I need help in economics ExAM. exam is at 11 AM new york time and i will post 3 questions and i need it back in 35 min.

Problem Set 4

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Friday, May

1

st

1. (a) What is the “dual mandate” of the Federal Reserve of the United States?

https://www.federalreserve.gov/faqs/money_1

2

848.htm

(b) What are some of the priorities of other central banks? Looking on their websites,

identify the goals of each of the following central banks.

i. The Bank of England

ii. The Bank of Canada

iii. The European Central Bank

(c) Are any of the above more or less similar to the Fed’s dual mandate?

(d) San Diego is in Federal Reserve district twelve.

i. Where is the Federal Reserve Bank that supports the twelfth district?

ii. Which other states are located (partially or wholly) in the twelfth district?

2. Suppose the money supply is $2.25 trillion dollars and the reserve ratio is 10%. As a

result of economic trends the, Federal Reserve decides it wants to increase the money

supply to $2.5 trillion.

(a) If the Fed is increasing the money supply, which of their dual mandate are they

exercising?

(b) What open market operation will the Fed undertake to inject money into the econ-

omy?

(c) If banks hold no excess reserves, what value of bonds will the Fed buy/sell to increase

the money supply

to $2.5 trillion?

1

https://www.federalreserve.gov/faqs/money_12848.htm

(d) Suppose that as a result of economic conditions, banks actually hold 25% of deposits

in reserves, so that the effective reserve ratio is 25%, not 10%. Knowing this, what

value of bonds will the Fed buy/sell to increase the money supply from $2.25 trillion

to $2.5 trillion?

(e) As a result of the open market operation in (d), banks no longer feel the need to

hold so many excess reserves, so they now hold only 15% of deposits in reserves,

making the effective reserve ratio 15%. Since the Fed implemented monetary policy

in (d) under the assumption of a 25% reserve ratio, what value of bonds will the Fed

buy/sell to bring the money supply back to $2.5 trillion?

(f) If it knew the effective reserve ratio would be 15% upon implementing monetary

policy, what value of bonds would the Fed buy/sell to increase the money supply

from $2.25 trillion to $2.5 trillion? Does this match the difference between your

answers in (d) and (e)?

2

Problem Set 4 Solutions

ECON

3

− Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Friday, May

1

st

1. (a) The “dual mandate” of the Federal Reserve of the United States is to maximize

employment while maintaining stable inflation.

(b) What are some of the priorities of other central banks? Looking on their websites,

identify the goals of each of the following central banks.

i. The Bank of England has the mission “…to promote the good of the people

by maintaining monetary and financial stability.” The bank does this through

supervision of banks and setting the interest rate through monetary policy.

ii. The Bank of Canada works “…to preserve the value of money by keeping inflation

low and stable.”

iii. The European Central Bank has the mission “…to serve the people of Europe

by safeguarding the value of the euro and maintaining price stability.”

(c) It seems as though the Bank of England has a similar mission in setting monetary

policy to maintain stability in the economy through the interest rate at which banks

can loan. Although it is not said explicitly, this has the effect of balancing employ-

ment and inflation, just like the US Federal Reserve. Although all banks share some

form of the Fed’s “dual mandate,” the Bank of Canada and the European Central

Bank are explicit that price stability is their priority.

(d) San Diego is in Federal Reserve district twelve.

i. The Federal Reserve Bank that supports the twelfth district is located in San

Francisco.

1

ii. The twelfth district includes Alaska, Arizona, California, Hawaii, Idaho, Nevada,

Oregon, Utab, and Washington. The territories of American Samoa, Guam, and

the Northern Mariana Islands are also supported by the twelfth district.

2

. Suppose the money supply is $2.25 trillion dollars and the reserve ratio is 10%. As a

result of economic trends the, Federal Reserve decides it wants to increase the money

supply to $2.5 trillion.

(a) If the Fed is increasing the money supply, it is doing so in order to stimulate em-

ployment. The increase in the money supply is of course in tension with its other

mandate, which is to control inflation.

(b) The Fed will buy federal bonds in the open market, exchanging currency for financial

assets in order to put more money into the economy.

(c) If banks hold no excess reserves, then every dollar of currency put into the economy

increases money supply by the money multiplier, 1

0.1

= 10. The Fed must then

increase currency by only 10% of the desired increase of money supply. Since the

desired increase is $250 billion, the cash amount of bonds they would buy is $25

billion.

(d) If banks actually hold 25% of deposits in reserves, then then the money multiplier

is 1

0.25

= 4, so that every dollar of bonds sold by the Fed will increase deposits by

4 dollars. The Fed would then buy 250

4

billion in bonds, so the Fed’s open market

operation would be to buy $62.5 billion in bonds.

(e) If the effective reserve ratio is 15%, then the injection of $62.5 by the Fed would

increase money supply (in billions of $) by

62.5 ·

(

1

0.15

)

=

(

1250

3

)

≈ 416.67

Thus the money supply has increased more than the desired $250 billion. The Fed

would like to reduce the money supply by approximately $416.67b−$250b = $166.67b.

In order to decrease the money supply, the Fed would sell bonds. With a reserve

ratio of 15%, the Fed would sell (in billions of $)(

1250

3

− 250

)

· 0.15 =

(

500

3

)

· 0.15 = 25

So the Fed would sell $25 billion of treasury bills.

2

(f) If the Fed knew the effective reserve ratio would be 15% upon implementing monetary

policy, it would have only injected $250b · 0.15 = $37.5b. Between (d) and (e), the

Fed bought $62.5 billion in bonds and sold $25 billion, with a net result of buying

$37.5 billion. This exactly matches what the Fed would have done had it known the

effective reserve ratio would be 15%.

3

Problem Set

3

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April

2

0th

1

. (a) Discuss the six sources of economic growth and give an example of each.

(b) Suppose that population grows at a rate of 1% per year and the share of the popu-

lation with jobs levels out to 45%.

i. If GDP remains constant, what will be the growth rate of GDP per capita?

ii. What would the growth rate of GDP need to be for GDP per capita to remain

constant?

iii. What would the growth rate of GDP need to be for GDP per capita to increase

by 1% each year?

2. (a) Using the “years to double” shortcut, find the number of years one dollar takes to

double in value if it earns compound interest at a rate of: (i) 2%, (ii) 4%, (iii) 7%,

and (iv) 9% (years need not be whole numbers).

(b) Using the exact compound interest calculation, find the multiple by which each dollar

actually increases in (i)-(iv) in the number of years the shortcut implies (e.g. for

10% each dollar increases by a factor of 1.986). Does our shortcut provide a good

estimate? For which rate is it most accurate?

(c) Can you come up with a “years to triple” shortcut?

3. Suppose country A has grown its GDP at a rate of 2% over the past 30 years. Country

B, on the other hand, has only grown at a rate of 0.5% over the past 30 years.

(a) What are some reasons that country B might be experiencing a slower rate of growth

over this 30 years?

1

(b) If the countries start with the same GDP, how much larger (as a percentage) is the

GDP of country A after 30 years than that of country B?

(c) Suppose country B transitions to a free-market economy with well-defined property

rights and as a result, its growth rate increases. If country A continues to grow at

a rate of 2% per year, what must be the rate of growth for country B if its GDP

catches up to that of country A after another 30 years?

(d) Now 60 years have passed and the countries have the same GDP. What if the growth

rates in (c) continue for another 30 years? Whose GDP will by larger and by what

percentage?

4. Suppose Robert is a taxi driver and is considering starting his own business. It costs

$10,000 to buy a taxi, and Robert is willing to use his savings of $5,000 to pay for the car.

He can borrow or lend any amount at an interest rate of 5%. Based on his experience

with driving, Robert expects that for each hour he works, he will earn in taxi fares:

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$19 $23 $21 $20 $19 $18 $17 $15 $13 $12

Moreover, he anticipates using one gallon of gas per hour and the cost of gas is $3.00 per

gallon. Robert places a value of $13 per hour on his leisure time, meaning he will not

work for any hourly rate lower than that.

Alternatively, Robert can continue working for a large livery business where he earns $540

per week and does not pay for any of the car’s expenses.

Assume Robert would work 5 days per week at either job.

(a) If Robert were to buy a car, how many hours per day would he drive it and what

would be his daily profit?

(b) Assume that Robert must pay the loan off plus the 5% interest after 52 weeks. Also

assume that after 52 weeks he can sell the car for exactly what he paid for it, $10,000.

If the hours worked are the same either way, would Robert buy the car and start his

own business or continue working at his current job?

(c) If the car depreciated at a rate of 10% per year, would Robert still start his own

business?

2

(d) At what rate of depreciation would Robert be indifferent between starting his own

business or continuing his current job?

(e) Suppose again that depreciation is 10%. If the interest rate at which Robert can

borrow or lend were instead 10%, would he start his own business?

(f) With 10% depreciation, at what rate of interest would Robert be indifferent between

starting his own business or continuing his current job?

(g) If Robert were to buy a car and gas prices rose to $4.50 per gallon, how many hours

per day would he drive and what would be his daily profit?

3

Problem Set

1

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

April 4,

2

020

1. For each of the following transactions, state the effect both on U.S. GDP and on the four

components of aggregate expenditure.

(a) Your mother buys a BMW made in North Carolina.

(b) Your friend buys a SAAB imported from Sweden.

(c) You buy 10 shares of stock in

Amazon.

(d) You buy 20 shares of stock in MercadoLibre, an Argentine-owned competitor of

Amazon.

(e) You buy a used car from across the country and pay $1,000 to have it shipped to

you.

(f) Nike produces 100,000 Air Jordan shoes and sells half to consumers for $90 each.

(g) Napa valley vineyards produces 40,000 bottles of wine priced at $10 each, exports

10,000 to New York, 10,000 to Canada, sells 10,000 to the U.S. government for its

upcoming holiday party, and stores the remainder.

2. Consider a small economy in which people eat carrots, draw exclusively economics graphs

with markers, and use tractors for the production of carrots.

Carrots Markers Tractors

Quantity Price Quantity Price Quantity Price

2010 1,200 $1.50 120 $2.50 5 $10,000

2011 1,300 $1.15 150 $2.45 7 $11,000

1

(a) Calculate nominal and real GDP for 2010 and 2011 using 2010 as the base year.

(b) Calculate the GDP deflator for each year. What is the inflation rate according to

GDP deflator?

(c) Calculate the CPI for each year using 2010 as the base year with all goods included

in the representative basket. What is the inflation rate according the the CPI?

(d) What is the relationship between CPI and GDP deflator?

(e) Is the basket you used in (c), a “representative” basket for consumers? What would

be a better representative basket? What goods should be left out?

(f) Calculate CPI using the representative basket in (e). How does this change your

answer? If your answer has changed dramatically, why is this so?

