examples of problems

The difference between the expenditure and income

approaches to GDP 

Calculating GDP (expenditure approach)

GDP = C + G + I + (EX - IM)

In this case:C = $10.003G = $2.798 I = $2.056

 (EX - IM) = -$706

Therefore:

GDP = $ 10.003 + $ 2.798 + $ 2.056+(-$ 706)

GDP = $14.151 

Personal consumption expenditures 10.003Gross private domestic investment 2.056Depreciation 1.778Government expenditure 2.798Net exports -706Compensation of employees 8.037Proprietors' income 1.072Net Interest 915Rental Income 39Corporate profits 1.195Indirect taxes less subsidies 1.071Statistical discperancy 44Net Factor Income from Abroad 145

Calculating GDP (income approach)

Compensations of employees + 

Rental income + Interest income + Profits +Indirect

Business Taxes + Depreciation

GDP = $14.151

Therefore:GDP = $8.037 + $1.072 + $915 + $39 + $1.195 + $1.071+

$1.778 + $44

Personal consumption expenditures 10.003Gross private domestic investment 2.056Depreciation 1.778Government expenditure 2.798Net exports -706Compensation of employees 8.037Proprietors' income 1.072Net Interest 915Rental Income 39Corporate profits 1.195Indirect taxes less subsidies 1.071Statistical discperancy 44Net Factor Income from Abroad 145

Net Domestic Product = GDP – Depreciation

NDP= $ 14.151 - $1.778 = $ 12.373

Gross National Product = GDP + NFIANet Factor Income from Abroad =

Receipts of factor income from the rest of the World – Payments of factor income

to the rest of the World

GNP = $ 14.151 + $145 = $ 14.296

Net National Product = GNP – Depreciation

NNP = $ 14.296 – $1.778 = $ 12.518

National Income = NNP - indirect taxes

NI = $ 12.518 - $ 1.071 = $11.447

Calculating GNP, NDP, NNP and National Income

Personal consumption expenditures

10.003

Gross private domestic investment 2.056

Depreciation 1.778Government expenditure 2.798Net exports -706Compensation of employees 8.037Proprietors' income 1.072Net Interest 915Rental Income 39Corporate profits 1.195Indirect taxes less subsidies 1.071Statistical discperancy 44Net Factor Income from Abroad 145

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 million.

Measuring Nominal and Real GDP

GDP Deflator = (Nominal GDP/Real GDP)100

GDP Deflator = ($ 300/ $ 160)100 = %187.5

Calculating the CPI and the Inflation Rate

Measuring UnemploymentThe 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 UnemploymentUse 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?

Quantity theory of money and Fisher effect(solution)

a. 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 effectSuppose 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 = 60000The 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+GE = 200 + 0.75Y - 75 +100 +100 = 325 + 0.75Y

Keynesian Cross(solution)

2. Y=E

Y=325+0.75 YY=1300

3. Now the planned expenditure is given by: E = 350 + 0.75YThe new equilibrium level:

Y=350+0.75 YY=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 theessence of the government expenditure multiplier effect. In particular this implies that the multiplier of G is equal to 4.

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

IS-LM and Crowding Out(solution)a)

The IS curve:Y=C+I+GY=100+0,5 (Y-T)+100-10r+50Y=100+0,5 Y-(0,5x50)+100-10r+50Y=100+0,5 Y-25+100-10r+5010r=225-0,5YR=22,5-0,05YThe LM curve:M/P=(M/P)d

1000/5=100Y-50r200-100Y=-50r50r=100Y-200r= 100Y/50-200/50r = 2Y – 4Equilibrium: 22,5-0,05Y=2Y-422,5+4=2Y+0,05Y26,5=2,05Y Y=12,9 ; r=2x12,9-4=21,8

IS-LM and Crowding Out(solution)

b)G=100Y=C+I+GY=100+0,5 (Y-T)+100-10r+10010r=275-0,5YR=27,5-0,05YThe LM curve:M/P=(M/P)d

1000/5=100Y-50r200-100Y=-50r50r=100Y-200r= 100Y/50-200/50r = 2Y – 4Equilibrium: 27,5-0,05Y=2Y-427,5+4=2Y+0,05Y31,5=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-MPCG1=50G2=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 = 112.9The 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.

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)

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?

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.

Unemployment