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The difference between the
expenditure and income approaches to GDP
Calculating GDP (expenditure approach)
Personal consumption expenditures
Gross private domestic investment
Depreciation
Government expenditure
Net exports
Compensation of employees
Proprietors' income
Net Interest
Rental Income
Corporate profits
Indirect taxes less subsidies
Statistical discperancy
Net Factor Income from Abroad
GDP = C + G + I + (EX - IM)
10.003
In this case:
2.056
C = $10.003
1.778
G = $2.798
2.798
I = $2.056
-706
(EX - IM) = -$706
8.037
1.072
Therefore:
915
39
1.195 GDP = $ 10.003 + $ 2.798 + $
2.056+(-$ 706)
1.071
44
GDP = $14.151
145
Calculating GDP (income approach)
Personal consumption expenditures
Gross private domestic investment
Depreciation
Government expenditure
Net exports
Compensation of employees
Proprietors' income
Net Interest
Rental Income
Corporate profits
Indirect taxes less subsidies
Statistical discperancy
Net Factor Income from Abroad
10.003
2.056
1.778
Compensations of employees +
2.798
Rental income + Interest
-706 income + Profits +Indirect Business
Taxes + Depreciation
8.037
1.072
915
39
1.195
GDP = $14.151
1.071
44
145
Therefore:
GDP = $8.037 + $1.072 + $915 + $39 + $1.195 + $1.071+ $1.778 + $44
Calculating GNP, NDP, NNP and
National Income
Net Domestic Product = GDP – Depreciation
NDP= $ 14.151 - $1.778 = $ 12.373
Personal consumption expenditures
Gross private domestic investment
Depreciation
Government expenditure
Net exports
Compensation of employees
Proprietors' income
Net Interest
Rental Income
Corporate profits
Indirect taxes less subsidies
Statistical discperancy
Net Factor Income from Abroad
10.003 Gross National Product = GDP + NFIA
2.056
Net Factor Income from Abroad =
Receipts of factor income
1.778
from the rest of the World –
2.798
Payments of factor income
-706
to the rest of the World
8.037
1.072 GNP = $ 14.151 + $145 = $ 14.296
915
Net National Product =
39
GNP – Depreciation
1.195
NNP = $ 14.296 – $1.778 = $ 12.518
1.071
National Income =
44
NNP - indirect taxes
145 NI = $ 12.518 - $ 1.071 = $11.447
Measuring Nominal and Real GDP
Calculating Real GDP
 Table (a) shows the quantities
produced and the prices in
2000 (the base year).
 Nominal GDP in 2000 is $100
million.
 Because 2000 is the base year,
real GDP and nominal GDP
both are $100 million.
Measuring Nominal and Real GDP
 Table (b) shows the quantities
produced and the prices in 2009.
 Nominal GDP in 2009 is $300
million.
 Nominal GDP in 2009 is three
times its value in 2000.
Measuring Nominal and Real GDP
 In Table (c), we calculate real
GDP in 2009.
 The quantities are those of 2009,
as in part (b).
 The prices are those in the base
year (2000) as in part (a).
 The sum of these expenditures is
real GDP in 2009, which is $160
GDP Deflator = (Nominal GDP/Real GDP)100
million.
GDP Deflator = ($ 300/ $ 160)100 = %187.5
Calculating the CPI and the Inflation Rate
Measuring Unemployment
The Bureau of Statistics conducts a monthly survey to estimate the unemployment
rate. Respondents’ answers are used to estimate the number of people who are
employed, unemployed, and in the labor force.
a. Calculate the unemployment rate.
b. Calculate the unemployment rate taking into account discouraged workers.
a. Unemployment rate = 12,036 / (99,093 + 12,036) = 10.83%
b. (12,036 + 1,849) / (99,093 + 12,036 + 1,849) = 12.29%
Measuring Unemployment
Use the information in the figure to calculate the unemployment rate and
the labor force participation rate.
