higher population growth rate meansthat more savings are needed to provide capital for new workers and less is available forgrowth in capital per worker.

Take heed: The savings rate s offsets the population growth rate n and the depreciation

rate *, and it supplies funds for further growth in capital per worker. As the capital perworker grows, the savings needed to support depreciation and population growth is larger.

When capital is large enough that savings just offsets depreciation and population growththe economy is in its steady state.

Savings and population growth differ by country. They are (in part) culturally determined.

Some cultures place more stress on large families than others do, or they are moreopposed to birth control, family planning, and abortion. Contrast the large families in theMiddle East and Latin America with small families in Western Europe, Canada, and China.We do not know if economic growth in the Middle East and Latin America will reduce thepopulation growth rate to European levels or if Islamic and Catholic cultures will continuewith large families.

Some cultures have higher savings rates than others. Japan and other Asian countrieshave higher savings rates than North America and Western Europe.

! An economy with a high population growth rate and a low savings rate may be near itssteady state capital per worker even at a low capital level (Nigeria, Congo).

! An economy with a low population growth rate and a high savings rate may be belowits steady state capital per worker even at a high capital level (Japan).

The countries above in parentheses are illustrations to help you understand the concepts.

Take heed: Distinguish between capital and the technology level. A higher technology levelraises the marginal product of capital and leads to more capital per worker. To rememberthis, think of two workers:

! Jacob lives in a shepherd culture, with no knowledge of industrial society (A is low). Theonly capital is knives, jars, and tents.

! Jacques lives in Paris and works in an information-age society (A is high). He uses cell-phones and laptop computers (high capital).

Take heed: Some exam problems specify the Solow growth model. Unless specifiedotherwise, the exam problems use the Solow growth model.

The Solow growth model has several forms: fixed values for A, s, and n; exogenous andendogenous changes in the parameters. The type of model should be clear from thecontext of the exam problem.

Macroeconomics Final Exam Practice Problems Implicit Price Deflator


In prosperous years with positive inflation, both nominal and real GDP grow over time. Theexam problems may combine negative inflation with real GDP growth or positive inflationwith real GDP decline. Review the practice problem here and the examples in the textbook.

! Know how to construct the implicit price deflator using the chain-linked method. ! The exam problems derive the implicit price deflator and real GDP in each year.

*Exercise 1.1: Real GDP and the Implicit Price Deflator

A country makes bread and wine in 20X7 and 20X8, at the quantities and prices shown inthe table below. The implicit price deflator in 20X7 is 100.

20X7 20X8

Bread W ine Bread W ine

Quantity 26000 5000 32000 4000

Price 4 10 5 20

Use the average prices in 20X7 and 20X8 as base prices (the chain-link method).

A. What is nominal GDP in 20X7 and 20X8?B. What are the base prices of bread and wine for comparing 20X7 and 20X8?C. What is GDP in 20X7 and 20X8 at the base prices?D. What is the ratio of real GDP in 20X8 to real GDP in 20X7? E. What is real GDP in 20X7 and 20X8?F. What is the implicit price deflator in 20X8?G. Explain the error in the following statement: The price of bread rose 25% from 20X7

to 20X8, yet consumers bought more bread. The demand curve for bread must havechanged from 20X7 to 20X8.

H. Explain the error in the following statement: Real GDP depends on the quantities ofgoods, not their prices. To determine if real GDP increased or decreased, we ne

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