3. Suppose you receive the following limited information about the labor market:

Working-age

Employment Unemployment Participation

Not in

population labor force

Rate 100% 4% 65%

Total 50m

Using what you know about employment statistics, fill in the blank entries.

4. The following is a report from a BLS survey taker:

There were 65 people in the houses I visited, 10 of them children under 16;

25 people had full-time jobs, and 5 of them had part-time jobs. There were 10

retirees, 5 full-time homemakers, 5 full-time students over age 16, and 2 people

who were disabled and cannot work. The remaining people did not have jobs

but all said they would like one. One of these people had not looked actively for

work for 3 months, however.

Assuming this is a representative sample, find the labor force, the unemployment rate,

and the participation rate implied by the survey taker’s report

2

Problem Set

3

Solutions

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April

2

0th

1

. (a) Discuss the six sources of economic growth and give an example of each.

• See lectures slides.

(b) If population grows at a rate of 1% per year and the share of the population with

jobs levels out to

4

5

%, then the population in year 2 with respect to year 1

is

POP2 = POP1 · (1.01)

i. If GDP remains constant, then Y2 = Y1. Then the growth rate of GDP per

capita from year 1 to year 2 is(

Y2

POP2

− Y1

POP1

Y1

POP1

)

· 100% =

(

Y1

POP1(1.01)

− Y1

POP1

Y1

POP1

)

· 100%

=

POP1

Y1

·

(

Y1

POP1(1.01)

−

Y1

POP1

)

· 100% =

1 − (1.01)

1.01

· 100%

= −

(

0.1

1.01

)

· 100% = −0.99%

ii. The growth rate g of GDP that would leave GDP per capita constant satisfies

Y2

POP2

=

Y1

POP1

⇐⇒

Y1(1 + g)

POP1(1.01)

=

Y1

POP1

=⇒ 1 + g = 1.01 =⇒ g

= 0.01

so that in percentage terms GDP growth is 1%, exactly the rate of population.

iii. The growth rate g of GDP that would grow GDP per capita by 1% each year

1

satisfies(

Y2

POP2

− Y1

POP1

Y1

POP1

)

· 100% = 1% ⇐⇒

(

Y1(1+g)

POP1(1.01)

− Y1

POP1

Y1

POP1

)

= 0.01

⇐⇒

POP1

Y1

·

(

Y1(1 + g)

POP1(1.01)

−

Y1

POP1

)

= 0.01 ⇐⇒

(1 + g) − (1.01)

1.01

= 0.01

⇐⇒ 1 + g = (1.01) · 0.01 + 1.01 = (1.01)2 ⇐⇒ g = (1.01)2 − 1 = 0.0201

so that in percentage terms, GDP would need to grow by 2.01% per year for

GDP per capita to grow by 1% per year.

2. (a) Using the “years to double” shortcut, the number of years it would take one dollar

to double is

i. 72

2

= 36 years

ii. 72

4

= 18 years

iii. 72

7

≈ 10.29 years

iv. 72

9

= 8 years

(b) Using the exact compound interest calculation, the multiple by which each dollar

actually increases in the number of years implied by the shortcut is

i. (1.02)36 ≈ 2.040

ii. (1.04)18 ≈ 2.026

iii. (1.07)72/7 ≈ 2.006

iv. (1.02)9 ≈ 1.993

The shortcut provides a good estimate, and in fact a near-perfect estimate for an

interest rate of 7%.

(c) A “years to triple” shortcut can be obtained through guessing and checking, starting

with numbers higher than 72. For example if you tried 100/i for i = 2%, this would

give you 50 years, and checking this would give (1.02)50 ≈ 2.69, so you would need

more years to triple. Eventually you would find that some numerator in the range

of 110-115 would provide a decent estimate, giving you an estimate of 110

i

years to

triple.

If you wanted to solve for this analytically, you could solve the equation (1 + i)n = 3

for n. Taking the natural log of each side gives

n ln(1 + i) = ln(3) =⇒ n = ln(1 + i) =

ln(3)

ln(1 + i)

2

For i = 0.02 this reduces to n ≈ 55.5 years. Then taking 111

i

is a pretty good estimate

for i = 2. Notice that the estimates get worse much more quickly than in our years

to double estimate.

3. Suppose country A has grown its GDP at a rate of 2% over the past 30 years. Country

B, on the other hand, has only grown at a rate of 0.5% over the past 30

years.

(a) Country B may have a slower rate of growth because of poor business structure,

inadequate incentives for innovation, turbulent political climate, etcetera.

(b) If the countries start with the same GDP, then after 30 years country A would have

GDP Y0 ·(1.02)30 ≈ 1.81·Y0 and country B would have GDP Y0 ·(1.005)30 ≈ 1.16·Y0.

Then as a percentage

1.81 ·Y0 − 1.16 ·Y0

1.16 ·Y0

· 100% ≈ 55.96%

the GDP of country A would be about 55.96% higher than that of country B.

(c) If country B were to grow at a rate g for 30 more years, its GDP would be the result

of growing 1.16 ·Y0 at rate g for 30 years, so GDP would be Y0 · (1.005)30 · (1 + g)30.

For this to equal the GDP of country A which has grown steadily at 2% for 60 years,

Y0 · (1.005)30 · (1 + g)30 = Y0 · (1.02)60 ⇐⇒ (1.005)(1 + g) = (1.02)2

=⇒ g =

(1.02)2

1.005

− 1 ≈ 0.03522

so country B must grow at a rate of about 3.52%.

(d) In 60 years countries again have the same GDP, call it Y60. If these growth rates

continue then after another 30 years country A would have GDP Y60·(1.02)30 ≈ 1.81·

Y60 ≈ 5.94·Y0, and country B would have GDP Y60·(1.03522)30 ≈ 2.82·Y60 ≈ 9.27·Y0.

Then as a percentage, after another 30 years

2.82 ·Y60 − 1.81 ·Y60

1.81 ·Y60

· 100% ≈ 55.96%

the GDP of country B would be about 55.96% higher than that of country A. Notice

that this is exactly the percentage difference country A was ahead after only 30

years.

4. Suppose Robert expects that for each hour he works, he will earn taxi fares

3

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$19 $23 $21 $20 $19 $18 $17 $15 $13 $12

If Robert must pay for one gallon of gas per hour at a price of $3.00 per gallon, for each

hour Robert is left with profit

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$16 $20 $18 $17 $16 $15 $14 $12 $10 $9

(a) If Robert decides to buy a car, he will work as long as his profit exceeds his value of

leisure time and he will thus work 7 hours per day. His daily profit will be

$(16 + 20 + 18 + 17 + 16 + 15 + 14) = $116

(b) If Robert works 5 hours per week then each week he can make $116 · 5 = $580 per

week. If Robert faces a time-frame of 52 weeks, Robert expects his total revenue

from driving will be $580 · 52 = $30, 160. At the end of the year he can sell his car

for the full amount, but must pay back the loan of $5,000 with interest. Since he

paid $5,000 of his own money, we must account for that as well. Then his net profit

is

− $5, 000 + $10, 000 − $5, 000(1 + 0.05) + $30, 160 = $30, 160 − $5, 000 · 0.05

= $29, 910

If, on the other hand, Robert keeps his current job, he will make $540·52 = $28, 080

in wages for the year, but he can also lend his $5,000 at the interest rate of 5%.

Then his total earnings will be $28, 080 + $5, 000 · 0.05 = $28, 330. Thus his outside

option is less profitable than investing in his own business ($29, 910 > $28, 330) so

Robert will buy

the car.

(c) If the car depreciated at a rate of 10% per year, Robert’s profit from investing at

the end of the year would be

− $5, 000 + $10, 000(1 − 0.1) − $5, 000(1 + 0.05) + $30, 160

= $30, 160 − $5, 000 · 0.05 − $10, 000 · 0.1

= $28, 910

which is still greater than his outside option of $28,330 so he would still invest in

the car.

4

(d) Robert would be indifferent between investing and staying at his current job if de-

preciation δ satisfies

− $5, 000 + $10, 000(1 − δ) − $5, 000(1 + 0.05) + $30, 160 = $28, 330

⇐⇒ $29, 910 − $10, 000 · δ = $28, 330 =⇒ δ = 0.158

So if the car depreciates at a rate of 15.8%, Robert would be indifferent between

starting his

own business and continuing his current job.

(e) If depreciation is 10% and the interest rate is also 10%, by investing Robert would

make profit

− $5, 000 + $10, 000(1 − 0.1) − $5, 000(1 + 0.1) + $30, 160

= $30, 160 − $5, 000 · 0.1 − $10, 000 · 0.1

= $28, 660

If Robert keeps his current job he will make $28,080 in wages and by lending his

$5,000 at a rate of 10% he would make $500, so his outside option is worth $28,580.

His outside option is still less than his payoff from investing in the car, so Robert

will invest.

(f) With depreciation of 10%, Robert would be indifferent between investing and staying

at his current job if interest i satisfies

− $5, 000 + $10, 000(1 − 0.1) − $5, 000(1 + i) + $30, 160 = $28, 080 + $5, 000 · i

⇐⇒ $30, 160 − $5, 000 · i− $10, 000 · 0.1 = $28, 080 + $5, 000 · i

⇐⇒ $10, 000 · i = $1, 080 =⇒ i = 0.108

So if the rate of interest is 10.8% Robert would be indifferent between starting his

own business and continuing his current job.

(g) If Robert were to buy a car and gas prices rose to $4.50 per gallon, how many hours

per day would he drive and what would be his daily profit? If gas prices were instead

$4.50 per gallon, for each hour Robert earns net profit

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$14.50 $18.50 $16.50 $15.50 $14.50 $13.50 $12.50 $11.50 $10.50 $8.50

So if Robert values his leisure time at $13 per hour, he will only work 6 hours per

day.

5

Problem Set

2

ECON

3

− Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April

1

3th

1. Consider a small economy in which consumers only consume apples and bananas. In year

1, qA1 apples and q

B

1 bananas are consumed. The price of apples in year 1 is p

A

1 and of

bananas pB1 . The quantities and prices for subsequent years are analogous, as described

in the following table.

Apples Bananas

Quantity Price Quantity Price

1 qA1 p

A

1 q

B

1 p

B

1

2 qA2 p

A

2 q

B

2 p

B

2

3 qA3 p

A

3 q

B

3 p

B

3

Take year 1 as the base year for all calculations.

(a) Which quantities or prices in the above table are irrelevant for the calculation of CPI

in years 1-3 (for example: qA6 , p

A

6 , q

B

6 and p

B

6 )?

(b) Which quantities or prices in the above table are irrelevant for the calculation of

nominal

GDP in years 1-3?

