MATH REVIEW - Chapter 1 # 1

Below is one way to do it. Another way is to put total enrollment on the X axis and economics enrollment on the Y axis and calculate the slope.

Slope is 100 interpreted as 100 new students each academic year.

Slope is 25 interpreted as 25 new economics students each academic year.

PPF AND OPPORTUNITY COST- CHAPTER 3 # 2,3

2. Graphically show the production possibilities frontier for the nation of Stromboli,

using the data given in the following table. Does the principle of increasing cost hold in

Stromboli?

Stromboli’s 2018 Production Possibilities

Pizzas per Year Pizza Ovens per Year

75,000,000 0

60,000,000 6,000

45,000,000 11,000

30,000,000 15,000

15,000,000 18,000

0 20,000

Figure 1 shows the production possibilities frontier. The principle of increasing cost holds, because the curve is concave. For example, begin at the point of producing 20 pizza ovens and 0 pizzas. To produce 15 pizzas we must give up the production of 2 pizza ovens; this brings us the point of 18 pizza ovens and 15 pizzas. To gain another 15 pizzas, we must now give up the production of 3 pizza ovens. As we continue to produce more pizzas we must give up increasing quantities of pizza ovens. There are diminishing returns as resources are shifted from pizzas to pizza ovens, or vice versa.

FIGURE 1 (Pizza numbers are in millions, ovens are in thousands)

3. Consider two alternatives for Stromboli is 2018. In one case (a) its inhabitants eat 60 million pizzas and build 6,000 pizza ovens. In case (b), the population eats 15million

pizzas but builds 18,000 ovens. Which case will lead to a more generous production possibilities frontier for Stomboli in 2018?

In case (b), the production possibilities frontier will be further from the origin in future years, since Stromboli will have more pizza ovens with which it can produce more pizzas.

SUPPLY AND DEMAND -Chapter 4 # 3,5,8

3. Suppose the supply and demand schedules for bicycles are as they appear in the

following table.

Price Quantity

Demanded per

Year (millions)

Quantity

Supplied per

Year

(millions)

$170 43 27

210 39 31

250 35 35

300 31 39

330 27 43

370 23 47

a. Graph these curves and show the equilibrium price and quantity.

b. Now suppose that it becomes unfashionable to ride a bicycle, so that the quantity demanded

at each price falls by 8 million bikes per year. What is the new equilibrium price and

quantity? Show this solution graphically. Explain why the quantity falls by less than 8 million

bikes per year.

c. Suppose instead that several major bicycle producers go out of business, thereby reducing the

quantity supplied by 8 million bikes at every price. Find the new equilibrium price and

quantity, and show it graphically. Explain again why quantity falls by less than 8 million.

d. What are the equilibrium price and quantity if the shifts described in Test Yourself

Questions 3(b) and 3(c) happen at the same time?

The answers to all three parts are shown in Figure 2. (a) Initially, the equilibrium price is $250, and the equilibrium quantity is 35 million

bicycles, as shown by the intersection of D0 and S0. (b) If demand falls by 8 million bikes per year, the new demand curve is D1. The price

falls to $210, and the quantity falls to 31 million, as shown by the intersection of D1 and S0. Although demand falls by 8 million at each price, the quantity exchanged falls by only 4 million because the price fall has induced a movement out along the new demand curve, as well as a movement back along the old supply curve.

(c) If supply falls by 8 million bikes per year, the new supply curve is S1. The price rises to $300, and the quantity falls to 31 million, as shown by the intersection of D0 and S1. Although supply falls by 8 million at each price, the quantity exchanged falls by

only 4 million because the price increase has induced a movement out along the new supply curve, as well as a movement back along the old demand curve.

(d) If demand and supply each fall by 8 million bikes per year, the equilibrium price is $250, and the equilibrium quantity is 27 million bicycles, as shown by the intersection of D1 and S1.

FIGURE 2

5. How are the following demand curves likely to shift in response to the indicated changes?

a. The effect of a drought on the demand curve for umbrellas

b. The effect of higher popcorn prices on the demand curve for movie tickets

c. The effect on the demand curve for coffee of a decline in the price of Coca-Cola

The same diagram, Figure 4, can be used for all three cases, because they all entail a

decline in demand, from D0 to D1. Price falls from P0 to P1, and quantity falls from Q0 to

Q1. (a) In a drought, people have less need for umbrellas, so demand falls. (b) Popcorn is a complement for movie tickets, so when popcorn prices rise, the demand

for tickets falls. (c) Coca-Cola is a substitute for coffee, so when the price of the soda falls, the demand

for coffee falls.

