Finance 30220: Macroeconomic Analysis
Problem Set #2 Solutions: A Deeper Look at the US Economy
Section #1: The National Income and Product Accounts
1) Suppose that we have the following information for General Motors:
Sales: $150B
Expenses: $130B
• Material Expenses: $40B
• Utilities: $5B
• Labor Costs: $60B
• Advertising: $10B
• Property Taxes: $15B
Capital Expenditures: $4B
Change In Inventories: $750M
a) Calculate value added for GM
Value Added = Sales – Material Expenses - Utilities – Advertising + Change in Inventories
Value Added = $150B - $40B - $5B - $10B + $750M = $95.75B
b) Calculate Gross Investment for GM
Gross Investment = $4B + $750M = $4.75B
2) Consider the following data for General Electric. Assume that all of GE’s business took place
in the US. Assume that 80% of GE shareholders are US residents and that GE pays out 10%
of its profits to shareholders.
Sales
Expenditures
Materials
Labor Costs
Domestic Labor
Foreign Labor
Capital Expenditures
Depreciation
Change in Inventories
$125M
$117.5M
$60M
$32.5M
$28M
$4.5M
$25M
$6.5M
-$15M
Calculate the contribution of GE to GDP, GNP, National Income, and Personal Income.
GDP is just GM’s value added:
GDP = Value Added = $125M - $60 + (-$15M) = $50M = Labor Income + Corporate Profits
(EBITDA)
Change in
Revenues
Materials
Expense
Inventories
GDP = $50M = $32.5M + $17.5M
Total Wages
Profits (EBITDA)
GNP (Represents Income Earned by Americans) = GDP + Net Primary Income
• GM pays out 10% of its profits ($17.5M) to shareholders, 20% of which are foreign.
($17.5M)(.10)(.20) = $.35M Paid to foreign shareholders
• GM pays out $4.5M to foreign labor
GNP = $50 - $0.35 - $4.5 = $45.15
Income Payments to ROW
National Income = GNP – Depreciation = $45.15M - $6.5M = $38.65M
National Income = $38.65M = $28M + $10.65M
American
Wages
American
Profits (EBIT)
Personal Income represents only income received by households.
• GE pays out 10% of its profits ($17.5M) to shareholders, 80% of which are American.
($17.5M)(.10)(.80) = $1.4M Paid to American shareholders
• GE pays out $28M to American labor
Personal Income = $38.65M - $10.65M + $1.4M = $29.4M = $28M + $1.4M
National
Income
American
Profits
(EBIT)
Income
from
Assets
American
Wages
Dividends
received
3) Consider the following data for expenditures in the US economy.
Category
Consumption
Gross Investment
Government
Net Exports
Exports
Imports
GDP
(Billions of Dollars)
$13,233.2
$3,337.9
$3,360.0
-$571.9
$2,316.3
$2,888.2
$19,359.2
Annualized Growth
2.9%
5.7%
0.0%
--3.6%
2.5%
???
Calculate annualized real growth in Gross Domestic Product
GDP growth is the weighted average of each sector’s growth where the weights are that
sector’s share of GDP.
GDP = Consumption + Gross Investment + Government + Exports - Imports
 13,233.2 
 3,337.9 
 3,360.0 
 2,316.3 
 2,888.2 
Growth = 
 (2.9% ) + 
 (5.7% ) + 
 (0% ) + 
 (3.6% ) − 
 (2.5% ) = 3%
 19,359.2 
 19,359.2 
 19,359.2 
 19,359.2 
 19,359.2 
Don’t forget the minus sign!!!
4) Suppose that we have the following data:
Variable
Retail Sales
GDP
2019Q4
$4,558.5B
$21,729.1B
Suppose that retail sales for the month of January grew at 0.25% (for the month). Assuming
that every other expenditure category grows at the prior quarter’s rate of GDP growth (2%
per year), calculate an estimate for annualized growth in GDP for the first quarter of 2020.
First, calculate retail sales as a percentage of GDP:
 4,558.5 