(c) Which quantities or prices in the above table are irrelevant for the calculation of real

GDP in years 1-3?

(d) Which quantities or prices in the above table are irrelevant for the calculation of

GDP deflator in years 1-3?

2. Consider a small economy in which the representative consumer eats only cheese and

drinks only wine.

1

Cheese (pounds) Wine (bottles)

Quantity Price Quantity Price

2000 1,200 $1.00 40 $10

2001 1,300 $1.20 60 $12

2002 700 $2.00 120 $4

(a) Calculate CPI for all three years, using the complete quantities in 2000 as the rep-

resentative basket.

(b) Does the CPI in 2001 suffer from substitution bias? If so, does this bias overestimate

or underestimate inflation?

(c) Does the CPI in 2002 suffer from substitution bias? If so, does this bias overestimate

or underestimate inflation?

(d) Suppose that the representative consumer has a utility function u(qc, qw) = q

2

c · qw,

where qc is the number of pounds of cheese consumed in a year and qw the number

of bottles of wine consumed. Show that in 2002 the consumer is actually better off

in terms of utility and spends less money by consuming the 2002 quantities of cheese

and wine compared to the 2000 quantities.

(e) Show that GDP deflator is a better representative for 2002 price level than CPI in

light of part (d).

3. Esmerelda entered the labor force in 2000. A shrewd negotiator, her employer agreed to

pay her $10.00 per hour in 2000, and guaranteed a 10% raise in her real wage every year,

indexed to inflation. Using the CPI values you calculated in 2(a) above, what will be

Esmerelda’s nominal wage in 2001 and 2002?

4. (a) Suppose that the nominal interest rate is 6% and inflation is 1%.

i. What is the exact real interest rate?

ii. What is the real interest rate implied by the approximation rule?

(b) Suppose that the nominal interest rate is 10% and inflation is 5%.

i. What is the exact real interest rate?

ii. What is the real interest rate implied by the approximation rule?

(c) Suppose that the nominal interest rate is 15% and inflation is 10%.

2

i. What is the exact real interest rate?

ii. What is the real interest rate implied by the approximation rule?

(d) How do the approximate estimates of the real interest rate vary with nominal interest

and inflation rates?

3

Midterm

1

(Practice)

ECON

3

− Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April

2

7th

Multiple choice

1 2 3

4

5 6 7 8 9 10

For the following questions, choose the best answer. Choose only one. Multiple choice questions

are worth 3 points each.

1. If real GDP increases, we know for certain that

(a) the price of some goods in the economy decreased.

(b) the production of some goods in the economy increased.

(c) the price of some goods in the economy increased.

(d) the production of some goods in the economy decreased.

2. If CPI decreases, we know for certain that

(a) the price of some goods in the economy decreased.

(b) the production of some goods in the economy increased.

(c) the price of some goods in the economy increased.

(d) the production of some goods in the economy decreased.

3. Unemployment may suffer from underestimation as a result of

(a) retired workers.

(b) unreliable workers.

(c) voluntary part-time workers.

(d) disabled workers

1

(e) discouraged workers.

(f) temporary workers.

4. The labor force participation rate is

(a) the fraction of the population that is of working-age.

(b) the fraction of the working-age population that is actively seeking employment.

(c) the fraction of the population that is employed.

(d) the fraction of the population that is employed or actively seeking employment.

(e) the fraction of the working-age population that is not a student, retired, or disabled.

(f) the fraction of the working-age population that is employed or actively seeking em-

ployment.

5. The Fisher effect predicts that

(a) nominal interest rates and real interest rates move together.

(b) real interest rates and GDP move together.

(c) real interest rates and inflation move together.

(d) GDP and inflation move together.

(e) nominal interest rates and inflation move together.

(f) nominal interest rates and GDP move together.

6. Which of the following contributes to GDP?

(a) You buy a bond from the Federal Reserve.

(b) You buy stock in Facebook from a broker who charges commission.

(c) Your sister-in-law sells you a house that she has lived in for 3 years before it is on

the market to the public.

(d) You pay your hairdresser to watch your dog, knowing full well that she will not

report the income on her taxes.

7. If nominal interest is 8% and inflation is 2%, the exact real interest rate (not the approx-

imate rate) would be

(a) 8%

(b) 6%

(c) Between 6% and 8%

(d) Less than 6%

8. One reason the CPI might not measure the true price level is

(a) the income effect.

(b) the substitution effect.

(c) the output effect.

2

(d) the conglomeration effect.

9. If CPI rises more than GDP deflator, there is

(a) unemployment in the economy.

(b) inflation in the economy.

(c) deflation in the economy.

(d) a looming recession.

10. Workers who would like a job but have not looked recently enough to be counted as

unemployed are referred to as

(a) abandoned workers.

(b) berated workers.

(c) condemned workers.

(d) discouraged workers.

(e) excluded workers.

(f) frustrated workers.

Short answer

1. (25 points total)

(a) (5 points) Name three “costs of inflation” and provide an example for each.

(b) (15 points total) Suppose an economy produces the following three goods

Year

Groceries Clothing Industrial equipment

Quantity Price Quantity Price Quantity Price

2029 15 $1.00 20 $3.00 3 $10.50

2030 16 $1.50 25 $2.00 3 $9.50

2031 17 $2.00 19 $2.50 2 $9.00

i. (5 points) Which of the three does not belong in consumer price index and why?

ii. (10 points) Calculate CPI with the two most appropriate consumer goods, using

2029 as the base year.

(c) (5 points) From 2030 to 2031 is the real interest rate higher or lower than the nominal

interest rate?

2. (25 points total)

(a) (5 points) Name three sources of growth and provide an example for each.

You’ve invested your savings in the republic of up and coming (RUC) and passed on

investing in the republic of established savings (RES). RUC has had a hard go of it the

past few years and has only grown at an annual rate of 1% per year. Meanwhile RES has

enjoyed a steady annual growth of 5% per year.

3

(b) (10 points) After three years, your savings would clearly have been better had you

invested in RES. By what percentage?

(c) (10 points) Over the next three years RUC grew by 10% per year. Would you have

preferred to have invested in RES after all?

3. (20 points total) Suppose that in 2023, you have entered the labor force and, as a successful

UCSD student, you secure a job with a starting salary of $100,000 per year. With your

new salary, you rent an amazing apartment for $2,000 per month.

(a) (10 points total) In one year you are given a 5% raise. You are confused, however,

because after paying your new rent of $2,200, you find that you are able to afford

fewer goods and services than you were the year before.

i. (4 points) Given this information alone, what explains your reduced purchasing

power?

ii. (6 points) If all prices in the economy move identically, what is the percentage

change in your real wage?

(b) (10 points) Suppose instead that inflation is 6% per year. What must be your wage

in 2024 in order to assure a 5% increase in real wage?

4

Problem Set

3

Solutions

ECON 3 − Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April

2

0th

1

. (a) Discuss the six sources of economic growth and give an example of each.

• See lectures slides.

(b) If population grows at a rate of 1% per year and the share of the population with

jobs levels out to

4

5

%, then the population in year 2 with respect to year 1

is

POP2 = POP1 · (1.01)

i. If GDP remains constant, then Y2 = Y1. Then the growth rate of GDP per

capita from year 1 to year 2 is(

Y2

POP2

− Y1

POP1

Y1

POP1

)

· 100% =

(

Y1

POP1(1.01)

− Y1

POP1

Y1

POP1

)

· 100%

=

POP1

Y1

·

(

Y1

POP1(1.01)

−

Y1

POP1

)

· 100% =

1 − (1.01)

1.01

· 100%

= −

(

0.1

1.01

)

· 100% = −0.99%

ii. The growth rate g of GDP that would leave GDP per capita constant satisfies

Y2

POP2

=

Y1

POP1

⇐⇒

Y1(1 + g)

POP1(1.01)

=

Y1

POP1

=⇒ 1 + g = 1.01 =⇒ g

= 0.01

so that in percentage terms GDP growth is 1%, exactly the rate of population.

iii. The growth rate g of GDP that would grow GDP per capita by 1% each year

1

satisfies(

Y2

POP2

− Y1

POP1

Y1

POP1

)

· 100% = 1% ⇐⇒

(

Y1(1+g)

POP1(1.01)

− Y1

POP1

Y1

POP1

)

= 0.01

⇐⇒

POP1

Y1

·

(

Y1(1 + g)

POP1(1.01)

−

Y1

POP1

)

= 0.01 ⇐⇒

(1 + g) − (1.01)

1.01

= 0.01

⇐⇒ 1 + g = (1.01) · 0.01 + 1.01 = (1.01)2 ⇐⇒ g = (1.01)2 − 1 = 0.0201

so that in percentage terms, GDP would need to grow by 2.01% per year for

GDP per capita to grow by 1% per year.

2. (a) Using the “years to double” shortcut, the number of years it would take one dollar

to double is

i. 72

2

= 36 years

ii. 72

4

= 18 years

iii. 72

7

≈ 10.29 years

iv. 72

9

= 8 years

(b) Using the exact compound interest calculation, the multiple by which each dollar

actually increases in the number of years implied by the shortcut is

i. (1.02)36 ≈ 2.040

ii. (1.04)18 ≈ 2.026

iii. (1.07)72/7 ≈ 2.006

iv. (1.02)9 ≈ 1.993

The shortcut provides a good estimate, and in fact a near-perfect estimate for an

interest rate of 7%.

(c) A “years to triple” shortcut can be obtained through guessing and checking, starting

with numbers higher than 72. For example if you tried 100/i for i = 2%, this would

give you 50 years, and checking this would give (1.02)50 ≈ 2.69, so you would need

more years to triple. Eventually you would find that some numerator in the range

of 110-115 would provide a decent estimate, giving you an estimate of 110

i

years to

triple.

If you wanted to solve for this analytically, you could solve the equation (1 + i)n = 3

for n. Taking the natural log of each side gives

n ln(1 + i) = ln(3) =⇒ n = ln(1 + i) =

ln(3)

ln(1 + i)

2

For i = 0.02 this reduces to n ≈ 55.5 years. Then taking 111

i

is a pretty good estimate

for i = 2. Notice that the estimates get worse much more quickly than in our years

to double estimate.

3. Suppose country A has grown its GDP at a rate of 2% over the past 30 years. Country

B, on the other hand, has only grown at a rate of 0.5% over the past 30

years.

(a) Country B may have a slower rate of growth because of poor business structure,

inadequate incentives for innovation, turbulent political climate, etcetera.

(b) If the countries start with the same GDP, then after 30 years country A would have

GDP Y0 ·(1.02)30 ≈ 1.81·Y0 and country B would have GDP Y0 ·(1.005)30 ≈ 1.16·Y0.