FIGURE 4

8. (More difficult) The demand and supply curves for T-shirts in Touristtown, U.S.A., are given

by the following equations:

Q = 24,000 − 500P Q = 6,000 + 1,000P

where P is measured in dollars and Q is the number of T-shirts sold per year.

a. Find the equilibrium price and quantity algebraically.

b. If tourists decide they do not really like T-shirts that much, which of the following might

be the new demand curve?

Q = 21,000 − 500P Q = 27,000 + 500P

Find the equilibrium price and quantity after the shift of the demand curve.

c. If, instead, two new stores that sell T-shirts open up in town, which of the following

might be the new supply curve?

Q = 4,000 + 1,000P Q = 9,000 + 1,000P

Find the equilibrium price and quantity after the shift of the supply curve. (a) In equilibrium, quantity demanded equals quantity supplied: 24,000 – 500P = 6,000 + 1,000P 1,500P = 18,000 P = 12 Substitute P = 12 in either the supply or the demand equation to derive Q = 18,000. (b) If tourists like t-shirts less, the new demand curve might be Q = 21,000 – 500P. Using

the same method as in part (a), in equilibrium, P = 10 and Q = 16,000. (c) Opening of the new stores might lead to an increase in the supply curve to Q = 9000

+ 1000P. Set equal to the original demand curve, and using the method of part (a), this yields equilibrium price and quantity of P = 10 and Q = 19000.

PRESENT VALUE AND BONDS- CHAPTER 13 # 4 a,b, and c

4. Treasury bills have a fixed face value (say, $1,000) and pay interest by selling at a

discount. For example, if a one-year bill with a $1,000 face value sells today for $950, it

will pay $1,000 – $950 = $50 in interest over its life. The interest rate on the bill is

therefore $50/$950 = 0.0526, or 5.26 percent.

a. Suppose the price of the Treasury bill falls to $925. What happens to the interest rate?

b. Suppose, instead, that the price rises to $975. What is the interest rate now?

c. (More difficult) Now generalize this example. Let P be the price of the bill and r be the

interest rate. Develop an algebraic formula expressing r in terms of P. (Hint: The interest

earned is $1,000 – P. What is the percentage interest rate?) Show that this formula

illustrates the point made in the text: Higher bond prices mean lower interest rates.

(a) If the price of the $1,000 one-year Treasury bill falls to $925, it will earn $75 over its life, so the interest rate is $75/$925, or 0.08108 (8.11 percent).

(b) At a price of $975, the interest rate is $25/$975, or 0.0256 (2.56 percent). (c) for a one-year Treasury bill with a face value of $1,000, interest rate r and current

price P: r = (1000 – P)/P. Thus an increase in P lowers r, because it reduces the numerator and increases the denominator.

UNEMPLOYMENT -CHAPTER 6 # 3 AND DISCUSSION QUESTION # 4

3. Most economists believe that from 2010 to 2013, actual GDP in the United States grew

slightly faster than potential GDP. What, then, should have happened to the

unemployment rate over those three years? Before that, from 2006 to 2010, actual

GDP grew slower than potential GDP, even contracting for several quarters. What

should have happened to the unemployment rate over those three years? (Check the

data on the inside back cover of this book to see what actually happened.)

If actual GDP grew faster than potential GDP from 2010 to 2013, unemployment should have decreased, which it did. Similarly, from 2006 to 2010, unemployment should have increased because actual GDP was growing slower than potential GDP. Unemployment did, in fact, fall between 2010 and 2013 and increase between 2006 and 2010.

Discussion question # 4

4. Why is it so difficult to define full employment? What unemployment rate should the

government be shooting for today?

“Full employment” certainly implies some unemployment, that is to say, frictional unemployment, and it is difficult to determine just how much that is. In addition, many economists are willing to concede that some level of structural unemployment can remain at “full employment,” since the attempt to eliminate it would entail more inflation than the country should tolerate. The experience of the mid 1990’s indicates that a realistic goal may be an unemployment rate in the neighborhood of 5 to 5.5 percent.

