Principles of Macroeconomics - 2e, 2017a
Principles of Macroeconomics - 2e, 2017a
Principles of Macroeconomics - 2e, 2017a
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Budget = P 1 × Q 1 + P 2 × Q 2<br />
<br />
<br />
<br />
Budget = P 1 × Q 1 + P 2 × Q 2<br />
$10 budget = $2 per burger × quantity <strong>of</strong> burgers + $0.50 per bus ticket × quantity <strong>of</strong> bus tickets<br />
$10 = $2 × Q burgers + $0.50 × Q bus tickets<br />
<br />
<br />
y = b + mx<br />
$10 = $2 × Q burgers + $0.50 × Q bus tickets<br />
<br />
<br />
<br />
2 × 10 = 2 × 2 × Q burgers + 2 × 0.5 × Q bus tickets<br />
20 = 4 × Q burgers + 1 × Q bus tickets<br />
20 – Q bus tickets = 4 × Q burgers<br />
5 – 0.25 × Q bus tickets = Q burgers<br />
or<br />
Q burgers = 5 – 0.25 × Q bus tickets
% change in quantity > % change in price % change in quantity<br />
% change in price<br />
% change in quantity = % change in price % change in quantity<br />
% change in price<br />
% change in quantity < % change in price % change in quantity<br />
% change in price<br />
>1<br />
=1<br />
% change in quantity =<br />
3,000 – 2,800<br />
(3,000 + 2,800)/2 × 100<br />
=<br />
2,900 200 = 6.9<br />
% change in price = 60–70<br />
(60 + 70)/2 × 100<br />
= –10<br />
65 × 100<br />
= –15.4<br />
Price Elasticity <strong>of</strong> Demand =<br />
–15.4%<br />
6.9%<br />
= 0.45<br />
<br />
–15.4% 6.9%
Price Elasticity <strong>of</strong> Demand =<br />
<br />
% change in quantity<br />
% change in price<br />
% change in quantity =<br />
% change in price =<br />
Q 2 –Q 1<br />
⎛<br />
⎝Q 2 +Q 1 )/2 × 100<br />
P 2 –P 1<br />
⎛<br />
⎝P 2 +P 1 )/2 × 100<br />
<br />
% change in quantity =<br />
1,600 – 1,800<br />
⎛<br />
⎝1,600 + 1,800)/2 × 100<br />
=<br />
1,700 –200 = –11.76<br />
% change in price = 130 – 120<br />
(130 + 120)/2 × 100<br />
=<br />
125 10 = 8.0<br />
<br />
% change in quantity<br />
Price Elasticity <strong>of</strong> Demand =<br />
% change in price<br />
= –11.76<br />
8<br />
= 1.47
% change in quantity =<br />
13,000 – 10,000<br />
(13,000 + 10,000)/2 × 100<br />
= 3,000<br />
11,500 × 100<br />
= 26.1<br />
% change in price =<br />
$700 – $650<br />
⎛<br />
⎝$700 + $650)/2 × 100<br />
=<br />
675 50 = 7.4<br />
Price Elasticity <strong>of</strong> Supply = 26.1%<br />
7.4%<br />
= 3.53
% change in Qd > % change in P <br />
<br />
% change in Qd = % change in P <br />
<br />
% change in Qd < % change in P
Income elasticity <strong>of</strong> demand =<br />
% change in quantity demanded<br />
% change in income<br />
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Cross-price elasticity <strong>of</strong> demand =<br />
% change in Qd <strong>of</strong> good A<br />
% change in price <strong>of</strong> good B
Elasticity <strong>of</strong> labor supply =<br />
% change in quantity <strong>of</strong> labor supplied<br />
% change in wage<br />
<br />
<br />
<br />
<br />
<br />
<br />
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Elasticity <strong>of</strong> savings =<br />
% change in quantity <strong>of</strong> financial savings<br />
% change in interest rate<br />
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Income elasticity <strong>of</strong> demand =<br />
% change in Qd<br />
% change in income<br />
Cross-price elasticity <strong>of</strong> demand =<br />
