Principles of Macroeconomics - 2e, 2017a

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Budget = P 1 × Q 1 + P 2 × Q 2
Budget = P 1 × Q 1 + P 2 × Q 2
$10 budget = $2 per burger × quantity of burgers + $0.50 per bus ticket × quantity of bus tickets
$10 = $2 × Q burgers + $0.50 × Q bus tickets
y = b + mx
$10 = $2 × Q burgers + $0.50 × Q bus tickets
2 × 10 = 2 × 2 × Q burgers + 2 × 0.5 × Q bus tickets
20 = 4 × Q burgers + 1 × Q bus tickets
20 – Q bus tickets = 4 × Q burgers
5 – 0.25 × Q bus tickets = Q burgers
or
Q burgers = 5 – 0.25 × Q bus tickets

% change in quantity > % change in price % change in quantity
% change in price
% change in quantity = % change in price % change in quantity
% change in price
% change in quantity < % change in price % change in quantity
% change in price
>1
=1

% change in quantity =
3,000 – 2,800
(3,000 + 2,800)/2 × 100
=
2,900 200 = 6.9
% change in price = 60–70
(60 + 70)/2 × 100
= –10
65 × 100
= –15.4
Price Elasticity of Demand =
–15.4%
6.9%
= 0.45
–15.4% 6.9%

Price Elasticity of Demand =
% change in quantity
% change in price
% change in quantity =
% change in price =
Q 2 –Q 1
⎛
⎝Q 2 +Q 1 )/2 × 100
P 2 –P 1
⎛
⎝P 2 +P 1 )/2 × 100
% change in quantity =
1,600 – 1,800
⎛
⎝1,600 + 1,800)/2 × 100
=
1,700 –200 = –11.76
% change in price = 130 – 120
(130 + 120)/2 × 100
=
125 10 = 8.0
% change in quantity
Price Elasticity of Demand =
% change in price
= –11.76
8
= 1.47

% change in quantity =
13,000 – 10,000
(13,000 + 10,000)/2 × 100
= 3,000
11,500 × 100
= 26.1
% change in price =
$700 – $650
⎛
⎝$700 + $650)/2 × 100
=
675 50 = 7.4
Price Elasticity of Supply = 26.1%
7.4%
= 3.53

% change in Qd > % change in P
% change in Qd = % change in P
% change in Qd < % change in P

Income elasticity of demand =
% change in quantity demanded
% change in income
Cross-price elasticity of demand =
% change in Qd of good A
% change in price of good B

Elasticity of labor supply =
% change in quantity of labor supplied
% change in wage
Elasticity of savings =
% change in quantity of financial savings
% change in interest rate
Income elasticity of demand =
% change in Qd
% change in income
Cross-price elasticity of demand =
% change in Qd of good A
% change in price of good B

Wage elasticity of labor supply =
Wage elasticity of labor demand =
Interest rate elasticity of savings =
% change in quantity of labor supplied
% change in wage
% change in quantity of labor demanded
% change in wage
% change in quantity of savings
% change in interest rate
Interest rate elasticity of borrowing =
% change in quantity of borrowing
% change in interest rate
–600,000/[(24 million + 24.6 million)/2]
=
$6/[($10 + $16)/2]
=
–600,000/24.3 million
$6/$13
= –0.025
0.46
= –0.05

GDP = Consumption + Investment + Government + Trade balance
GDP = C + I + G + (X – M)

GDP = Consumption + Investment + Government spending + (Exports – Imports)
= C + I + G + (X – M)
= $400 + $60 + $120 + ($100 – $120)
= $560 billion
Net exports = X – M
= $100 – $120
= –$20 billion
NNP = GDP + Income receipts from the rest of the world
– Income payments to the rest of the world – Depreciation
= $560 + $10 – $8 – $40
= $522 billion

Value = Price × Quantity
or
Nominal GDP = GDP Deflator × Real GDP
Coolshirt's nominal revenue from sales = Price × Quantity
= $9 × 10
= $90
Coolshirt's real income = Nominal revenue
Price
=
$90
$9
= 10
Real GDP = Nominal GDP
Price Index