Then as a percentage

1.81 ·Y0 − 1.16 ·Y0

1.16 ·Y0

· 100% ≈ 55.96%

the GDP of country A would be about 55.96% higher than that of country B.

(c) If country B were to grow at a rate g for 30 more years, its GDP would be the result

of growing 1.16 ·Y0 at rate g for 30 years, so GDP would be Y0 · (1.005)30 · (1 + g)30.

For this to equal the GDP of country A which has grown steadily at 2% for 60 years,

Y0 · (1.005)30 · (1 + g)30 = Y0 · (1.02)60 ⇐⇒ (1.005)(1 + g) = (1.02)2

=⇒ g =

(1.02)2

1.005

− 1 ≈ 0.03522

so country B must grow at a rate of about 3.52%.

(d) In 60 years countries again have the same GDP, call it Y60. If these growth rates

continue then after another 30 years country A would have GDP Y60·(1.02)30 ≈ 1.81·

Y60 ≈ 5.94·Y0, and country B would have GDP Y60·(1.03522)30 ≈ 2.82·Y60 ≈ 9.27·Y0.

Then as a percentage, after another 30 years

2.82 ·Y60 − 1.81 ·Y60

1.81 ·Y60

· 100% ≈ 55.96%

the GDP of country B would be about 55.96% higher than that of country A. Notice

that this is exactly the percentage difference country A was ahead after only 30

years.

4. Suppose Robert expects that for each hour he works, he will earn taxi fares

3

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$19 $23 $21 $20 $19 $18 $17 $15 $13 $12

If Robert must pay for one gallon of gas per hour at a price of $3.00 per gallon, for each

hour Robert is left with profit

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$16 $20 $18 $17 $16 $15 $14 $12 $10 $9

(a) If Robert decides to buy a car, he will work as long as his profit exceeds his value of

leisure time and he will thus work 7 hours per day. His daily profit will be

$(16 + 20 + 18 + 17 + 16 + 15 + 14) = $116

(b) If Robert works 5 hours per week then each week he can make $116 · 5 = $580 per

week. If Robert faces a time-frame of 52 weeks, Robert expects his total revenue

from driving will be $580 · 52 = $30, 160. At the end of the year he can sell his car

for the full amount, but must pay back the loan of $5,000 with interest. Since he

paid $5,000 of his own money, we must account for that as well. Then his net profit

is

− $5, 000 + $10, 000 − $5, 000(1 + 0.05) + $30, 160 = $30, 160 − $5, 000 · 0.05

= $29, 910

If, on the other hand, Robert keeps his current job, he will make $540·52 = $28, 080

in wages for the year, but he can also lend his $5,000 at the interest rate of 5%.

Then his total earnings will be $28, 080 + $5, 000 · 0.05 = $28, 330. Thus his outside

option is less profitable than investing in his own business ($29, 910 > $28, 330) so

Robert will buy

the car.

(c) If the car depreciated at a rate of 10% per year, Robert’s profit from investing at

the end of the year would be

− $5, 000 + $10, 000(1 − 0.1) − $5, 000(1 + 0.05) + $30, 160

= $30, 160 − $5, 000 · 0.05 − $10, 000 · 0.1

= $28, 910

which is still greater than his outside option of $28,330 so he would still invest in

the car.

4

(d) Robert would be indifferent between investing and staying at his current job if de-

preciation δ satisfies

− $5, 000 + $10, 000(1 − δ) − $5, 000(1 + 0.05) + $30, 160 = $28, 330

⇐⇒ $29, 910 − $10, 000 · δ = $28, 330 =⇒ δ = 0.158

So if the car depreciates at a rate of 15.8%, Robert would be indifferent between

starting his

own business and continuing his current job.

(e) If depreciation is 10% and the interest rate is also 10%, by investing Robert would

make profit

− $5, 000 + $10, 000(1 − 0.1) − $5, 000(1 + 0.1) + $30, 160

= $30, 160 − $5, 000 · 0.1 − $10, 000 · 0.1

= $28, 660

If Robert keeps his current job he will make $28,080 in wages and by lending his

$5,000 at a rate of 10% he would make $500, so his outside option is worth $28,580.

His outside option is still less than his payoff from investing in the car, so Robert

will invest.

(f) With depreciation of 10%, Robert would be indifferent between investing and staying

at his current job if interest i satisfies

− $5, 000 + $10, 000(1 − 0.1) − $5, 000(1 + i) + $30, 160 = $28, 080 + $5, 000 · i

⇐⇒ $30, 160 − $5, 000 · i− $10, 000 · 0.1 = $28, 080 + $5, 000 · i

⇐⇒ $10, 000 · i = $1, 080 =⇒ i = 0.108

So if the rate of interest is 10.8% Robert would be indifferent between starting his

own business and continuing his current job.

(g) If Robert were to buy a car and gas prices rose to $4.50 per gallon, how many hours

per day would he drive and what would be his daily profit? If gas prices were instead

$4.50 per gallon, for each hour Robert earns net profit

1st hr 2nd hr 3rd hr 4th hr 5th hr 6th hr 7th hr 8th hr 9th hr 10th hr

$14.50 $18.50 $16.50 $15.50 $14.50 $13.50 $12.50 $11.50 $10.50 $8.50

So if Robert values his leisure time at $13 per hour, he will only work 6 hours per

day.

5

Problem Set

2

Solutions

ECON

3

− Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April

1

3th

1. If the following table describes consumption and prices for a small economy, with year 1

as the base year,

Apples Bananas

Quantity Price Quantity Price

1 qA1 p

A

1 q

B

1 p

B

1

2 qA2 p

A

2 q

B

2 p

B

2

3 qA3 p

A

3 q

B

3 p

B

3

(a) Quantities qA2 , q

A

3 , q

B

2 , and q

B

3 are irrelevant for the calculation of CPI in years 1-3.

(b) All quantities and prices are needed to calculate nominal GDP in years 1-3.

(c) Prices pA2 , p

A

3 , p

B

2 , and p

B

3 are irrelevant for the calculation of real GDP in years 1-3.

(d) All quantities and prices are needed to calculate GDP deflator in years 1-3.

2. Consider a small economy in which the representative consumer eats only cheese and

drinks only wine.

Cheese (pounds) Wine (bottles)

Quantity Price Quantity Price

2000 1,200 $1.00

4

0 $10

2001 1,300 $1.20 60 $12

2002 700 $2.00 120 $

4

1

(a)

CPI2000 =

(

Qc2000 · Pc2000 + Qw2000 · Pw2000

Qc2000 · Pc2000 + Qw2000 · Pw2000

)

· 100 =

(

$1, 600

$1, 600

)

·

100

= 100

CPI2001 =

(

Qc2000 · Pc2001 + Qw2000 · Pw2001

Qc2000 · Pc2000 + Qw2000 · Pw2000

)

· 100 =

(

$1, 920

$1, 600

)

· 100

=

120

CPI2002 =

(

Qc2000 · Pc2002 + Qw2000 · Pw2002

Qc2000 · Pc2000 + Qw2000 · Pw2000

)

· 100 =

(

$2, 560

$1, 600

)

· 100

= 160

(b) CPI in 2001 suffers from no substitution bias. Given that the prices both increased

by 20%, the consumer has no incentive to substitute toward one good over the other.

(c) CPI in 2002 suffers from substitution bias. Since wine becomes relatively less ex-

pensive, the consumer would substitute away from consuming cheese and toward

consuming wine. This is exactly what we see in the consumption pattern.

Given that CPI does not account for substitution away from the relatively more

expensive good, it exaggerates the burden of the price change on the consumer and

hence overestimates inflation.

(d) With utility u(qc,qw) = q

2

c · qw, in 2000 the consumer enjoys utility

u(1200, 40) = 12002 · 40 = 57, 600, 000

while in 2002 utility is

u(700, 120) = 7002 · 120 = 58, 800, 000

so it is clear that utility is higher in 2002. Moreover, expenditure on 2000 quantities

would be

Qc2000 · P

c

2002 + Q

w

2000 · P

w

2002 = $2 · 1200 + $4 · 40

= $2, 560

while actual expenditure is

Qc2002 · P

c

2002 + Q

w

2002 · P

w

2002 = $2 · 700 + $4 · 120

= $1, 880

so the consumer spends less than they would have on the base year basket.

2

(e) GDP

deflator is

GDPd2002 =

(

Qc2002 · Pc2002 + Qw2002 · Pw2002

Qc2002 · Pc2000 + Qw2002 · Pw2000

)

· 100 =

(

$1, 880

$1, 900

)

· 100

= 98.9

5

Since 2000 is the base year, GDP deflator is 100, so inflation according to GDP

deflator is

π =

(

98.95 − 100

100

)

· 100% = −1.05%

while according to CPI

π =

(

160 − 100

100

)

· 100% = 60%

GDP deflator indicates deflation, consistent with the price burden of the consumer

as shown above, while CPI indicates large inflation. This discrepancy shows that

GDP deflator seems to be a better representative for 2002 price level than CPI.

3. Beginning with a wage of $10 per hour and increasing 10% per year in real terms, we

know that in 2000 dollars, Esmerelda should make $11 per hour in 2001 and $12.10 in

2002. From (2), inflation in 2001 is

π =

(

120 − 100

100

)

· 100% = 20%

while inflation from 2000 to 2002 is

π =

(

160 − 100

100

)

· 100% = 60%

Inflating real wage to compensate for price changes gives a nominal wage of $11 · (1.2) =

$13.20 in 2001 and f $12.10 · (1.6) = $19.36 in 2002.

Note that you could also have grown nominal wage in 2001 by 10% and applied inflation

from 2001 to 2002, which is

π =

(

160 − 120

120

)

· 100% =

100

3

% ≈ 33.33%

Then wage in 2002 is

w2002 = $11 · (1.2) · (1.1) ·

(

1 +

1

3

)

= $11 · (1.1)

(

6

5

)

·

(

4

3

)

= $12.10 ·

(

8

5

)

= $19.36.

3

4. The exact real interest rate is given by

r =

i − π

1 + π

(a) If the nominal interest rate is 6% and inflation is 1%.

i. The exact real interest rate (as a percent) is

r =

(

0.06 − 0.01

1 + 0.01

)

· 100% ≈ 4.95%

ii. The real interest rate implied by the approximation rule (as a percent) is

r = (0.06 − 0.01) · 100% = 5%

(b) If the nominal interest rate is 10% and inflation is 5%.

i. The exact real interest rate (as a percent) is

r =

(

0.1 − 0.05

1 + 0.05

)

· 100% ≈ 4.76%

ii. The real interest rate implied by the approximation rule (as a percent) is

r = (0.1 − 0.05) · 100% = 5%

(c) If the nominal interest rate is 15% and inflation is 10%.

i. The exact real interest rate (as a percent) is

r =

(

0.15 − 0.1

1 + 0.1

)

· 100% ≈ 4.55%

ii. The real interest rate implied by the approximation rule (as a percent) is

r = (0.15 − 0.1) · 100% = 5%

(d) The approximations all indicate the real interest rate is 5%, while the exact real

interest rates are all lower than this. As inflation increases, the real interest rate

decreases, so the approximations become more inaccurate.