% change in Qd <strong>of</strong> good A<br />
% change in price <strong>of</strong> good B
Wage elasticity <strong>of</strong> labor supply =<br />
Wage elasticity <strong>of</strong> labor demand =<br />
Interest rate elasticity <strong>of</strong> savings =<br />
% change in quantity <strong>of</strong> labor supplied<br />
% change in wage<br />
% change in quantity <strong>of</strong> labor demanded<br />
% change in wage<br />
% change in quantity <strong>of</strong> savings<br />
% change in interest rate<br />
Interest rate elasticity <strong>of</strong> borrowing =<br />
% change in quantity <strong>of</strong> borrowing<br />
% change in interest rate<br />
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–600,000/[(24 million + 24.6 million)/2]<br />
=<br />
$6/[($10 + $16)/2]<br />
=<br />
–600,000/24.3 million<br />
$6/$13<br />
= –0.025<br />
0.46<br />
= –0.05
GDP = Consumption + Investment + Government + Trade balance<br />
GDP = C + I + G + (X – M)
GDP = Consumption + Investment + Government spending + (Exports – Imports)<br />
= C + I + G + (X – M)<br />
= $400 + $60 + $120 + ($100 – $120)<br />
= $560 billion<br />
<br />
<br />
Net exports = X – M<br />
= $100 – $120<br />
= –$20 billion<br />
NNP = GDP + Income receipts from the rest <strong>of</strong> the world<br />
– Income payments to the rest <strong>of</strong> the world – Depreciation<br />
= $560 + $10 – $8 – $40<br />
= $522 billion
Value = Price × Quantity<br />
or<br />
Nominal GDP = GDP Deflator × Real GDP<br />
<br />
<br />
Coolshirt's nominal revenue from sales = Price × Quantity<br />
= $9 × 10<br />
= $90<br />
<br />
Coolshirt's real income = Nominal revenue<br />
Price<br />
=<br />
$90<br />
$9<br />
= 10<br />
<br />
<br />
<br />
Real GDP = Nominal GDP<br />
Price Index
Real GDP =<br />
Nominal GDP<br />
Price Index / 100
Real GDP = Nominal GDP<br />
Price Index / 100<br />
=<br />
$543.3 billion<br />
19 / 100<br />
= $2,859.5 billion<br />
<br />
<br />
<br />
Real GDP = Nominal GDP<br />
Price Index / 100<br />
=<br />
$743.7 billion<br />
20.3 / 100<br />
= $3,663.5 billion
GDP deflator = Nominal GDP<br />
Real GDP<br />
<br />
Real GDP = Nominal GDP<br />
Price Index / 100<br />
=<br />
$13,095.4 billion<br />
100 / 100<br />
= $13,095.4 billion<br />
× 100<br />
<br />
<br />
<br />
<br />
Real GDP = Nominal GDP<br />
Price Index / 100<br />
=<br />
$14,958.3 billion<br />
110 / 100<br />
= $13,598.5 billion
2010 real GDP – 1960 real GDP × 100 = % change<br />
1960 real GDP<br />
13,598.5 – 2,859.5<br />
× 100 = 376%<br />
2,859.5<br />
<br />
<br />
<br />
<br />
Nominal = Price × Quantity<br />
% change in Nominal = % change in Price + % change in Quantity<br />
OR<br />
% change in Quantity = % change in Nominal – % change in Price
Brazil's GDP in $ U.S. = Brazil's GDP in reals<br />
Exchange rate (reals/$ U.S.)<br />
= 4.8 trillion reals<br />
2.230 reals per $ U.S.<br />
= $2.2 trillion
GDP per capita = GDP/population
GDP at starting date × (1 + growth rate <strong>of</strong> GDP) years = GDP at end date
Future Value = Present Value × (1 + g) n<br />
<br />
<br />
Future Value = 1.67 × (1+0.028) 5 = $1.92 trillion
Unemployment rate =<br />
Unemployed people<br />
Total labor force<br />
× 100
Percentage in the labor force = 159.716<br />
254.082<br />
= 0.6286<br />
= 62.9%<br />
<br />
<br />
<br />
<br />
Percentage in the labor force =<br />