Real GDP =
Nominal GDP
Price Index / 100

Real GDP = Nominal GDP
Price Index / 100
=
$543.3 billion
19 / 100
= $2,859.5 billion
Real GDP = Nominal GDP
Price Index / 100
=
$743.7 billion
20.3 / 100
= $3,663.5 billion

GDP deflator = Nominal GDP
Real GDP
Real GDP = Nominal GDP
Price Index / 100
=
$13,095.4 billion
100 / 100
= $13,095.4 billion
× 100
Real GDP = Nominal GDP
Price Index / 100
=
$14,958.3 billion
110 / 100
= $13,598.5 billion

2010 real GDP – 1960 real GDP × 100 = % change
1960 real GDP
13,598.5 – 2,859.5
× 100 = 376%
2,859.5
Nominal = Price × Quantity
% change in Nominal = % change in Price + % change in Quantity
OR
% change in Quantity = % change in Nominal – % change in Price

Brazil's GDP in $ U.S. = Brazil's GDP in reals
Exchange rate (reals/$ U.S.)
= 4.8 trillion reals
2.230 reals per $ U.S.
= $2.2 trillion

GDP per capita = GDP/population

GDP at starting date × (1 + growth rate of GDP) years = GDP at end date

Future Value = Present Value × (1 + g) n
Future Value = 1.67 × (1+0.028) 5 = $1.92 trillion

Unemployment rate =
Unemployed people
Total labor force
× 100

Percentage in the labor force = 159.716
254.082
= 0.6286
= 62.9%
Percentage in the labor force =
254.082
94.366
= 0.3714
= 37.1%
Unemployment rate =
159.716
7.635
= 0.0478
= 4.8%

⎛
⎝Level in new year – Level in previous year ⎞ ⎠
Level in previous year
x 100 = Percentage change
(106.50 – 100)
100.0
= 0.065 = 6.5%
(107 – 106.50)
106.50
= 0.0047 = 0.47%
(117.50 – 107)
107
= 0.098 = 9.8%

(99.5 – 93.4)
93.4
= 0.065 = 6.5%
100
1.07 = 93.4
106.50
1.07
= 99.5 (99.5 – 93.4)
93.4
= 0.065 = 6.5%
107
1.07 = 100.0 100 – 99.5
99.5
= 0.005 = 0.5%
117.50
1.07
= 109.8 109.8 – 100
100
= 0.098 = 9.8%

Supply of financial capital = Demand for financial capital
S + (M – X) = I + (G – T)
Trade deficit = Domestic investment – Private domestic saving – Government (or public) savings
(M – X) = I – S – (T – G)

Trade surplus = Private domestic saving + Public saving – Domestic investment
(X – M) = S + (T – G) – I
Domestic investment – Private domestic savings – Public domestic savings = Trade deficit
I – S – (T – G) = (M – X)

(X – M) = S + (T – G) – I
–200 = S + (T – G) – I
–200 = 500 + (T – G) – I
–200 = 500+ (T – G) – 500
–200 = 500 + (–200) – 500
(X – M) = S + (T – G) – I
–200 = 500 + (–200) – 500
(X – M) = S + (T – G) – I
–100 = S + (–200) – 500
600 = S

Supply of financial capital = Demand for financial capital
S + (M – X) = I + (G – T)

ΔY
ΔSpending >1

1
Reserve Requirement

Total Change in the M1 Money Supply = 1 × Excess Requirement
Reserve Requirement
= 1 × $9 million
0.10
= 10 × $9 million
= $90 million

Velocity = nominal GDP
money supply

Money supply × velocity = Nominal GDP
Nominal GDP = Price Level (or GDP Deflator) × Real GDP.
Money Supply × velocity = Nominal GDP = Price Level × Real GDP.

