Homework 1

1. Given the information in the following table for three consecutive years in the U.S. economy,
calculate the missing data.

Nominal Inflation
Real GDP Real GDP
GDP GDP (percent
(in billions per Capita Population
Year (in billions Deflator change in
of 2005 (in 2005 (in millions)
of U.S. (2005=100) GDP
dollars) dollars)
dollars) deflator)
2005 12,623 12,623 100.0 3.3 42,445 297.4
2006 13,374 12,959 103.2 3.2 43,154 300.3
2007 14,669 13,813 106.2 2.9 45,542 303.3

2. Assume an economy with a car manufacturer, a car seller, and some consumers (there is no
government). The consumers are workers who earn a wage to finance their consumption. In a
given year, the car manufacturer produces 50,000 cars and sells them for $10,000 per car. The
workers’ wages take up 70% of the car manufacturer’s revenue. All the materials used for
producing cars are imported from other countries at a cost of $1,000 per car. Half of the
manufactured cars are exported overseas and the remaining cars are sold to the domestic car
seller. The car seller sells the domestic cars and imported cars at the same price of $14,000 per
car. The car seller sells all domestic cars and 5,000 of the imported cars to domestic consumers.
After paying $6,000 for the cost of an imported car, the remaining sales revenue is equally
distributed between wages and profits.

a. Calculate GDP using (i) the product approach, (ii) the expenditure approach, and (iii) the
income approach.

Product approach:
Value added for the car manufacturer = 50,000 cars × ($10000 − $1000) = $450,000,000
Revenue received by the car seller = (25,000 cars) × ($14000 − $10000) + 5,000 cars ×
($14,000 − $6,000) = $140,000,000
GDP = $590,000,000

Expenditure approach:
Consumption = (25,000 cars + 5,000 cars) × $14,000 = $420,000,000
Export = 25,000 cars × $10,000 = $250,000,000
Import = 50,000 cars × $1,000 + 5,000 cars × $6,000 = $80,000,000
GDP = Consumption + Export − Import = $590,000,000
 Income approach:

Car manufacturer:
Wages = (50,000 cars × $10,000) × 0.7 = $350,000,000
Profits = Revenue − Wages − Costs of intermediate purchase = $500,000,000 −
$350,000,000 − $50,000,000 = $100,000,000

Car seller:
Revenue = 30,000 cars × $14,000 = $420,000,000
Costs of intermediate purchase = 25,000 cars × $10,000 + 5,000 cars × $6,000 =
$280,000,000
Wages = ($420,000,000 − $280,000,000) × 0.5 = $70,000,000
Profits = ($420,000,000 − $280,000,000) × 0.5 = $70,000,000

GDP = Wages + Profits = $590,000,000

b. Calculate the current account balance. Does the economy have a current account
surplus or deficit?

Current account balance = Trade balance + Net factor income from abroad + Net
unilateral transfers
In this economy, there is neither net factor income from abroad nor net unilateral
transfers.
Current account balance = Trade balance = Export − Import
Export = 25,000 cars × $10,000 = $250,000,000
Import = 50,000 cars × $1,000 + 5,000 cars × $6,000 = $80,000,000
Trade balance = $170,000,000
The economy experiences a current account surplus in 2016.

c. Suppose that the car manufacturer is a foreign entity and all of its profits belong to
foreigners. What would GNP and GDP in this economy be in this case?

GNI = GDP + Net factor payments from abroad

GNI = $590,000,000 − $100,000,000 = $490,000,000, where $100,000,000 is the amount
of profit paid to the foreign owner of the car manufacturer.