Quantity theory of money and Fisher effect
Suppose that the velocity of money V is constant, the money
supply M is growing 5% per year, real GDP Y is growing at 2%
per year, and the real interest rate is r = 4%. Assume that π=πe ,
meaning the ex-post inflation rate is always equal to the expected
inflation rate.
a) Find the value of the nominal interest rate i in this economy;
b) If the central bank increases the money growth rate by 2% per
year, find the change in the nominal interest rate ∆i;
c) Suppose the growth rate of Y falls to 1% per year.
 What will happen to ?
 What must the Central Bank do if it wishes to keep 
constant?
a.
Quantity theory of money and Fisher effect
(solution)
First, find .
 = 5  2 = 3 %.
Then, find i = r +  = 4 + 3 = 7 %.
b.
i = 2, because, according to the quantity theory, changes in the
money growth rate will translate in a one-to-one change in the
inflation rate. Therefore, a change of 2% in the growth rate will
simply change the inflation rate by 2%, leaving the real interest rate
unchanged. Therefore, the change in the nominal interest rate is the
same as the change in inflation, therefore ∆ i = 2%.
c. If the Central Bank does nothing,  = 1.
Because, If the Y falls by 1% (so it grows a -1%) a year, while everything
else is constant, the inflation rate will increase by 1% every year.
To prevent inflation from rising, Central Bank must reduce the money
growth rate by 1 percentage point per year.
Money demand and Fisher effect
Suppose that the money demand in an economy
is given by the following linear function:
a) Suppose that P=100, Y=1000 and i=0.1. Determine the
demand for real balances and the velocity of money in this
economy;
b) Suppose that now P=200 while everything else remains
unchanged. Determine the new demand for real balances
and the new velocity in this economy.
Money demand and Fisher effect
(solution)
a) Given the data in the problem we have:
and total money supply is:
M = 600 x 100 = 60000
The velocity of money according the quantity theory is given by:
b) Now the price doubles. However, we assume that everything else remains
unchanged, meaning that the real Income and the nominal interest rate do
not change. In this case the demand for real balance must be the same since
nothing has changed apart the prices:
In this case the total money supply simply has double as well:
M = 600 x 200 = 120 000, and
Keynesian Cross
Consider the Keynesian cross model and assume that the
consumption function is given by: C = 200 + 0.75 (Y - T)
I=100, G=100; T=100.
1. Graph planned expenditure as a function of income;
2. Find the equilibrium level of income;
3. If government purchases increase to 125, find the new
equilibrium level of income;
4. Calculate multiplier of G.
Keynesian Cross
(solution)
1. The planned expenditure is: E=C+I+G
E = 200 + 0.75Y - 75 +100 +100 = 325 + 0.75Y
Keynesian Cross
(solution)
2.
Y=E
Y=325+0.75 Y
Y=1300
3. Now the planned expenditure is given by: E = 350 + 0.75Y
The new equilibrium level:
Y=350+0.75 Y
Y=1400
4. The multiplier of G is defined as
, where MPC=marginal propensity to consume.
G has increased by 25 and this leads to an increase in Y of 100. This is the
essence of the government expenditure multiplier effect. In particular this
implies that the multiplier of G is equal to 4.
IS-LM and Crowding Out
Consider the following IS-LM model:
C = 100 + 0.5(Y - T) , I = 100 -10r , G = T = 50
M/P=100Y – 50r, where M = 1000 and P = 5;
a) Find the IS curve and the LM curve and solve for the
equilibrium levels of real income and the interest rate;
b) Suppose that government expenditure increases by 50, find
the new equilibrium values for Y and r. Calculate the level of
Crowding Out.