254.082<br />
94.366<br />
= 0.3714<br />
= 37.1%<br />
<br />
<br />
<br />
Unemployment rate =<br />
159.716<br />
7.635<br />
= 0.0478<br />
= 4.8%
⎛<br />
⎝Level in new year – Level in previous year ⎞ ⎠<br />
Level in previous year<br />
x 100 = Percentage change<br />
<br />
<br />
(106.50 – 100)<br />
100.0<br />
= 0.065 = 6.5%<br />
<br />
<br />
(107 – 106.50)<br />
106.50<br />
= 0.0047 = 0.47%<br />
<br />
(117.50 – 107)<br />
107<br />
= 0.098 = 9.8%
(99.5 – 93.4)<br />
93.4<br />
= 0.065 = 6.5%<br />
<br />
<br />
<br />
100<br />
1.07 = 93.4<br />
106.50<br />
1.07<br />
= 99.5 (99.5 – 93.4)<br />
93.4<br />
= 0.065 = 6.5%<br />
107<br />
1.07 = 100.0 100 – 99.5<br />
99.5<br />
= 0.005 = 0.5%<br />
117.50<br />
1.07<br />
= 109.8 109.8 – 100<br />
100<br />
= 0.098 = 9.8%
Supply <strong>of</strong> financial capital = Demand for financial capital<br />
S + (M – X) = I + (G – T)<br />
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Trade deficit = Domestic investment – Private domestic saving – Government (or public) savings<br />
(M – X) = I – S – (T – G)
Trade surplus = Private domestic saving + Public saving – Domestic investment<br />
(X – M) = S + (T – G) – I<br />
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<br />
<br />
<br />
<br />
Domestic investment – Private domestic savings – Public domestic savings = Trade deficit<br />
I – S – (T – G) = (M – X)
(X – M) = S + (T – G) – I<br />
<br />
<br />
–200 = S + (T – G) – I<br />
<br />
–200 = 500 + (T – G) – I<br />
<br />
–200 = 500+ (T – G) – 500<br />
<br />
<br />
–200 = 500 + (–200) – 500<br />
<br />
(X – M) = S + (T – G) – I<br />
–200 = 500 + (–200) – 500<br />
<br />
<br />
(X – M) = S + (T – G) – I<br />
–100 = S + (–200) – 500<br />
600 = S
Supply <strong>of</strong> financial capital = Demand for financial capital<br />
S + (M – X) = I + (G – T)
ΔY<br />
ΔSpending >1
1<br />
Reserve Requirement
Total Change in the M1 Money Supply = 1 × Excess Requirement<br />
Reserve Requirement<br />
= 1 × $9 million<br />
0.10<br />
= 10 × $9 million<br />
= $90 million
Velocity = nominal GDP<br />
money supply
Money supply × velocity = Nominal GDP<br />
Nominal GDP = Price Level (or GDP Deflator) × Real GDP.<br />
<br />
Money Supply × velocity = Nominal GDP = Price Level × Real GDP.
MV = PQ<br />
4,000 × 3 = 100 × Q<br />
Q = 120<br />
<br />
<br />
MV = PQ<br />
4,800 × 3 = 110 × Q<br />
Q = 130.9
Total savings = Private savings (S) + Public savings (T – G)
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
Private savings + Inflow <strong>of</strong> foreign savings = Private investment + Government budget deficit<br />
S + (M – X) = I + (G –T)<br />
<br />
<br />
<br />
<br />
Private investment = Private savings + Public savings + Trade deficit<br />
I = S + (T – G) + (M – X)<br />
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Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
Private savings + Trade deficit + Government surplus = Private investment<br />
S + (M – X) + (T – G) = I
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
Private savings = Private investment + Outflow <strong>of</strong> foreign savings + Government budget deficit<br />
S = I + (X – M) + (G – T)<br />
<br />
<br />
<br />
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital demand<br />
Private savings = Private investment + Government budget deficit + Trade surplus<br />