3. Suppose in the US the overall population is 330 million of which the working age population is
250 million. If the labor force is 160 million and unemployment rate is 3.15%, calculate the
following.
 d. Number of unemployed: U/160 = 3.75% -> U = 6mil

e. Employment rate (= Employment/Population ratio): 154/250 = 61.6%

f. Participation rate: 160/250 = 64%

4. In year 1 and year 2, there are two products produced in a given economy, smartphones and
earphones. Suppose that there are no intermediate goods. In year 1, 4,000 smartphones and
2,000 earphones are produced and sold at $2,000 and $200 each, respectively. However, due to
an earthquake in year 2, some production lines are destroyed and the production of smart-
phones are earphones falls to 1,000 and 1,500 units, respectively. However, the price of each
pair of smartphone doubled and the price of each pair of earphones increased to $300.

a. Calculate nominal GDP for year 1 and year 2.

2015 Quantity (Q) Price (P) Q×P

Smartphones 4,000 2,000 8,000,000
Earphones 2,000 200 400,000
Nominal GDP 8,400,000
2016
Smartphones 1,000 4,000 4,000,000
Earphones 1,500 300 450,000
Nominal GDP 4,450,000

b. Calculate real GDP in each year and the percentage change in real GDP from year 1 to
year 2 using year 1 as the base year. Next, do the same calculations using the chaing-
weighting method.

2015 Quantity (Q) Price (P) Q × P based on 2015

Smartphones 4,000 2,000 8,000,000
Earphones 2,000 200 400,000
Real GDP 8,400,000
2016
Smartphones 1,000 2,000 2,000,000
Earphones 1,500 200 300,000
Real GDP 2,300,000

Change in real GDP from 2015 to 2016 = (2,300,000 − 8,400,000)/8,400,000 = −73%

 chain-weighting method:
g1 = RGDP 2016 using price based on 2015/RGDP 2015 using price based on 2015 =
8,400,000/2,300,000 = 0.274
g2 = RGDP 2016 using price based on 2016/RGDP 2015 using price based on 2016 =
4,200,000/16,800,000 = 0.268
The chain-weighted ratio of real GDP in 2016 and 2015 is:
gc = (0.274 × 0.268)^0.5 = 0.271

The real GDP of 2015 in 2015 dollar rate: $8,400,000

The real GDP of 2016 in 2015 dollar rate: $8,400,000 × 0.271 = $2,275,776.05

c. Calculate the implicit GDP price deflator and the percentage inflation rate from year 1 to
year 2 using year 1 as the base year. Next do the same calculations using the chain-
weighting method.

With 2015 as the base year, the base year nominal GDP equals the base year real GDP,
so the base year implicit GDP deflator is 100.
For 2016, the implicit GDP deflator is ($4,450,000/2,300,000) × 100 = 193.5. The
percentage change in the deflator is equal to 93.5%.
With chain weighting, and the base year set at 2015, the 2015 GDP deflator equals
($8,400,000/$8,400,000) × 100 = 100. The chain-weighted deflator for 2016 is equal to
($4,450,000/$2,275,776.05) × 100 = 195.5.
The percentage change in the chain-weighted deflator equals to 95.5%.

d. Suppose that the design and quality of smart-phone improved significantly in year 2. For
example, the battery life of smartphones in year 2 was twice as long in year 1. Discuss
how this quality improvement may affect real GDP through the output and the price
level.

The higher price of a smartphone in 2016 than in 2015 partly reflects the reduction in
supply, but some of the increase in price may represent an improvement in quality. For
the national income accounting, we do not have the quality-adjusted price. In this sense,
the inflation rate is biased upward, so the real GDP may be biased downward. On the
other hand, we may measure the quality of new smartphones in terms of productivity.
For example, the productivity of a new smartphone is twice as an old smartphone.
Therefore, the quality-adjusted smartphone produced in 2006 may double, i.e., 2,000 (=
1,000 × 2). In this sense, the real GDP is biased downward, given the price.