IS-LM and Crowding Out
(solution)
a)
The IS curve:
Y=C+I+G
Y=100+0,5 (Y-T)+100-10r+50
Y=100+0,5 Y-(0,5x50)+100-10r+50
Y=100+0,5 Y-25+100-10r+50
10r=225-0,5Y
R=22,5-0,05Y
The LM curve:
M/P=(M/P)d
1000/5=100Y-50r
200-100Y=-50r
50r=100Y-200
r= 100Y/50-200/50
r = 2Y – 4
Equilibrium: 22,5-0,05Y=2Y-4
22,5+4=2Y+0,05Y
26,5=2,05Y
Y=12,9 ; r=2x12,9-4=21,8
IS-LM and Crowding Out
(solution)
b)
G=100
Y=C+I+G
Y=100+0,5 (Y-T)+100-10r+100
10r=275-0,5Y
R=27,5-0,05Y
The LM curve:
M/P=(M/P)d
1000/5=100Y-50r
200-100Y=-50r
50r=100Y-200
r= 100Y/50-200/50
r = 2Y – 4
Equilibrium: 27,5-0,05Y=2Y-4
27,5+4=2Y+0,05Y
31,5=2,05Y
Y=15,4 ; r=2x15,4-4=26,8
IS-LM and Crowding Out
(solution)
The Crowding out is measured as the difference between the level of income
we obtain after the change in G if there was no increase in the interest rate.
In practice is the level of income implied by the government expenditure
multiplier in the Keynesian Cross.
∆Y=(1/1-MPC) ∆G= ∆G/1-MPC
G1=50
G2=100
∆Y=50/1-0,5=100
The initial equilibrium (before the change in G) was Y = 12.9.
After the change in G, if there is not interest rate effect, the new income should
be Y = 12.9 +100 = 112.9
The new equilibrium however, when there is an interest rate effect is Y=15.4.
Meaning that the level of Crowding out is: CO = 112.9 -15.4 = 97.5
This means that given our model specification, most of the change in G will
crowding out private investment through the increase in the real interest rate
and so fiscal policy is not really effective in this case.
Phillips Curve(1)
Suppose that an economy has the Phillips curve
a. What is the natural rate of unemployment?
b. How much cyclical unemployment is necessary to reduce inflation by 5
percentage points?
Phillips Curve(1)
(solution)
To solve for the natural rate of unemployment, we look for the
unemployment rate where inflation remains constant. Thus:
Solve for natural rate of unemployment = 0.06 or 6%.
b. To figure this out, set the change in inflation to 0.05 and solve for
the gap between unemployment and the natural rate:
0.10 = [u – 0.06]
Thus, we need 10 percentage points of cyclical unemployment to
reduce inflation by 5 percentage points.
Phillips Curve(2)
Suppose the Phillips curve is given by
where
1. What is the natural rate of unemployment in this economy?
2. For now assume that θ=0. (What does that mean?) Suppose that the
government decides to lower unemployment to 3% and keep it there forever.
What is the rate of inflation for t=100?
3. Assume that only for the first three periods (t=1, t=2, and t=3) people form
their expectations using θ=0. After the third period, from t=4 on, they start
using θ=1 forever. Also, the government still wants to keep unemployment at
3%. What is the rate of inflation for t = 4, 5, and 6? What is the expected rate
of inflation for t=4, 5, and 6?
Unemployment
The city of Hope has a labor force of 1000. Twenty people lose their jobs
each month and remain unemployed for exactly one month before finding
jobs. On January 1, May 1, and September 1 of each year 50 people lose
their jobs for a period of four months before finding new jobs.
(a) What is the unemployment rate in any given month?
70/1000 = 7%
(b) How many unemployment spells are there in a year?
Short spells: 20 each month × 12 months = 240.
Long spells: 50 each × 3 times a year = 150.
Total spells: 240 + 150 = 390.
(c) What is the average duration of an unemployment spell?
The total duration of all spells is (240 spells ×1 month) + (150 spells × 4
months) = 240 + 600 = 840 months.
Average duration = total duration/total spells = 840/390 = 2.15 months.