 = 21%
 21,729.1
Now, calculate annualized retail sales growth:
.
(10025
)12
= 10304
.
→ 3%
Now, calculate growth in GDP as a weighted average of retail sales growth and everything
else
Growth =.21(3)+.79(2) = 2.21%
5) Suppose that you have the following information on an economy:
•
•
•
•
•
•
•
•
Gross Domestic Product: $5,000
Government Consumption: $1,500
Government Investment = $500
Tax Revenues: $500
Net Exports: -$1,000
Net Primary Income: $200
Depreciation: $400
Consumption Expenditures: $3,000
Find (a) Gross National Product (b) National Income, the (c) Current Account, (d)
Personal Savings (Assume that national income and personal income are equal), (e)
Gross Savings, (f) Gross Private Savings, and Gross Public Savings.
First, we can convert GNP = GDP + NPI:
a) GNP = $5,000 + $200 = $5,200
Now, to get National Income, we subtract depreciation
b) National Income = $5,200 - $400 = $4,800
The current account is given by net exports plus net primary income:
c) Current Account = -$1,000 + $200 = -$800.
Gross savings is GNP – Consumption – Government Cons.
d) Gross Savings = $5,200 - $3,000 - $1,500 = $700
Gross Public Savings is taxes minus government consumption
e) Gross Public Savings = $500 - $1,500 = -$1,000
Gross Savings is Gross Private Savings (Personal Savings plus business savings) plus Gross
Public Savings (Taxes minus government consumption), so Gross Private savings is Gross
Savings minus Gross Public Savings
f) Gross Private Savings = $700 – (-$1,000) = $1,700
6) Consider the following numbers for WWII:
Variable
Government Consumption (% of GDP)
Government Investment (% of GDP)
Government Deficit (% of GDP)
Gross Savings (% of GDP)
Gross Private Investment (% of GDP)
1943
30%
18%
29%
23%
5%
Trade in 1943 was balanced (NX = CA =0). Assuming personal income equals GDP, no
undistributed profits, and that there are no transfer payments, calculate the private savings
rate in (GDP – Taxes – Consumption) 1943 (as a % of GDP).
So, we have
Now,
GC
G
G + GI − T
T
= 19%
= 29% , so
= 30% , I = 18% and C
GDP
GDP
GDP
GDP
G
SG
C
C
= 23% = 1 −
− C , so
= 47%
GDP
GDP GDP
GDP
Finally,
PS
T
C
= 1−
−
= 34%
GDP
GDP GDP
Alternately, we could use taxes and government consumption to get government savings
(as a percentage of GDP)
G
T
− C = 19 − 30 = −11%
GDP GDP
PS
SG
GS
=
−
= 23 − ( −11) = 34% (Private savings = gross savings minus
GDP GDP GDP
government savings)
7) Consider the following information from the international transaction accounts (ITA):
Current Account
Exports
Goods
Services
Income Receipts
Imports
Goods
Services
2018
$400,000
$250,000
$30,000
$640,000
$180,000
Income Payments
$10,000
Also, the US acquired $175,000 of foreign assets (Foreign Direct Investment, Portfolio
Assets, deposits, etc.)
a) Calculate the US Trade Deficit (Net Exports)
Net Exports = ($400,000 + $250,000) – ($640,000 + $180,000) = -$170,000
Exports of goods
and services
Imports of goods
and services
b) Calculate the US Current Account
Current Account = -$170,000 + ($30,000 - $10,000) = -$150,000
Net Exports
Net Primary Income
c) Is the US a borrower or lender? Explain.
The US is a net borrower. Start with Output equals expenditures:
GDP = C + I G + G + NX
+ NPI
+ NPI (Add net primary income to both sides)
G
GNP = C + I + G + CA
Solve for the current account:
CA = GNP − (C + I G + G )
Our Income
Our Spending
So, a current account that in negative means we spend more than we earn. To do
this, we must either sell assets or incur liabilities. (In this case, $170,000 worth of lost
assets or increased liabilities)
d) Calculate the increase/decrease in US incurrence of liabilities.
In addition to our current account deficit, we acquired $175,000 in foreign assets, so
our total increase in liabilities is
$150,000 + $175,000 = $325,000
Section #2: Price Indices and Inflation
8) In 1965, the base price for a Chevrolet Corvette was $4,100. Today, the base price of a
Chevrolet Corvette is $55,900. We have the following information for the consumer price
index:
Year
1965
2000
2019
CPI (1983 =
100)
31.5
172.7
255.5
a) Calculate the inflation adjusted price of a 1965 Corvette in year 2019 $s
. 
 2555
P2019 = $4,100
 = $33,255
 315
. 
b) Calculate the inflation adjusted price of both the 2019 and 1965 Corvette in year 2000
$s.
2019 Corvette
 172.7 
P2000 = $55,900
 = $37,784
 2555
. 
1965 Corvette
 172.7 
P2000 = $4,100
 = $22,478
 315
. 
9) Suppose that you are tasked with reporting the price for “rent of primary residence”. In past
years, you have reported the rent of a 1,000 square foot apartment without an attached
garage (the norm for the past several years) at $1,250 per month. Now, you find that the
new norm is a 1,300 square foot apartment with an attached garage. You run the following
regression to gauge the impact of square footage and the garage on price:
ln(rent ) = 6.38+.70( sqft )+.10( garage)
Where RENT is the monthly rent, SQFT is the square footage of the apartment in thousands
and GARAGE is a dummy variable equal to 1 if the apartment has a garage and 0 If it
doesn’t.
You find that the monthly rent for a 1,300 square foot apartment with a garage is $1,600.
a) Calculate the inflation rate for the rent.
So, here we just calculate the percentage change the rental price:
 1,600 − 1,250 
INF = 
 = 28%