5. Suppose that the government deficit is 10, interest on the government debt is 5, taxes are 40,
government expenditures are 30, consumption expenditures are 80, net factor payments are 10,
the current account surplus is -5, and national saving is 20. Calculate the following.
 a. Private disposable income

𝑌 ! = 𝑆 " + 𝐶 = 𝑆 + 𝐷 + 𝐶 = 20 + 10 + 80 = 110

b. Transfers from the government to the private sector

𝐷 = 𝐺 + 𝑇𝑅 + 𝐼𝑁𝑇 − 𝑇
𝑇𝑅 = 𝐷 − 𝐺 − 𝐼𝑁𝑇 + 𝑇 = 10 − 30 − 5 + 40 = 15

c. Gross national product

𝑆 = 𝐺𝑁𝑃 − 𝐶 − 𝐺
𝐺𝑁𝑃 = 𝑆 + 𝐶 + 𝐺 = 20 + 80 + 30 = 130

d. Gross domestic product

𝐺𝐷𝑃 = 𝐺𝑁𝑃 − 𝑁𝐹𝑃 = 130 − 10 = 120

e. The government surplus

𝑆# = −𝐷 = −10

f. Net exports

𝐶𝐴 = 𝑁𝑋 + 𝑁𝐹𝑃
𝑁𝑋 = 𝐶𝐴 − 𝑁𝐹𝑃 = −5 − 10 = −15

g. Investment expenditures

𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝑁𝑋
𝐼 = 𝐺𝐷𝑃 − 𝐶 − 𝐺 − 𝑁𝑋 = 120 − 80 − 30 + 15 = 25

6. Consider and economy described as follows:

Y= C+I+G
Y=8000
G=2500
T=2000
C=1000+2/3(Y-T)
I=1200-100r
 a. In this economy, compute private saving, public saving, and national saving.
Private Saving = Y-T-C = 8000 – 2000 – (1000 + 2/3(8000-2000)) = 1000
Public Saving = T-G = 2000 – 2500 = -500
National Saving = Y-C-G = 8000 – (1000 + 2/3(8000-2000)) – 2500 = 500

b. Find the equilibrium interest rate.

1200-100r = 500
r=7

c. Now suppose that G is reduced by 500. Compute private saving, public saving, and
national saving.
Private Saving = No change
Public Saving = 2000-2000 = 0
National Saving = 1000

d. Find the new equilibrium interest rate.

1200 -100r = 1000
r=2

7. Answer questions using the Asian Development Bank database, at https://kidb.adb.org/

Choose Taipei,China and download table (XLSX).

a. Find C,I,G,NX of 2020 both in nominal and real.

Nominal (in billion NT$)

C = 9,474.5 + 125.9 = 9600.4
I = 4,789.9
G= 2,771.2
NX = 11,491.0 - 8,853.9 = 2637.1

Real (in billion NT$ at 2016 prices) (chain-weighted)

C = 9,363.7 + 122.7 = 9486.4
I = 4,622.8
G = 2,652.8
NX = 12,600.8 - 9,540.9 = 3059.9
b. Then calculate the percentage of each expenditure category to total GDP. Compared
with the US data we saw in the class, what differences do you notice?

C = 48.5%
I = 24.2%
G = 14.0%
NX = 13.3%

Compared to the US data, (C=68.4%, I=16.8%, G=17.8%, NX=3%), we can notice Taiwan’s
export-led growth strategy. (High NX and low C)

c. Find CPI and Implicit GDP deflator of 2021. Also find the growth rate of CPI and GDP
deflator.

(2016 = 100)
CPI = 104.3
Implicit GDP deflator = 102.7

Growth rate
CPI = 2.0%
Implicit GDP deflator = 3.0%

d. Find the average annual inflation rate between 2000 and 2021 using CPI and implicit
GDP deflator. Does the data confirm the upward bias of CPI measure of inflation?

Avg inflation
CPI = 1%
Implicit GDP deflator = -0.1%

Yes.

e. Calculate 2021 unemployment rate, employment rate, and participation rate.

Unemployment rate = Unemployed / Labor force = 471 / 11,919 = 3.95%

Participation rate = Labor force / Working age population = 11,919 / W = 59% à
Working age population = 20,202 (million)
 Employment rate = Employed / Working age population = 11,447 / 20,202 = 56.7%

f. (optional) If there are any numbers/facts/fields in the table that interest you, please feel
free to share it here.