GDP - CHAPTER 5 # 3

3. Which of the following transactions are included in gross domestic product, and by

how much does each raise GDP?

a. Smith pays a carpenter $50,000 to build a garage.

b. Smith purchases $10,000 worth of materials and builds himself a garage, which is

worth $50,000.

c. Smith goes to the woods, cuts down a tree, and uses the wood to build himself a

garage that is worth $50,000.

d. The Jones family sells its old house to the Reynolds family for $400,000. The

Joneses then buy a newly constructed house from a builder for $500,000.

e. You purchase a used computer from a friend for $200.

f. Your university purchases a new mainframe computer from IBM, paying $25,000.

g. You win $100 in an Atlantic City casino.

h. You make $100 in the stock market.

i. You sell a used economics textbook to your college bookstore for $60.

j. You buy a new economics textbook from your college bookstore for $100.

(a) Raises GDP by $50,000.

(b) Raises GDP by $10,000.

(c) GDP does not rise, because there is no market transaction.

(d) GDP rises by $500,000, the value of the newly constructed house.

(e) GDP does not rise, because nothing new was produced.

(f) Raises GDP by $25,000.

(g) GDP actually falls by $100. The casino is selling “gambling services” to you, which are measured by how much you lose. Winning $100 therefore reduces sales of gambling services.

(h) GDP does not rise. Because nothing new is produced, capital gains and losses do not count in GDP.

(i) GDP does not change because you did not produce a good or service. (j) Raises GDP by $100. CPI – CHAPTER 6 # 1

1. Below you will find the yearly average values of the Dow Jones Industrial Average,

the most popular index of stock market prices, for five different years. The Consumer

Price Index for each year (on a base of 1982–1984 = 100) can be found on the inside

back cover of this book. Use these numbers to deflate all five stock market values. Do

real stock prices always rise every decade?

Year Dow Jones

Industrial Average

1970 753

1980 891

1990 2,679

2000 10,735

2010 10,663

1970 1980 1990 2000 2010

Dow Jones

Industrial

Average (DJIA)

753 891 2,679 10,735 10,663

CPI 38.8 82.4 130.7 172.2 218.1

Deflated DJIA 1,941 1,081 2,050 6,234 4,889

The deflated DJIA is found by dividing the DJIA by the CPI of the same year, then multiplying by the base year CPI, which is 100. Stock prices do not rise every decade. They declined notably during the decades between 1970 and 1980 and between 2000 and 2010 but rose between 1980 and 2000. Stocks were most valuable in 2000.

INFLATION - CHAPTER 6 # 5, 6 5. What is the real interest rate paid on a credit card loan bearing 12 percent nominal

interest per year, if the rate of inflation is

a. zero?

b. 4 percent?

c. 8 percent?

d. 15 percent?

(a) 12 percent (b) 8 percent (c) 4 percent (d) -3 percent

(b)

6. Suppose you agree to lend money to your friend on the day you both enter college at

what you both expect to be a zero real rate of interest. Payment is to be made at

graduation, with interest at a fixed nominal rate. If inflation proves to be lower during

your college years than what you both had expected, who will gain and who will lose? If inflation is lower than expected, you the lender will gain and your friend the borrower

will lose. Since prices are lower than expected, the repaid money is worth more QUNTITY THEORY - CHAPTER 15 # 2

2. The following table provides data on nominal gross domestic product and the money

supply (M1 definition) in recent selected years. Compute velocity for each year. Do

you see any trend? How does it compare with the trend that prevailed from about

1996 to about 2006? (See Figure 1(a).)

Year End-of-Year Money Supply (M1) Nominal GDP

2010 $1,836 $14,958

2011 2,160 15,534

2012 2,447 16,245

2013 2,648 16,798

Year Velocity

2010 8.15

2011 7.19

2012 6.64

2013 6.34

The money supply was increased in 2008 in response to the financial crisis and economic

downturn. At the same time, the velocity of money has declined most likely as a result of this

significant economic downturn. The decline in velocity over these years is in contrast to the

substantial increase from 1975 to 1995. However, of that time period there was some volatility

and years in which velocity declined. In that sense, the trends from both time periods are

somewhat similar.