1,250
b) Calculate the hedonically adjusted inflation rate for the rent.
To do this, we need to hedonically adjust to correct for the increase in size and the
addition of the garage. We know from the regression that each 1,000 square feet in size
adds 70% to the price and the garage adds another 10%, so:
rent = $1,250(170
. ) (110
. ) = $1,612
.3
Now, the inflation rate is
 1,600 − 1,612 
INF = 
 = −0.74%


1,612
Note: an approximation would be to say that if 1,000 square feet adds 70%, then 300
square feet adds 70%/3.3 = 21%
rent = $1,250(121
. )(110
. ) = $1,663
 1,600 − 1,663
.
INF = 
 = −38%


1,663
Note: You could also just plug in the variables into the regression equation:
ln(rent ) = 6.38+.70(13
. )+.10(1) = 7.39
e 7.39 = $1,619
 1,600 − 1,619 
.
INF = 
 = −12%


1,619
10) Suppose that you have the following price data:
Year
2010
2011
2012
2013
Apples ($/lb.)
$2.00
$2.50
$2.75
$3.10
Oranges ($/lb.)
$3.50
$3.60
$3.90
$4.25
Bananas ($/lb.)
$1.75
$1.95
$2.25
$2.40
a) Using 2011 as your base year, calculate a consumer price index (CPI) assuming that the
average household spent 30% of their income on apples, 50% on oranges, and 20% on
bananas in the base year.
The CPI is a weighted average of each goods relative price (current year price divided by
base year price) where the weights are each good’s expenditure share.
2010
. 
. 
 2.00 
 350
 175
CPI =.30
 +.50
 +.20
 =.91
 2.50 
 3.60 
 195
. 
2011
. 
 2.50 
 3.60 
 195
CPI =.30
.
 +.50
 +.20
 = 100
 2.50 
 3.60 
 195
. 
2012
 2.75
 3.90 
 2.25
CPI =.30
.
 +.50
 +.20
 = 110
 2.50 
 3.60 
 195
. 
2013
. 
 310
 4.25
 2.40 
.
CPI =.30
 +.50
 +.20
 = 121
 2.50 
 3.60 
 195
. 
b) Calculate the annual inflation rate using your constructed CPI.
2010 – 2011
 1−.91
Inflation = 
 = 9.9%
 .91 
2011 – 2012
. − 1
 11
Inflation = 
 = 10%
 1 
2012 – 2013
. − 110
. 
 121
Inflation = 
 = 10%

 110
.
11) Suppose that we have the following information:
Year
GDP
1950
2000
$280.8
$10,248
Real GDP (2012
$s)
$2,185
$12,924
Calculate the average annual inflation rate for the GDP deflator.
The GDP Deflator is defined as the ratio of GDP (current price) and GDP (Base Year Price)
1950
Def 1950 =
2000
Def 2000 =
280.8
=.13
2,185
10,248
=.79
12,924
1


50
.
79


Inflation =   − 1 = 3.6%
 .13 



12) Suppose that we have an economy that produces manufactured goods and services.
Further, assume that the average consumer spends 65% of their income on services and
35% on manufactured goods. We have the following information for production and prices
in this economy.
January 1983
January 2018
January 2019
Manufacturing
Price
Quantity
$55
250
$115
450
$125
495
Price
$25
$30
$38
Services
Quantity
550
800
750
a) Using 1983 as the base year, calculate the inflation rate for the CPI from 2018 to
2019.
2018
 115
 30 
CPI =.35
.
 +.65  = 151
 55 
 25
2019
 38 
 125
.
CPI =.35
 +.65  = 178
 25
 55 
. − 151
. 
 178
Inflation = 
 = 17.9%
 151

.
b) Using 2018 as the base year, calculate the inflation rate for the GDP deflator from
2018 to 2019.
2018
GDP(2018$) = $115(450) + $30(800) = $75,750
GDP( BY$) = $115(450) + $30(800) = $75,750
$75,750
Def 2018 =
=1
$75,750
2019
GDP(2019$) = $125(495) + $38(750) = $90,375
GDP( BY$) = $115(495) + $30(750) = $79,425
$90,375
.
= 114
Def 2018 =
$79,425
. − 1
 114
Inflation = 
 = 14%
 1 