4

Problem Set

1

Solutions

ECON

3

− Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Thursday, April 9th

1. For each of the following transactions, state the effect both on U.S. GDP and on the four

components of aggregate expenditure.

(a) Your mother buys a BMW made in North Carolina.

• Consumption increases by the cost of the car.

• GDP increases by the cost of the car.

(b) Your friend buys a SAAB imported from Sweden.

• Consumption increases by the cost of the car.

• Imports increase by the cost of the car.

• GDP is unchanged.

(c) You buy 10 shares of stock in Amazon.

• Stock purchase is a transfer of ownership, no GDP component is affected.

• GDP is unchanged.

(d) You buy

2

0 shares of stock in MercadoLibre, an Argentine-owned competitor of

Amazon. Stock purchase is a transfer of ownership, no GDP component is affected.

• Stock purchase is a transfer of ownership, no GDP component is affected.

• GDP is unchanged.

(e) You buy a used car from across the country and pay $1,000 to have it shipped to

you.

• The used car does not affect any component of current GDP.

1

• Consumption increases by $1,000 from the service of the car being shipped.

• GDP increases by $1,000

(f) Nike produces 100,000 Air Jordan shoes and sells half to consumers for $90 each.

• Consumption increases by $

4

,

5

00,000.

• Investment increases by $4,500,000 in the form of change in inventories.

• GDP increases by $9,000,000.

(g) Napa valley vineyards produces 40,000 bottles of wine priced at $10 each, exports

10,000 to New York, 10,000 to Canada, sells 10,000 to the U.S. government for its

upcoming holiday party, and stores the remainder.

• Consumption increases by $100,000 from New York purchase.

• Exports increase by $100,000 from Canada purchase.

• Government purchases increase by $100,000

• Investment increases by $100,000 in the form of change in inventories.

• GDP increases by $400,000.

2. Consider a small economy in which people eat carrots, draw exclusively economics graphs

with markers, and use tractors for the production of carrots.

Carrots Markers Tractors

Quantity Price Quantity Price Quantity Price

2010 1,200 $1.50 120 $2.50 5 $10,000

2011 1,300 $1.15 150 $2.45 7 $11,000

2

(a)

NGDP2010 = Q

c

2010 ·P

c

2010 + Q

m

2010 ·P

m

2010 + Q

t

2010 ·P

t

2010

= $1.50 · 1200 + $2.50 · 120 + $10, 000 · 5

=

$52, 100.00

NGDP2011 = Q

c

2011 ·P

c

2011 + Q

m

2011 ·P

m

2011 + Q

t

2011 ·P

t

2011

= $1.15 · 1300 + $2.45 · 150 + $11, 000 · 7

= $78, 862.50

RGDP2010 = Q

c

2010 ·P

c

2010 + Q

m

2010 ·P

m

2010 + Q

t

2010 ·P

t

2010 = $52, 100.00

RGDP2011 = Q

c

2011 ·P

c

2010 + Q

m

2011 ·P

m

2010 + Q

t

2011 ·P

t

2010

= $1.50 · 1300 + $2.50 · 150 + $10, 000 · 7

=

$72, 325.00

(b)

GDPd2010

=

(

NGDP2010

RGDP2010

)

· 100 =

100

GDPd2010 =

(

NGDP2011

RGDP2011

)

· 100 =

(

$78, 862.50

$72, 325.00

)

· 100

= 109.04

According to GDP deflator, inflation from 2010 to 2011 is

π =

(

109.04 − 100

100

)

· 100% = 9.04%

(c)

CPI2010 =

(

Qc2010 ·Pc2010 + Qm2010 ·Pm2010 + Qt2010 ·P t2010

Qc2010 ·Pc2010 + Qm2010 ·Pm2010 + Qt2010 ·P t2010

)

· 100 = 100

CPI2011 =

(

Qc2010 ·Pc2011 + Qm2010 ·Pm2011 + Qt2010 ·P t2011

Qc2010 ·Pc2010 + Qm2010 ·Pm2010 + Qt2010 ·P t2010

)

· 100

=

(

$56, 674.00

$52, 100.00

)

· 100 = 108.78

According to CPI, inflation from 2010 to 2011 is

π =

(

108.78 − 100

100

)

· 100% = 8.78%

3

(d) CPI and GDP deflator move in the same direction in this case, but have slightly

different values given that GDP deflator used 2011 quantities, while CPI used only

2010 quantities.

(e) It is probably not representative of the price burden faced by the consumer to include

tractors, so we might leave that out.

(f) Using the basket of goods leaving tractors out, CPI is as

follows.

CPI2010 =

(

Qc2010 ·Pc2010 + Qm2010 ·Pm2010

Qc2010 ·Pc2010 + Qm2010 ·Pm2010

)

· 100 = 100

CPI2011 =

(

Qc2010 ·Pc2011 + Qm2010 ·Pm2011

Qc2010 ·Pc2010 + Qm2010 ·Pm2010

)

· 100

=

(

$1, 674.00

$2, 100.00

)

· 100 = 79.71

According to CPI, inflation from 2010 to 2011 is

π =

(

79.71 − 100

100

)

· 100% = −20.29%

CPI without tractors actually indicates deflation, a dramatic difference from (c).

The reason is that while tractor prices increased, increasing GDP deflator, food and

marker prices actually decreased. If the consumer only cares about these two things

then the price burden has decreased as well, resulting in deflation.

3. Recall the definitions:

Labor force = Employed + Unemployed

Participation rate =

Labor force

Working-age population

Unemployment rate =

Unemployed

Labor force

Then if unemployment is 4% this leaves 96% employed. If 65% of the working age are

participating in the labor force this leaves 35% not in the labor force. It 35% of the

population is 50 million then the working-age population (Pop16+) is

(Pop16+) · 0.35 = 50m =⇒ (Pop16+) =

50m

0.35

≈ 142.86m

Taking 65% of the working-age population of 142.86m gives a labor force of 92.86m. If 4%

of this total is unemployed and the rest are employed, we have all the necessary figures

to fill out the table.

4

Working-age

Employment Unemployment Participation

Not in

population labor force

Rate 100% 96% 4% 65% 35%

Total 142.62m 89.14m 3.71m 92.86m 50m

4. The following is a report from a BLS survey taker:

There were 65 people in the houses I visited, 10 of them children under 16;

25 people had full-time jobs, and 5 of them had part-time jobs. There were 10

retirees, 5 full-time homemakers, 5 full-time students over age 16, and 2 people

who were disabled and cannot work. The remaining people did not have jobs

but all said they would like one. One of these people had not looked actively for

work for 3 months, however.

If 10 people are under 16, the working-age population is 55. 30 people are employed, 22

are not in the labor force, leaving 3 people saying they would like a job. If one of these

people has not actively looked for work in 3 months this person is not in the labor force.

If we assume the remaining 2 people are actively looking, then the labor force is 32, and

there are 23 not in the labor force. If this is a representative sample, the statistics are as

follows.

Working-age

Employment Unemployment Participation

Not in

population labor force

Rate 84.62% 93.75% 6.25% 58.18% 41.81%

Total 55 30 2 32 23

5

Midterm

1

(Practice) Solutions

ECON

3

− Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April

2

7th

Multiple choice

1 2 3

4

5

6

7 8 9 10

B A E F E B D B B D

For the following questions, choose the best answer. Choose only one. Multiple choice questions

are worth 3 points each.

1. If real GDP increases, we know for certain that

(a) the price of some goods in the economy decreased.

(b) the production of some goods in the economy increased.

(c) the price of some goods in the economy increased.

(d) the production of some goods in the economy decreased.

2. If CPI decreases, we know for certain that

(a) the price of some goods in the economy decreased.

(b) the production of some goods in the economy increased.

(c) the price of some goods in the economy increased.

(d) the production of some goods in the economy decreased.

3. Unemployment may suffer from underestimation as a result of

(a) retired workers.

(b) unreliable workers.

(c) voluntary part-time workers.

(d) disabled workers

1

(e) discouraged workers.

(f) temporary workers.

4. The labor force participation rate is

(a) the fraction of the population that is of working-age.

(b) the fraction of the working-age population that is actively seeking employment.

(c) the fraction of the population that is employed.

(d) the fraction of the population that is employed or actively seeking employment.

(e) the fraction of the working-age population that is not a student, retired, or disabled.

(f) the fraction of the working-age population that is employed or actively seeking em-

ployment.

5. The Fisher effect predicts that

(a) nominal interest rates and real interest rates move together.

(b) real interest rates and GDP move together.

(c) real interest rates and inflation move together.

(d) GDP and inflation move together.

(e) nominal interest rates and inflation move together.

(f) nominal interest rates and GDP move together.

6. Which of the following contributes to GDP?

(a) You buy a bond from the Federal Reserve.

(b) You buy stock in Facebook from a broker who charges commission.

(c) Your sister-in-law sells you a house that she has lived in for 3 years before it is on

the market to the public.

(d) You pay your hairdresser to watch your dog, knowing full well that she will not

report the income on her taxes.

7. If nominal interest is 8% and inflation is 2%, the exact real interest rate (not the approx-

imate rate) would be

(a) 8%

(b) 6%

(c) Between 6% and 8%

(d) Less than 6%

8. One reason the CPI might not measure the true price level is

(a) the income effect.

(b) the substitution effect.

(c) the output effect.

2

(d) the conglomeration effect.

9. If CPI rises more than GDP deflator, there is

(a) unemployment in the economy.

(b) inflation in the economy.

(c) deflation in the economy.

(d) a looming recession.

10. Workers who would like a job but have not looked recently enough to be counted as

unemployed are referred to as

(a) abandoned workers.

(b) berated workers.

(c) condemned workers.

(d) discouraged workers.

(e) excluded workers.

(f) frustrated workers.

3

Short answer

1. (25 points total)

(a) (5 points) Name three “costs of inflation” and provide an example for each

i. Price as a signal of scarcity

• For example: Have prices of rice increased because rice is becoming harder

to grow or is it just inflation?

ii. Distortions caused by taxes

• For example: Not all taxes are indexed to inflation, such as the deduction

from capital depreciation.

iii. Increases in the cost of cash

• For example: The cost of having to reprint menus to reflect higher prices

iv. Unexpected redistribution of wealth

• For example: Inflation decreases the real interest rate, hurting lenders but

benefiting borrowers.

v. Interference with long-term planning

• For example: Inability to predict prices will limit your ability to know how

much to save.