BANKING- CHAPTER 12 # 1,2,3 4 AND DISCUSSION Q # 2

1. Suppose banks keep no excess reserves and no individuals or firms hold on to cash. If

someone suddenly discovers $12 million in buried treasure and deposits it in a bank, explain

what will happen to the money supply if the required reserve ratio is 10 percent.

Under those conditions, the money multiplier is 1/.10, or 10, so an infusion of $12 million into

reserves will support an increase in money of $120 million.

2. How would your answer to Test Yourself Question 1 differ if the reserve ratio were 25

percent? If the reserve ratio were 100 percent?

With a reserve ratio of 25 percent, the money multiplier is 1/.25, or 4; the money supply would

rise by $48 million. With a reserve ratio of 100 percent, the money multiplier is 1/1, or 1; the

money supply would rise by $12 million.

3. Use tables such as Tables 2 and 3 to illustrate what happens to bank balance sheets when

each of the following transactions occurs:

a. You withdraw $100 from your checking account to buy concert tickets.

b. Sam finds a $100 bill on the sidewalk and deposits it into his checking account.

c. Mary Q. Contrary withdraws $500 in cash from her account at Hometown Bank,

carries it to the city, and deposits it into her account at Big City Bank.

4. For each of the transactions listed in Test Yourself Question 3, what will be the ultimate

effect on the money supply if the required reserve ratio is one-eighth (12.5 percent)?

Assume that the oversimplified money multiplier formula applies.

a. In question 3(a), there is no initial effect on the money supply, since deposits of $100 are replaced with cash in circulation. However the bank is now deficient in reserves by $87.50, so eventually the money supply will fall by 8 times this, or $700.

b. Similarly in 3(b), there is no initial change in the money supply, but there are now excess reserves of $87.50, so eventually the money supply will rise by $700.

c. There is no change for the banking system as a whole; neither reserves nor deposits have changed.

DISCUSSION QUESTION

2. How is “money” defined, both conceptually and in practice? Does the U.S. money supply consist

of commodity money, full-bodied paper money, or fiat money?

Money is defined as whatever a society uses as its medium of exchange. The U.S. money supply is all fiat money. The narrowest definition, M1, includes currency in circulation plus certain demand deposits at banks and savings institutions. A broader definition, M2, includes M1 plus most savings accounts, checking deposits not counted in M1, and shares in money market mutual funds. There are even broader definitions as well.

GROWTH – CHAPTER 7 # 1, 4, 5

1. The following table shows real GDP per hour of work in four imaginary countries in the

years 2004 and 2014. By what percentage did labor productivity grow in each country?

Is it true that productivity growth was highest where the initial level of productivity was

the lowest? For which countries?

Output per Hour

2004 2014

Country A $40 $48

Country B 25 35

Country C 2 3

Country D 0.50 0.60

The productivity growth for each country is shown in the fourth column below:

2004 output

per hour

2014 output

per hour

Productivity

growth

2004-2014

Country A $40.00 $48.00 20%

Country B 25.00 35.00 40%

Country C 2.00 3.00 50%

Country D 0.50 0.60 20%

Productivity growth was highest for Country C, which had a very low initial level of productivity. But note that the productivity growth for Country D lagged far behind countries B and C despite Country D’s lower starting point. As mentioned in the text, not all countries (such as Country D here) are able to participate in the convergence process. However, Countries B and C did close some of the gap on Country A.

4. Two countries have the production possibilities frontier (PPF) shown in Figure 3.

Consumia chooses point C, whereas Investia chooses point I. Which country will have

the higher PPF the following year? Why?

Investia will enjoy a higher PPF in the following year because it devoted more of its resources toward capital goods. That is, it sacrificed consumer goods today to increase its potential for consumer goods the following year.

5. Show on a graph how capital formation shifts the production function. Use this graph to show that capital formation increases labor productivity. Explain in words why labor is more productive when the capital stock is larger.

Draw a graph similar to Figure 1 in the text. Higher levels of capital increase labor productivity, resulting in higher levels of output produced with the same quantity of labor. For example, in Figure 1 increasing the amount of capital from K1 to K2 increases the output from Ya to Yb. Labor productivity increases when the capital stock is larger because workers can use the additional capital to produce more goods and services. For example, imagine loading and unloading a semitrailer truck by hand vs. using a forklift. One forklift operator can load and unload the truck in far less time than can be done by hand.