MV = PQ
4,000 × 3 = 100 × Q
Q = 120
MV = PQ
4,800 × 3 = 110 × Q
Q = 130.9

Total savings = Private savings (S) + Public savings (T – G)

Quantity supplied of financial capital = Quantity demanded of financial capital
Private savings + Inflow of foreign savings = Private investment + Government budget deficit
S + (M – X) = I + (G –T)
Private investment = Private savings + Public savings + Trade deficit
I = S + (T – G) + (M – X)
Quantity supplied of financial capital = Quantity demanded of financial capital
Private savings + Trade deficit + Government surplus = Private investment
S + (M – X) + (T – G) = I

Quantity supplied of financial capital = Quantity demanded of financial capital
Private savings = Private investment + Outflow of foreign savings + Government budget deficit
S = I + (X – M) + (G – T)
Quantity supplied of financial capital = Quantity demanded of financial capital demand
Private savings = Private investment + Government budget deficit + Trade surplus
S = I + (G – T) + (X – M)

1 2
4

Qd T = 60 – P
Qs T = –5 + 1 4 P Qd J = 80 – P
Qs J
= –10 + 1 2 P

GPA = 0.25 × combined_SAT + 0.25 × class_attendance + 0.50 × hours_spent_studying

y = b + mx
y = 9 + 3x

= 0.100 – 0.307
= –0.207
= 6,000 – 4,000
= 2,000

Qd = 16 – 2P
Qs = 2 + 5P
Qd = Qs
Qd = Qs
16 – 2P = 2 + 5P
16 – 2P – 2 = 2 + 5P – 2
14 – 2P = 5P
14 – 2P + 2P = 5P + 2P
14 = 7P
14
7
= 7P
7
2 = P
Qd = 16 – 2P
= 16 – 2(2)
= 16 – 4
= 12
Qs = 2 + 5P
= 2 + 5(2)
= 2 + 10
= 12

Percentage change =
Change in quantity
Quantity
=
$1.03 trillion – $1.00 trillion
($1.03 trillion + $1.00 trillion) / 2
= 0.03
1.015
= 0.0296
= 2.96% growth

MPC + MPS = 1

AE = C + I + G + X – M
AE = 140 + 0.9(Y – T) + 400 + 800 + 600 – 0.15Y
Y = 140 + 0.9(Y – T) + 400 + 800 + 600 – 0.15Y
Y = 140 + 0.9(Y – 0.3Y) + 400 + 800 + 600 – 0.15Y
Y = 140 + 0.9Y – 0.27Y + 1800 – 0.15Y
Y = 1940 + 0.48Y
Y – 0.48Y = 1940
0.52Y = 1940
0.52Y = 1940
0.52 0.52
Y = 3730

Y = 140 + 0.9(Y – 0.3Y) + 400 + 800 + 600 – 0.1Y
Y = 1940 – 0.53Y
0.47Y = 1940
Y = 4127
Y = 140 + 0.9(Y – 0.3Y) + 500 + 800 + 600 – 0.15Y
Y = 2040 + 0.48Y
Y – 0.48Y = 2040
0.52Y = 2040
Y = 3923
Y = 200 + 0.9(Y – 0.3Y) + 600 + 1000 + 600 – 0.1(Y – 0.3Y)
Y – 0.63Y + 0.07Y = 2400
0.44Y = 2400
Y = 5454
6000 = 200 + 0.9(6000 – 0.3(6000)) + 600 + G + 600 – 0.1(6000 – 0.3(6000))
1
1 – 0.56 = 2.27

National Income (Y) $300
Taxes = 0.2 or 20% × 0.2
Tax amount (T) $60
National income minus taxes $300
–$60
After-tax income $240
After-tax Income $240
MPC × 0.9
Consumption $216

C = Consumption when national income is zero + MPC (after-tax income)
C = $20 + 0.9(Y – T)
= $20 + 0.9($300 – $60)
= $236
After-tax income $240
Imports of 0.2 or 20% of Y – T × 0.2
Imports $48
Y = AE
= C + I + G + X – M
= $20 + 0.9(Y – T) + $70 + $80 + $50 – 0.2(Y – T)
= $220 + 0.9(Y – T) – 0.2(Y – T)
Y = $220 + 0.9(Y – 0.2Y) – 0.2(Y – 0.2Y)
= $220 + 0.9Y – 0.18Y – 0.2Y + 0.04Y
= $220 + 0.56Y