(b) (15 points total) Suppose an economy produces the following three goods

Year

Groceries Clothing Industrial equipment

Quantity Price Quantity Price Quantity Price

2029 15 $1.00 20 $3.00 3 $10.50

2030 16 $1.50 25 $2.00 3 $9.50

2031 17 $2.00 19 $2.50 2 $9.00

i. (5 points) Which of the three does not belong in consumer price index and why?

Industrial equipment since it is not a consumer good.

ii. (10 points) Calculate CPI with the two most appropriate consumer goods, using

2029 as the base year.

CPI2029 = 100

CPI2030 = 83.33

CPI2031 = 106

4

(c) (5 points) From 2030 to 2031 is the real interest rate higher or lower than the nominal

interest rate?

Since there is inflation between 2030 and 2031 the real interest rate is lower than the

nominal rate, given that

r ≈ i − π

Note that it does not matter if you use the exact formula or the approximation. The

direction will be the same, as (1 + π) > 0.

2. (25 points total)

(a) (5 points) Name three sources of growth and provide an example for each

i. Increase of physical capital

• For example: More machines per worker.

ii. Increase of human capital

• For example: Training in Microsoft Office.

iii. Land and other natural resources

• For example: Finding new places to drill for oil.

iv. Technological advances

• For example: Inventing a new way to extract previously unattainable shale

oil (fracking)

v. Entrepreneurship and management

• For example: Allocating employees to the tasks where they would be most

productive. Incentivizing small business ownership through low-interest

loans.

vi. Legal systems

• For example: A system that protects property rights.

(b) (10 points) If after three years, RUC has only grown at an annual rate of 1% per

year while RES has enjoyed a steady annual growth of 5% per year, one dollar would

have grown as shown in the table below.

Time passed RUC RES

3 years 1.03 1.16

By investing in RES, after three years your savings would be higher by(

1.16 −

1.03

1.03

)

· 100% ≈ 12.36%

(c) (10 points) If over the next three years RUC grew by 10% per year while RES

maintained a 5% growth rate, one dollar would have grown as shown in the table

below.

Time passed RUC RES

3 years 1.03 1.16

6 years 1.37 1.34

5

Thus you would not have preferred to invest in RES, as your total return over 6

years with RUC would be 37% whereas your return with RES would be 34%.

3. (20 points total) Suppose that in 2023, you have entered the labor force and, as a successful

UCSD student, you secure a job with a starting salary of $100,000 per year. With your

new salary, you rent an amazing apartment for $2,000 per month.

(a) (10 points total) In one year you are given a 5% raise. You are confused, however,

because after paying your new rent of $2,200, you find that you are able to afford

fewer goods and services than you were the year before.

i. (4 points) Given this information alone, what explains your reduced purchasing

power?

With this information alone, it seems that prices have increased by 10%, since

the change in rent is (

2200 − 2000

2000

)

· 100% = 10%

Thus, a 5% increase in nominal income results in a decrease in real income and

hence purchasing power.

ii. (6 points) If all prices in the economy move identically, what is the percentage

change in your real income?

If inflation is 10% and nominal income increases by 5%, the approximation tells

us that real income is approximately 5% − 10% = −5%. Thus, a 5% increase in

nominal income results in a decrease in real income and hence purchasing power.

Using the exact formula, purchasing power changes from 100, 000/P to 105, 000/(1.1)P ,

so that the change in real income is(

105000

(1.1)P

−

100000

P

100000

P

)

· 100% = −

(

0.05

1.1

)

· 100% ≈ −4.55%

(b) (10 points) Suppose instead that inflation is 6% per year. What must be your income

in 2024 in order to assure a 5% increase in real income?

In order to guarantee a 5% increase in real income, a income of $100,000 must be

increased not only by 5%, but by an additional 6% to compensate for inflation, giving

income

$100, 000 · (1.05) · (1.06) = $111, 300

Income in 2024 must then be $111,300.

6

Chapter

2

2: Money, Prices, and the Federal Reserve

ECON

3

– Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Wednesday, April 29th – Monday, May

4

th

What is money?

Without money, how would people obtain goods and services?

• barter – the direct trade of goods or services for other goods or services

�

Animal pelts used to be a common item used for barter

Barter depends on a double coincidence of wants, a phenomenon where two parties each hold

an item the other wants, so they exchange these items directly without any monetary medium.

Instead, we might prefer something that is universally agreed upon to be valuable, avoiding

the double coincidence of wants.

• money – any asset that can be used in making purchases

�

Animal pelts served as early forms of money, but their effectiveness depended on a

shared belief in their value.

Money and its properties

We would like money to be widely agreed to be valuable. What are the other key roles does

money serves?

1

. medium of exchange – an asset used in purchasing goods and services

�

Basically it has to satisfy the definition of money

2. unit of account – a basic measure of economic value

�

Enables the value of different goods to be compared, even if rates of exchange between

two goods cannot be directly observed

3. store of value – an asset that serves as a means of holding wealth

�

Imagine if you were paid every two weeks with a box full of food; your “payment”

would spoil before you could consume it all!

1

Measuring money

We will focus on two measures of money called M1 and M2.

1. M1 – the sum of currency outstanding and balances held in checking accounts

2. M2 – all assets in M1 plus some additional assets that are usable in making payments

but at a greater cost or inconvenience

Notice that the difference between assets only in M2 and those in M1 is liquidity.

• Liquidity is the ability to quickly convert an asset into spendable currency without losing

its value

�

the less value that is lost, the more liquid is the asset

Money and commercial banks

Before banks, people would store all of their money at home (under their mattresses, for exam-

ple). Then people wanted to put their money into banks for at least two reasons.

1. It is risky to carry large amounts of cash, for fear of losing it

2. Banks may incentivize households to lend them their cash in exchange for paying interest

3. Making payments is easier when money is held in a bank.

Banks like taking customer’s cash

• Banks can lend out borrowed cash at a higher rate than they pay to borrow it!

But how much do they decide to lend out? Banks face competing incentives:

(i) The more cash banks lend out, the more they can make in terms of interest on these loans.

(ii) If banks lend out too much cash, they may not have enough to satisfy the demands of their

clients, who may either withdraw cash or transfer it directly in order to make a payment

(e.g. by writing a check)

Let us formalize the bank’s decision with a few definitions.

• bank reserves – cash or similar assets held by commercial banks for the purpose of

meeting depositor withdrawals and payments

• 100 percent reserve banking – a situation in which banks’ reserves equal 100 percent

of their deposits

�

This is one extreme of reserve banking

2

Again, it is in the bank’s interest to hold fewer than 100 percent of deposits in reserve since

they would like to earn interest by issuing loans. In fact, a 100 percent reserve banking system

could not be sustainable, because banks have expenses (interest payments on deposits, storage

for customers’ cash), and without income banks would go out of business!

Then as banks lend out their reserves and deposits remain, deposits exceed reserves! It is

useful to introduce terminology to measure this.

• reserve-deposit ratio – bank reserves divided by deposits

• fractional-reserve banking system – a banking system in which bank reserves are less

than deposits so that the reserve-deposit ratio is less than 100 percent

�

As the definition implies, if reserves equal deposits, the reserve ratio is 100 percent

and we have 100 percent reserve banking, as above.

• excess reserves – reserves that exceed the amount of reserves a bank would like to hold

to satisfy their reserve-deposit ratio.

�

If the bank would like to satisfy

Reserves

Deposits

= rr, then excess reserves are given by

Excess reserves = Reserves − rr · Deposits

Let’s look at how this results in money creation.

The creation of money

How is money created? The obvious answer is that the government prints it! But there is a

more subtle means of money creation that we will explore here.

Money is created through:

1. The government issuing (e.g. printing) new currency; and

2. The process of deposit creation through a fractional-reserve banking system

Let’s look at an example.

An example of money creation: No currency held

Suppose the central bank in the new economy of Wynneweld issues 1000 notes of its new

currency, the baskin. Not wanting to hold currency, the public brings this new currency to the

only bank in town, Bank Exotic. In order to protect against running out of reserves to satisfy

their clients’ demand for their deposits, the bank keeps 10% of deposits on reserve. These

assumptions are summarized as follows.

• The government of Wynneweld distributes 1000 baskins to the public.

• The public does not want to hold any currency as cash, and will always deposit it into

the bank

3

• Bank Exotic is the only bank in town and it keeps 10% of its deposits as reserves.

If this were a 100 percent reserve banking system, the bank would keep all of these deposits

and the total amount of money created in the economy would remain 1000 baskins. We know,

however, that the bank will loan out 90% of its deposits.

In Step 1, the public deposits the 1000b currency into the bank, increasing reserves and deposits.

Step 1

Assets Liabilities

Reserves 1000b Deposits 1000b

→

Step 2

Assets Liabilities

Reserves 100b Deposits 1000b

Loans 900b

In Step 2, the bank loans out its 900b excess reserves, leaving it with reserve ratio Reserves

Deposits

=

100b

1000b

= 0.1, as desired.

In Step 3, the public deposits the 900b loan since they do not wish to hold any cash, increasing

reserves back to 1000b and deposits to 1900b.

Step 3

Assets Liabilities

Reserves 1000b Deposits 1900b

Loans 900b

→

Step 4

Assets Liabilities

Reserves 190b Deposits 1900b

Loans 2

7

10b

In Step 4, given that banks have 1900b in deposits and would like to hold only 10% of this

in reserves, Bank Exotic finds that it has 1000b − 190b =

8

10b in excess reserves. The bank

will then loan out an additional 810b, increasing loans to 2710b and decreasing reserves to 190b.

In Step

5

and beyond, any loans issued will come back as deposits. Since reserves in Bank

Exotic will always be 1000b after the public deposits their cash, this process will continue until

deposits satisfy

Reserves

Deposits

= 0.1 =⇒ Deposits =

Reserves

0.1

=

1, 000b

0.1

= 10, 000b

The final balance sheet after this process will look as follows.

Assets Liabilities

Reserves 1,000b Deposits 10,000b

Loans 9,000b

So the central bank printing 1000b resulted in the creation of 10,000b in deposits. This increases

the money supply M1 by 10,000b

�

The currency as reserves does not count in M1 because it is not currency in circulation.

4

The money multiplier

This increase in deposits as a result of an influx of currency can also be found using the money

multiplier. The money multiplier is the inverse of the reserve ratio. In particular, for a

reserve ratio rr, the money multiplier is

MM =

1

rr

In our example, with rr = 0.1, MM = 1

0.1

= 10, so a 1000b increase in currency led to a

10 · 1000b = 10, 000b increase in deposits.