AGGREGATE DEMAND - CHAPTER 8 # 1, 2 1. What are the four main components of aggregate demand? Which is the largest?

Which is the smallest?

Consumption (largest), government spending, investment, net exports (smallest—actually negative in the U.S.)

2. Which of the following acts constitute investment according to the economist’s

definition of that term?

a. Pfizer builds a new factory in the United States to manufacture pharmaceuticals.

b. You buy 100 shares of Pfizer stock.

c. A small drugmaker goes bankrupt, and Pfizer purchases its factory and

equipment.

d. Your family buys a newly constructed home from a developer.

e. Your family buys an older home from another family. (Hint: Are any new

products demanded by this action?)

AGGREGATE SUPPLY - CHAPTER 10 # 4

4. Use an aggregate supply-and-demand diagram to show that multiplier effects are

smaller when the aggregate supply curve is steeper. Which case gives rise to more

inflation—the steep aggregate supply curve or the flat one? What happens to the

multiplier if the aggregate supply curve is vertical?

The steeper the aggregate supply curve, the smaller the multiplier effect of an increase in aggregate demand, and the larger the inflationary effect. So with an identical increase in aggregate demand, Figure 3(a) on the next page shows a larger output increase but a smaller price increase than Figure 3(b), because its aggregate supply curve is flatter. In the limiting case of Figure 3(c), where the aggregate supply curve is vertical, an increase in aggregate demand results only in inflation, and the multiplier is zero. In the other limiting case of Figure 3(d), where the aggregate supply curve is horizontal, inflation is absent and the multiplier is equal to the “oversimplified” multiplier of Chapter 9.

FIGURE 3

STABILIZATION POLICIES- CHAPTER 11 DISCUSSIN QUESTIONS 1 AND 3

1. The federal government spending (relative to the size of the economy) was cut back in

several dimensions after the gigantic budget deficits of 2009 and 2010. How would GDP in

the United States have been affected if this lower spending led to

a. smaller budget deficits?

b. more spending elsewhere in the budget, so that total government purchases remained

the same?

(a) If the decreases in government is not accompanied by cuts in taxes, then this decrease in government spending will lead to a smaller budget deficit. As a result GDP would decrease because while government spending has decreased by a specific amount, consumption has only increased by that amount multiplied by MPC.

(b) If government spending is switched toward other purchases, total G will not change, and GDP will not be affected.

3. If the government decides that aggregate demand is excessive and is causing inflation, what options are open to it? What if the government decides that aggregate demand is too weak instead?

To reduce aggregate demand, the government can reduce its spending on goods and services, raise taxes or reduce transfer payments. To increase aggregate demand, it can do the opposite: increase government spending, reduce taxes or increase transfer payments.

THE FINANCIAL CRISIS- CHAPTER 14 DISCUSSION QUESTIONS 1 AND 4

1. If you were watching house prices rise during the years 2000–2006, how might you have

decided whether or not you were witnessing a “bubble”?

There is typically debate about whether or not we have a bubble. If price increases were the result of improving fundamentals, then there was not a bubble. If price increases were the result of speculation or something else besides fundamentals, then there was a bubble. From 2000 to 2005 housing prices rose by 50% across the U.S. This relatively substantial increase might possibly suggest that a bubble existed. However, at the same time in markets like New York, Miami, and San Diego, housing prices rose by 77%, 96%, and 118%, respectively. It is very unlikely that these drastic price increases could have been fueled by changes in fundamentals. It would be reasonable to conclude that speculation on future price increases was fueling this price escalation which means it would be reasonable to conclude that a bubble existed at that point in time.

4 Explain how a collapse in house prices might lead to a recession.

The significant decrease in housing prices would make both buying and building homes less attractive. As a result, residential construction which is part of investment would decline significantly, decreasing real GDP. The decline in construction would lead to substantial unemployment in this sector. In addition, the decrease in home values would mean that homeowners have less wealth which generally leads to less consumption, another factor that would decrease real GDP. These homeowners cannot obtain additional funds through second mortgages to purchase various items. In fact, they may also have to cut back on some purchases if their mortgage rates increase because of limited or negative equity positions. Declining consumption would lead to more unemployment in other areas. Lastly, because most real estate purchases are financed through borrowing, the problems mentioned above could lead to significant issues in the banking and financial sectors.