S = I + (G – T) + (X – M)
1 2 <br />
4
Qd T = 60 – P<br />
Qs T = –5 + 1 4 P Qd J = 80 – P<br />
<br />
<br />
<br />
<br />
<br />
Qs J<br />
= –10 + 1 2 P
GPA = 0.25 × combined_SAT + 0.25 × class_attendance + 0.50 × hours_spent_studying
y = b + mx<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
y = 9 + 3x
= 0.100 – 0.307<br />
= –0.207<br />
<br />
= 6,000 – 4,000<br />
= 2,000
Qd = 16 – 2P<br />
<br />
<br />
Qs = 2 + 5P<br />
<br />
<br />
Qd = Qs<br />
<br />
<br />
Qd = Qs<br />
16 – 2P = 2 + 5P<br />
<br />
16 – 2P – 2 = 2 + 5P – 2<br />
14 – 2P = 5P<br />
14 – 2P + 2P = 5P + 2P<br />
14 = 7P<br />
14<br />
7<br />
= 7P<br />
7<br />
2 = P<br />
<br />
<br />
Qd = 16 – 2P<br />
= 16 – 2(2)<br />
= 16 – 4<br />
= 12<br />
<br />
<br />
Qs = 2 + 5P<br />
= 2 + 5(2)<br />
= 2 + 10<br />
= 12
Percentage change =<br />
Change in quantity<br />
Quantity<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
=<br />
$1.03 trillion – $1.00 trillion<br />
($1.03 trillion + $1.00 trillion) / 2<br />
= 0.03<br />
1.015<br />
= 0.0296<br />
= 2.96% growth
MPC + MPS = 1
AE = C + I + G + X – M<br />
AE = 140 + 0.9(Y – T) + 400 + 800 + 600 – 0.15Y<br />
<br />
<br />
<br />
<br />
<br />
Y = 140 + 0.9(Y – T) + 400 + 800 + 600 – 0.15Y<br />
<br />
<br />
Y = 140 + 0.9(Y – 0.3Y) + 400 + 800 + 600 – 0.15Y<br />
Y = 140 + 0.9Y – 0.27Y + 1800 – 0.15Y<br />
Y = 1940 + 0.48Y<br />
Y – 0.48Y = 1940<br />
0.52Y = 1940<br />
0.52Y = 1940<br />
0.52 0.52<br />
Y = 3730
Y = 140 + 0.9(Y – 0.3Y) + 400 + 800 + 600 – 0.1Y<br />
Y = 1940 – 0.53Y<br />
0.47Y = 1940<br />
Y = 4127<br />
<br />
<br />
Y = 140 + 0.9(Y – 0.3Y) + 500 + 800 + 600 – 0.15Y<br />
Y = 2040 + 0.48Y<br />
Y – 0.48Y = 2040<br />
0.52Y = 2040<br />
Y = 3923<br />
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<br />
<br />
<br />
Y = 200 + 0.9(Y – 0.3Y) + 600 + 1000 + 600 – 0.1(Y – 0.3Y)<br />
Y – 0.63Y + 0.07Y = 2400<br />
0.44Y = 2400<br />
Y = 5454<br />
<br />
<br />
<br />
6000 = 200 + 0.9(6000 – 0.3(6000)) + 600 + G + 600 – 0.1(6000 – 0.3(6000))<br />
<br />
<br />
<br />
<br />
<br />
<br />
1<br />
1 – 0.56 = 2.27
National Income (Y) $300<br />
Taxes = 0.2 or 20% × 0.2<br />
Tax amount (T) $60<br />
<br />
<br />
National income minus taxes $300<br />
–$60<br />
After-tax income $240<br />
<br />
<br />
<br />
After-tax Income $240<br />
MPC × 0.9<br />
Consumption $216
C = Consumption when national income is zero + MPC (after-tax income)<br />
<br />
C = $20 + 0.9(Y – T)<br />
= $20 + 0.9($300 – $60)<br />
= $236<br />
<br />
<br />
<br />
<br />
<br />
After-tax income $240<br />
Imports <strong>of</strong> 0.2 or 20% <strong>of</strong> Y – T × 0.2<br />
Imports $48<br />
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Y = AE<br />
= C + I + G + X – M<br />
= $20 + 0.9(Y – T) + $70 + $80 + $50 – 0.2(Y – T)<br />
= $220 + 0.9(Y – T) – 0.2(Y – T)<br />
<br />
Y = $220 + 0.9(Y – 0.2Y) – 0.2(Y – 0.2Y)<br />
= $220 + 0.9Y – 0.18Y – 0.2Y + 0.04Y<br />
= $220 + 0.56Y
Y = $220 + 0.56Y<br />
Y – 0.56Y = $220<br />
0.44Y = $220<br />
0.44Y =<br />
$220<br />
0.44 0.44<br />
Y = $500
Spending Multiplier = 1/(1 – MPC * (1 – tax rate) + MPI)
Spending Multiplier = 1<br />
1 – (0.7 – (0.10)(0.7) – 0.10)<br />
= 1<br />
0.47<br />
= 2.13
Multiplier = 1<br />
1 – (MPC × (1 – tax rate) + MPI)
AE = 400 + 0.85(Y – T) + 300 + 200 + 500 – 0.1(Y – T)<br />