An example of money creation: Half of currency held

Consider the previous example, but suppose instead that the public will deposit only half of

new currency issues. These new assumptions are summarized as follows.

• The government of Wynneweld distributes 1000 baskins to the public.

• The public deposit half on initial currency issues into the bank

• Bank Exotic is the only bank in town and it keeps 10% of its deposits as reserves.

Then if 500b is held in currency and 500b is deposited, using the money multiplier, total deposits

increase by 10 · 500b = 5000b, so deposits increase to 5000b. The total money change in the

money supply is the increase in currency in circulation (500b) and total deposits (5000b). The

increase in the money supply is thus 5,500b.

Clearly then, monetary policy (how the government changes the money supply) is affected

by at least two factors:

1. What percentage of deposits banks hold in reserves

�

This will be referred to as the effective reserve ratio

2. How much money the public wishes to hold as currency

�

This will be referred to as the demand for money

The federal reserve system

The Federal Reserve System (or the Fed) is the central bank of the United States

�

Other central banks include the Bank of Canada (BoC), the Bank of Mexico (BdeM), the

People’s Bank of China (PBoC), the European Central Bank (ECB)

The Fed’s key responsibilities include:

• Monetary policy – the determination of the nation’s money supply

• Supervision and regulation of financial markets

• Intervention in times of financial crisis (it’s more likely than you think).

5

�

e.g. the Fed can loan directly to banks

�

the Fed can change the reserve requirement, a much more extreme tool than mone-

tary policy (in fact as of March 15th, 2020, the Fed decreased all reserve requirements

to zero! https://www.federalreserve.gov/monetarypolicy/reservereq.htm)

The history of the Fed

Federal Reserve Act passed in 1913 and the Federal Reserve System started operations in 1914

in response to particularly severe banking panic in 1907.

In forming the Federal Reserve System, two competing forces needed to be balanced.

1. A central bank should be able to affect the money supply of the entire country, and should

thus be centralized.

2. The culture of the United States is U.S. culture is averse to centralized power, having been

founded as a country by fighting against the subjugation of the centralized government

of Great Britain

The compromise to address these competing forces led to the following structure of the Federal

Reserve System.

1. There are 12 regional Federal Reserve banks, each associated with a geographical area

called a Federal Reserve district.

�

Each bank is able to give input into the Fed’s decision making with knowledge of their

district’s needs that is more accessible at the local level.

�

San Diego is in district 12, whose main branch is in San Francisco.

• Board of governors – the leadership of the Fed, consisting of seven governors appointed

by the president to staggered 14-year terms

�

Terms are staggered so there is an appointment every two years (only one full term

may be served by each governor).

6

https://www.federalreserve.gov/monetarypolicy/reservereq.htm

�

There are currently two vacant seats on the board.

• Federal Open Market Committee (FOMC) – the committee that makes decisions

concerning monetary policy

– The FOMC consists of the seven Fed governors, the president of the Federal Reserve

Bank of New York, and 4 rotating members of other regional Federal Reserve banks.

�

The FRBNY president is always on the FOMC because monetary policy goes

through the trading desk in the New York Fed.

�

If there are un-appointed governors, those vacant seats on the board stay vacant

on the FOMC.

• open-market operations – the buying and selling of government bonds to affect the

money supply

• open-market purchase – the purchase of government bonds from the public by the Fed

for the purpose of increasing the supply of bank reserves and the money supply

�

The Fed executes open-market purchases in order to increase the money supply

• open-market sale – the sale by the Fed of government bonds to the public for the

purpose of reducing bank reserves and the money supply

�

The Fed executes open-market sales in order to decrease the money supply

Contractionary monetary policy: An example

Consider the example above, where the central bank’s addition of 1000 baskins in currency led

to 10,000 baskins worth of deposits being created.

Assets Liabilities

Reserves 1,000b Deposits 10,000b

Loans 9,000b

What if, for whatever reason, the central bank decides that there should only be 9,000b worth

of deposits in the economy? Given the money multiplier is 10, the government would need to

remove 100b from the bank’s reserves. This would entail the open market sale of 100b worth

of bonds, leading to a decrease of 10 · 100b = 1000b in deposits, and a final balance sheet as

follows.

Assets Liabilities

Reserves 900b Deposits 9,000b

Loans 8,100b

Expansionary monetary policy: An example

What if instead the central bank instead decides to increase the money supply to 15,000b?

Then it would execute an open market purchase of 500b worth of bonds, leading to an increase

of 10 · 500b = 5000b in deposits, and a final balance sheet as follows.

Assets Liabilities

Reserves 1,500b Deposits 15,000b

Loans 13,500b

7

How to stop a banking panic

• banking panic – a situation in which news or rumors of the imminent bankruptcy of one

or more banks leads to bank depositors to rush to withdraw their funds

�

If you think your bank is going to run out of money, it is rational to want to withdraw

your deposits while the bank still has reserves to honor them!

In order to prevent this sort of “run” on banks, it is essential that customers believe that their

deposits will remain accessible, even if the bank goes bankrupt! This is why in addition to

the Federal Reserve System being created in 1913, the Federal Deposit Insurance Corporation

(FDIC) was created in 1933 to stop banking panics.

• deposit insurance – a system under which the government guarantees that depositors

will not lose any money, even if their bank goes bankrupt

– The Federal Deposit Insurance Corporation (FDIC) is the deposit insurance for the

United States, created during the Great Depression by the 1933 Banking Act.

�

Up to $100,000 worth of deposits were insured until 2008, when this limit was

increased to $250,000 of deposits

The velocity of money

The velocity of money is a measure of how often money changes hands on average. It is defined

as follows

velocity =

value of transactions

money stock

In order to value transactions, we will take the nominal GDP, which is real GDP Y , scaled by

the current price level P . Then velocity of money can be written as M ·V = P ·Y .

While this equation in itself is not so informative (V can take whatever value ensures that it

holds), if we assume that velocity and real GDP are constant (at least in the short-term, then

we have the following relationship.

M ·V = P ·Y

This implies that increases in the money supply lead to inflation. As the following graph shows,

there is empirical support for this result.

8

Chapter

1

9: Economic Growth, Productivity, and Livin

g

Standards

ECON

3

– Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Wednesday, April 1

5

th – Monday, April

2

0th

Intro to growth and living standards

Growth and increases in productivity and living standards have been quite impressive. Take

the following examples.

1. Information Transmission from Coast to Coast U.S.

• 18

4

8: 4 –

6

months to deliver message via boat across the country

• 1861: Coast-to-coast telegraph; nearly instantaneous between stations

• 1915: First coast-to-coast telephone service

• Today: Cell phones are portable, relatively inexpensive, and instantaneous

2. History of Travel Across the U.S.

• 18th-19th century: Covered wagon takes more than 7 months to cross the U.S.

• 1869: Transcontinental railroad, takes 84 hours to cross the U.S. on express train

• Start of 20th century: Automobiles allow point-to-point travel

• Mid-20th century: Jet airplanes allow cross-country travel in 5-6 hours

1

The figure above shows the remarkable increase in GDP per capita in the United States. What

factors explain this incredible growth?

Compound interest

The difference between simple and compound interest is that

• with simple interest, you earn interest only on your principal

• with compound interest, you earn interest on your principal and your interest

For example, suppose you invest $100 at a rate of 4%. After 1 year, you have $100 · (1 + 0.04) =

104. After 2 years, with simple interest you have 104 + 0.04 · 100 = 108. With compound

interest you have 104 · (1 + 0.04)2 = 104 + 0.04 · 104 = 108.16. As the years go on, this difference

widens.

Years 1 2 3 10 50 n

Simple 104 108 112 140 300 100 + 100 · 0.4 · n

Compound 104 108.16 112.49 148.02 710.67 100(1.04)n

Moreover, the differences between growth rates becomes increasingly apparent as the time

horizon increases.

50 years 100 years

Interest Simple Compound Simple Compound

2% $200 $269.19 $300 $724.46

4% 300 710.67 500 5,050.49

6% 400 1,842.02 700 33,930.21

Growth of a country

As we saw above, small differences in growth rates matter! Consider two countries whose only

difference in growth is one percent per year.

12 years 24 years 36 years 72 years

Country A (2%) 1.27 1.61 2.04 4.16

Country B (3%) 1.43 2.03 2.90 8.40

After 72 years, a one percent difference in growth rates leads country B to be twice as advanced

as country A!

The figures below show different rates of growth for a few countries over varying time periods.

2

Rule of 72

A shortcut to estimate the number of years it takes a country to grow at a growth rate g% is

years to double =

72

g

As above, it takes 72

2

= 36 years to grow at a rate of 2%, and 24 years at a rate of 3%. This

means that

(1.02)36 ≈ 2 (actually 2.04 as above)

(1.03)24 ≈ 2 (actually 2.03 as above)

So for small interest rates, this shortcut is pretty accurate! As you can show, the approximation

becomes more precise as the rate increases to g = 7%, and then begins to become increasingly

less accurate.

3

Real GDP per capita

Real GDP per person is

Y

POP

, which can be broken down into

Y

POP

=

Y

N

·

N

POP

where Y is total real GDP, N is the number of employed workers, and POP is the total

population. Then GDP per person is

GDP per person = (Average labor productivity) · (share of population employed)

The benefit of writing RGDP per capita in this way is that it allows us to isolate two factors

relevant to its growth. As the first figure below shows, RGDP per worker and RGDP per person

move together. In addition, as the second figure below shows, the share of the population with

jobs increases until the early 1980s as more women enter the workforce, but then tends to level

out. If this is true, then we can focus on average labor productivity as the driving factor of

RGDP per capita growth.

4

Determinants of average labor productivity

Since it seems that average labor productivity drives economic growth, it is useful to consider

what determines average labor productivity.

1. Human capital – talents, education, skills, and training of workers

2. Physical capital – factories, machines, and equipment

• Diminishing returns to capital limits extent to which capital can spur growth

Pizza Pizzas Marginal

ovens per hour return

0 1 1

1 10 9

2 15 5

3 15 0

3. Land and other natural resources – land, raw materials, energy

• E.g. land for farming (like natural capital!)

4. Technological advancement is probably the most important determinant of growth

• This is not just new capital, but improvements on existing capital

• Cars, computers, mobile phones

5. Entrepreneurship and management

• Entrepreneurs are people who create new economic enterprises

• Managers arrange inputs to maximize efficiency

6. Political and legal environment

• For example, laws that ensure property rights encourage development of property

• Sharing of idea allows specialization and spread of knowledge

Costs of economic growth

The costs of economic growth are

• Deferred consumption today to create capital for the future

• Deferred consumption today to research and innovate technological progress

• Forgone leisure in possibly dangerous jobs

We also mentioned some other potential costs in class, including

• Pollution as a result of carbon-based energy

• Issues with rising inequality

5

Promoting growth

In order to promote growth of real GDP per person, we can target any of our determinants

described above.