Y = $220 + 0.56Y
Y – 0.56Y = $220
0.44Y = $220
0.44Y =
$220
0.44 0.44
Y = $500

Spending Multiplier = 1/(1 – MPC * (1 – tax rate) + MPI)

Spending Multiplier = 1
1 – (0.7 – (0.10)(0.7) – 0.10)
= 1
0.47
= 2.13

Multiplier = 1
1 – (MPC × (1 – tax rate) + MPI)

AE = 400 + 0.85(Y – T) + 300 + 200 + 500 – 0.1(Y – T)
AE = Y
Y = 400 + 0.85(Y – 0.25Y) + 300 + 200 + 500 – 0.1(Y – 0.25Y)
Y = 1400 + 0.6375Y – 0.075Y
0.4375Y = 1400
Y = 3200
Y = 400 + 0.85(Y – 0.25Y) + 300 + G + 500 + 0.1(Y – 0.25Y)
3500 = 400 + 0.85(3500 – 0.25(3500)) + 300 + G + 500 – 0.1(3500 – 0.25(3500))
G = 3500 – 400 – 2231.25 – 1300 – 500 + 262.5
G = 331.25
1
1 – 0.5625 = 2.2837

Y = $500 + 0.8(Y – T) + $2,000 + $1,000 + $2,000 – 0.05(Y – T)

% change in quantity = 2600 – 2800
(2600 + 2800) ÷2 × 100
= –200
2700 × 100
= –7.41
% change in price = 80–70
(80 + 70) ÷2 × 100
= 10
75 × 100
= 13.33
Elasticity of Demand = –7.41%
13.33%
= 0.56
% change in quantity = 2200 – 2400
(2200 + 2400) ÷2 × 100
= –200
2300 × 100
= –8.7
% change in price = 100–90
(100 + 90) ÷2 × 100
= 10
95 × 100
= 10.53
Elasticity of Demand =
10.53%
–8.7%
= 0.83
% change in quantity = 1600 – 1800× 100
1700
= –200
1700 × 100
= –11.76
% change in price = 130 – 120× 100
125
=
125 10 = 8.00
Elasticity of Demand = –11.76%
8.00%
= –1.47

% change in quantity = 70–50
(70 + 50) ÷2 × 100
= 20
60 × 100
= 33.33
% change in price =
$9–$8
($9 + $8) ÷2 × 100
= 1
8.5 × 100
= 11.76
Elasticity of Supply = 33.33%
11.76%
= 2.83
% change in quantity = 88–80
(88 + 80) ÷2 × 100
=
84 8 × 100
= 9.52
%change in price =
$11 – $10
($11 + $10) ÷2 × 100
= 1
10.5 × 100
= 9.52
Elasticity of Demand = 9.52%
9.52%
= 1.0
% change in quantity = 100–95
(100 + 95) ÷2 ×100
= 5
97.5 ×100
= 5.13
% change in price =
$13 – $12
($13 + $12) ÷2 × 100
= 1
12.5 × 100
= 8.0
Elasticity of Supply = 5.13%
8.0%
= 0.64

Percentage change in quantity demanded = [(change in quantity)/(original quantity)] × 100
= [22 – 30]/[(22 + 30)/2] × 100
= –8/26 × 100
= –30.77
Percentage change in income = [(change in income)/(original income)] × 100
= [38,000 – 25,000]/[(38,000 + 25,000)/2] × 100
= 13/31.5 × 100
= 41.27

Supply of capital = Demand for capital
S + (M – X) + (T – G) = I
Savings + (trade deficit) + (government budget surplus) = Investment

Quantity supplied of financial capital = Quantity demanded of financial capital
S + (T – G) = I + (X – M)
600 + 200 = I + 100
I = 700
Quantity supplied of financial capital = Quantity demanded of financial capital
S + (T – G) = I + (X – M)

Quantity supplied of financial capital = Quantity demanded of financial capital
S + (M – X) = I + (G – T)
4000 + 2000 = 5000 + 1000
Quantity supplied of financial capital = Quantity demanded of financial capital
(T – G) + (M – X) + S = I
Quantity supplied of financial capital = Quantity demanded of financial capital
S + (M – X) = I + (G – T)
130 + 20 = 100 + 50