AE = Y<br />
<br />
Y = 400 + 0.85(Y – 0.25Y) + 300 + 200 + 500 – 0.1(Y – 0.25Y)<br />
Y = 1400 + 0.6375Y – 0.075Y<br />
0.4375Y = 1400<br />
Y = 3200<br />
<br />
<br />
Y = 400 + 0.85(Y – 0.25Y) + 300 + G + 500 + 0.1(Y – 0.25Y)<br />
3500 = 400 + 0.85(3500 – 0.25(3500)) + 300 + G + 500 – 0.1(3500 – 0.25(3500))<br />
G = 3500 – 400 – 2231.25 – 1300 – 500 + 262.5<br />
G = 331.25<br />
<br />
<br />
<br />
<br />
<br />
1<br />
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<br />
(2600 + 2800) ÷2 × 100<br />
= –200<br />
2700 × 100<br />
= –7.41<br />
% change in price = 80–70<br />
(80 + 70) ÷2 × 100<br />
= 10<br />
75 × 100<br />
= 13.33<br />
Elasticity <strong>of</strong> Demand = –7.41%<br />
13.33%<br />
= 0.56<br />
<br />
<br />
% change in quantity = 2200 – 2400<br />
(2200 + 2400) ÷2 × 100<br />
= –200<br />
2300 × 100<br />
= –8.7<br />
% change in price = 100–90<br />
(100 + 90) ÷2 × 100<br />
= 10<br />
95 × 100<br />
= 10.53<br />
Elasticity <strong>of</strong> Demand =<br />
10.53%<br />
–8.7%<br />
= 0.83<br />
<br />
<br />
% change in quantity = 1600 – 1800× 100<br />
1700<br />
= –200<br />
1700 × 100<br />
= –11.76<br />
% change in price = 130 – 120× 100<br />
125<br />
=<br />
125 10 = 8.00<br />
Elasticity <strong>of</strong> Demand = –11.76%<br />
8.00%<br />
= –1.47
% change in quantity = 70–50<br />
(70 + 50) ÷2 × 100<br />
= 20<br />
60 × 100<br />
= 33.33<br />
% change in price =<br />
$9–$8<br />
($9 + $8) ÷2 × 100<br />
= 1<br />
8.5 × 100<br />
= 11.76<br />
Elasticity <strong>of</strong> Supply = 33.33%<br />
11.76%<br />
= 2.83<br />
<br />
<br />
% change in quantity = 88–80<br />
(88 + 80) ÷2 × 100<br />
=<br />
84 8 × 100<br />
= 9.52<br />
%change in price =<br />
$11 – $10<br />
($11 + $10) ÷2 × 100<br />
= 1<br />
10.5 × 100<br />
= 9.52<br />
Elasticity <strong>of</strong> Demand = 9.52%<br />
9.52%<br />
= 1.0<br />
<br />
<br />
% change in quantity = 100–95<br />
(100 + 95) ÷2 ×100<br />
= 5<br />
97.5 ×100<br />
= 5.13<br />
% change in price =<br />
$13 – $12<br />
($13 + $12) ÷2 × 100<br />
= 1<br />
12.5 × 100<br />
= 8.0<br />
Elasticity <strong>of</strong> Supply = 5.13%<br />
8.0%<br />
= 0.64
Percentage change in quantity demanded = [(change in quantity)/(original quantity)] × 100<br />
= [22 – 30]/[(22 + 30)/2] × 100<br />
= –8/26 × 100<br />
= –30.77<br />
Percentage change in income = [(change in income)/(original income)] × 100<br />
= [38,000 – 25,000]/[(38,000 + 25,000)/2] × 100<br />
= 13/31.5 × 100<br />
= 41.27
Supply <strong>of</strong> capital = Demand for capital<br />
S + (M – X) + (T – G) = I<br />
<br />
Savings + (trade deficit) + (government budget surplus) = Investment
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
S + (T – G) = I + (X – M)<br />
600 + 200 = I + 100<br />
I = 700<br />
<br />
<br />
<br />
<br />
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
S + (T – G) = I + (X – M)
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
S + (M – X) = I + (G – T)<br />
4000 + 2000 = 5000 + 1000<br />
<br />
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
(T – G) + (M – X) + S = I<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
Quantity supplied <strong>of</strong> financial capital = Quantity demanded <strong>of</strong> financial capital<br />
S + (M – X) = I + (G – T)<br />
130 + 20 = 100 + 50