1. Human capital – most countries provide free public education (at least through high

school)

2. Physical capital – Saving and investment incentives

• Favorable tax treatment for investment in physical capital

• Low interest rates to encourage investment

• Subsidies

3. Technological progress – promoting research (public funding like National Science Foun-

dation)

4. Entrepreneurship and management – small business loans to promote new businesses

5. Legal and political framework – Implement policies to promote innovation

• Well-defined property rights

• Patents

This is only a partial list of examples. Feel free to fill this in with some of your own ideas!

6

Chapter

2

1

: Saving and Capital Formation

ECON

3

– Principles of Macroeconomics

University of California San Diego

Christopher Gibson

Monday, April 20th

Saving

Let’s first get some definitions out of the way.

• saving – current income minus spending on current needs

• saving rate – saving divided by income

• assets – anything of value that one owns

• liabilities – the debts one owes

• wealth (or net worth) – the value of assets minus liabilities

• balance sheet – a list of an economic unit’s assets and liabilities on a specific date

For example:

Year-end balance sheet

Assets Liabilities

Cash $ 100 Car loan $ 10,000

Checking account

5

00 Credit card balance

4

50

Savings account 2,000 Insurance bill 150

Stock 900

Car 15,000

Total $1

8

,500 $10,

6

00

Net worth $

7

,900

Capital gains and losses

• capital gains – increases in the value of existing assets

• capital losses – decreases in the value of existing assets

1

For example, what if in the balance sheet above, the stock price increased in value to $1,000

and car decreased to $14,950? Then change in wealth is

∆(wealth) = savings + capital gains − capital losses

Assuming no additional savings, we have a capital gain of $100 and a capital loss of $50, so the

change in wealth is an increase of $50 to $7,950.

Stocks versus flows

• flow – a measure that is defined per unit of time

• stock – a measure that is defined at a point in time

Think about stocks and flows as water filling a bathtub. The stock is the total amount of water

in the tub at any given time, while the flow is the net inflow (inflows minus outflows) during

any period of time.

If, for example, 2 gallons of water flow in and 1 gallon of water flows out every minute, then

the net inflow would be 1 gallon of water per minute. If we start with an empty tub, this rate

of flow tells us that in 10 minutes, the stock in the tub will be 10 gallons.

Why do people save?

Some of the reasons that people save include the following.

• life-cycle saving – saving to meet long-term objectives such as retirement, college at-

tendance, or the purchase of a home

• precautionary saving – saving for protection against unexpected setbacks such as the

loss of a job or a medical emergency

• bequest saving – saving done for the purpose of leaving an inheritance

2

Savings: An example

The two families the Thrifts and the Spends are alike in all but one way. The Thrifts save 20%

of their income per year while the Spends only save 5%. Both families make income of $40,000

per year as well as any interest income from saving, with an 8% rate of return.

For example, since the Thrifts save 20% of income, in the first year their income is $40,000

and their savings is $8,000. In the second year, income is $40,000 plus 8% of their total savings

of $8,000, giving total income

40, 000 + 0.08 · 8, 000 = 40, 640

The Thrifts will save 20% of this income ($8,128) and consume the rest ($32,512). Total saving

will be $8,000 plus the $8,128 from the current year, giving $16,128. In 1987, income will

be $40, 000 + 0.08 · $16, 128 = $41, 290.24. They will save 20% of this income, adding to their

existing savings of $16,128. This process continues. The table below shows the paths of income,

savings, and consumption for several years.

Thrifts Spends

Year Income Savings (total) Consumption Income Savings (total) Consumption

1985 $40,000 $8,000 $32,000 $40,000 $2,000 $38,000

1986 40,640 16,128 32,512 40,160 4,008 38,152

1987 41,290.24 24,386.05 33,032.19 40,320.64 6,024.03 38,304.61

…

…

…

…

…

…

…

2000 50,753.45 144,568.88 40,602.76 42,468.38 32,978.16 40,344.96

…

…

…

…

…

…

…

2010 59,484.35 255,451.19 47,587.48 44,198.02 54,685.15 41,988.12

While the Thrifts initially do not consume as much as the Spends, by 2000 their consumption

catches up, as their interest income on savings more than compensates for their lower rate of

consumption, 80%.

Moreover, in 2000, total savings by the Thrifts reaches $144,568.88, while the Spends have

only saved $32,978.16. Then by 2000, the Spends had saved less than the Thrifts had by

1987! This difference in savings only increases as the years go on, attributable to the power of

compound interest.

The figure below shows the consumption path of both the Thrifts and the Spends. What the

figure does not show is the wild disparity in their total savings that the Thrifts have available

for retirement over the Spends!

3

Why don’t people save?

We have seen why people do save (and, arguably, why they should save), but why do people

not always save as much as they should?

• self-control – people prefer consumption today to consumption tomorrow

�

called present bias or discounting future consumption

• demonstration effects – effects on the behavior of individuals caused by observation of

the actions of others and their consequences

�

E.g., you want to keep up with neighbors so you get a summer house in the Hamptons

�

Then, when you summer in the Hamptons, all of your neighbors talk about their

chateaus in France! (should you then buy a French chateau?)

• capital gains grow wealth in other ways

4

As the above figure shows, there seems to be a tendency for household savings to decrease as

capital gains (on housing and stock market assets) increase. Households may be more concerned

with achieving wealth establishment goals instead of particular savings goals.

National saving

Recall that saving is current income minus spending on current needs. On a national level,

it is tricky to determine what should be included in spending on current needs and what is

not. Investment should not be in spending on current needs (mostly), since most of investment

involves the accumulation of long-term capital. It is more difficult to determine the role of

consumption and government expenditure, since these categories can include spending on long-

lived durable goods, or short-lived nondurable goods. For simplicity, we will make the following

assumptions.

1. All Consumption and Government expenditures are on current needs.

2. All Investment spending is on future needs.

3. The economy is closed, so that there is no international trade: M = X = NX = 0.

If we consider a closed economy, net exports are zero and

Y = C + I + G

We will define national saving as income minus spending: S = Y − C − G. Let T = Taxes −

transfers− interest, net taxes. Savings becomes

S = (Y −T −C) + (T −G)

If we define Sprivate = Y −T −C and Spublic = T −G, then savings can be rewritten as

S = Sprivate + Spublic

So national saving is the sum of private saving plus public saving.

Government saving

Public saving, Spublic = T − G, is the government’s savings, which can be positive or negative.

Notice the following.

Spublic > 0 =⇒ T > G =⇒ budget surplus

Spublic < 0 =⇒ T < G =⇒ budget deficit

Here is data from the federal as well as state and local governments in 2015 and 2016.

Government savings in 2015 and 2016

Federal government State and local governments

Year Receipts Expenditures Surplus Receipts Expenditures Surplus

2015 2,063.2 1,906.6 156.6 1,303.1 1,293.2 9.9

2016 3,452.1 4,149.4 -697.3 2,416.3 2,583.7 -167.4

5

As the table makes clear, the federal and state/local governments ran a budget surplus in 2015,

but ran a deficit in 2016.

As the figure above shows, business saving has increased over the time horizon between 1960

and 2017, while household saving has decreased. Government saving is typically negative, so

the government is typically a borrower.

Investment and capital formation

Like all economic decisions, capital projects will be undertaken if the benefits exceed the costs.

Investment and capital formation: An example

Carol is considering starting a junk disposal business and anticipates she can earn $49,000 per

year. She must rent hauling truck for $8,500 per year, and she can earn 10% on investment

funds. Alternatively, she can earn $40,000 per year if she keeps her current job. Will she start

the business?

1. If she starts her own business, Carol will make revenues of $49,000 and incur costs of

$8,500, yielding profit $49, 000 − $8, 500 = $40, 500

2. If she keeps her current job, Carol will make her salary of $40,000, but she can also

invest her $8,500 she would have paid to rent the hauling truck at a rate of 10%. At the

beginning of the year, this will be an outflow of the $8,500 investment, and at the end of

they year she will be returned her investment with 10% interest, yielding total profit

40, 000 + 8, 500 · (1 + 0.01) − 8, 500 = 40, 850

So Carol would make $40,850 by keeping her current job.

Since Carol will earn more by keeping her current job ($40,850) than starting her business

($40,500), Carol will keep her current job.

Suppose instead that investment funds yield 5%. Would Carol’s decision change?

6

1. If she starts her own business, Carol will still make $40,500 since this did not depend on

the interest rate.

2. If Carol keeps her current job, she will make only 5% on her investment of $8,500, yielding

total profit

40, 000 + 8, 500 · (1 + 0.005) − 8, 500 = 40, 425

So Carol would make $40,425 by keeping her current job.

Now, since Carol will earn more by starting her business ($40,500) than by keeping her current

job ($40,425), Carol will keep start her own business.

Factors that affect investment include

As the previous example illustrates, there are many factors that influence the decision of whether

or not to invest funds.

1. A decline in the price of new capital goods

• Imagine if Carol paid less to rent the junk hauling truck.

2. A decline in the real interest rate

• We saw this change Carol’s decision of whether to invest.

3. Technological improvement that raises the marginal product of capital

• This could increase Carol’s productivity and lead to revenue greater than the pro-

jected $49,000.

4. A higher relative price for the firm’s output

• Like higher productivity, a higher relative price would lead to revenue greater than

the projected $49,000.

5. Lower taxes on the revenues generated by capital

• While not addressed in our example above, any additional expense discourages in-

vestment spending.

The supply and demand of loanable funds

• Who supplies loanable funds?

– Households are typically the suppliers of loanable funds, as they put money into

savings, retirement accounts, and the stock market.

• Who demands loanable funds?

– Firms typically demand loanable funds, borrowing in order to finance long-term

capital projects.

– Governments can be net borrowers or net lenders, but since the government typically

runs a budget deficit it is more likely a net borrower, so it demands funds.

7

What is the price of loanable funds?

The price of loanable funds is the real interest rate. This is the reward to supplying loanable

funds (lending) and the cost of demanding loanable funds (borrowing).

Notice that the market for loanable funds reaches equilibrium just like any other market of

supply and demand.

• If the real interest rate is too high, the supply of savings exceeds demand so savers are

willing to take lower rates.

• If the real interest is too low, there is not enough lending (saving) in the market so firms

will bid real interest rate up.

Changes in any of the above factors that affect the demand for loanable funds (except changes

in the real interest rate) result in shifts in the demand for loanable funds. After a shift in

loanable funds, the market is forced out of equilibrium. The market regains equilibrium at a

higher/lower real interest rate through the forces described above.

8