Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
Set of Tasks, Tests and Exam examples Suggested by Participants
GDP and methods of its calculation
Andrey Velichko
1
The steel-producing company has purchased for 2000 raw materials and has sold for
3000 steels to the machines firm, other suppliers have sold to the machines firm the
components on 4000, and then all made machines were sold in 1999 for 10000 to
customers. Compute the contribution of these firms to a GDP of a country in 1999.
How the outcome will change if the machines were sold completely only in 2000?
How the outcome will change if the automobile company has made and sold in 1999
additional products for 500 to customers?
2
What is the largest category of different types of consumption in GDP?
(Consumer consumption)
2a
What is the largest category of income in GDP?
(Salaries)
3
What are the components of consumer spending in GDP?
3a
What are the components of investments in GDP?
4
What is the difference in reflection in the national accounts between granting of
"charge-free" dinners by special state organisations and making payments to those
who need "charge-free" dinners?
4a
If the state pays a fare for the citizens on public transport, not making transfer
payments to these customers, will consumption of the state be taken into account in its
GDP?
5
Are the spending on the import equipment by companies included in a GDP of the
country which imports it?
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
5a
Are the spending of the consumer goods exported by Russia to customers in other
countries included in the GDP of Russia?
6
If GNP of a country is less than its GDP, what does it mean? How is it connected to
the "earnings " in the country A of the person being the citizen of the country B(with
other things being equal)?
7
We shall assume the construction company has constructed the house by the cost
300,000 in 1999 but has not sold it. In what sub-account of a GDP this construction
for 1999 will be taken into account? If the construction company has sold the house
for 250,000 in 2000, how this bargain will be reflected in the national account?
8
The investments do not necessarily include:
a) Purchasing new plants by the companies
b) Purchasing new houses by house-owners
c) Purchasing the shares on exchange
d) Increase of the inventories by companies
9
One American newspaper has devoted a lot of the articles to the problem that the
additional charges of electric power industry made to prevent the pollution of
environment, should not be included in GDP. If we consider GDP as a measure of
national welfare, whether you agree that this consumption is necessary is to be
eliminated from a GDP?
10
The people who seek to attract attention to the jumbo sizes of corporations, often
compare their gross income with GNP of small countries. So, for example,
corporation "Exxon" in a definite sense is more than Sweden since its gross income
exceeds Sweden GNP. Is such a comparison correct?
11
The deflator of a GDP is calculated as:
a) Nominal GDP / Real GDP
b) Nominal GDP * Real GDP
c) Nominal GDP - Real GDP
d) Nominal GDP + Real GDP
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
12
In the beginning of the nineties the inflation in Russia was very high (about 1000 %
annually). How do you think, did the real GDP increase faster than nominal? More
slowly? With the same rate?
13
What is the distinction (difference) between a consumer price index and GDP
deflator?
14
Fill in the table:
Nominal GDP
Real GDP
3960
GDP deflator
3600
3800
4800
115
120
15
The GDP is a
a) Market value of production for final use
b) Sum of consumer spending, investment consumption, state expenditure and
net export
c) Sum of the value added of all firms
d) Sum of all income received by the macroeconomic agents as a result of
economic activity
e) All set above
(One right answer)
16
The value added is a sales minus
a) Costs
b) Cost of raw materials and transactions
c) Profit
d) Cost of raw and intermediate products
e) All set above
17
The calculus of the value added is made in order to
a) Avoid the double counting
b) Adjust GDP for inflation
c) Adjust GDP for the changes in goods and services quality
d) Adjust GDP for the distribution of income
e) All set above
3
Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
18
What categories below is eliminated from a GDP?
a) Non market goods
b) Goods made illegally
c) Services
d) a) and b)
e) All set above
19
The cost of the value added of all goods and services produced in 1999 expressed in
the 1982 prices has compounded to 11758.
Number 11758 is
a) Nominal GDP
b) GDP in current prices
c) Real GDP
d) Nominal national income
GDP and other basic macroeconomic indicators
Almagul Zhumabekova
1
Last year the country had the following parameters (in USD):
GNP-500; net investments of private sector - 75; state spending - 80; consumption of
households - 250; direct taxes to the state budget - 30; indirect taxes - 20; subventions
to enterprises - 25; exports - 150; imports - 110.
To define:
а) disposable income of households;
b) depreciation fund;
c) whether the state budget is in deficit.
2
GNP – 480 USD, total investments – 80 USD, net investments – 30 USD,
consumption – 300 USD, government charges – 96 USD, surplus of state budget – 3
USD.
To define:
1) NNP,
2) net export,
3) disposable income of households,
4) their savings.
3
National Income-500 USD, disposable income - 410 USD; excess of indirect taxes
over subventions to enterprises - 20 USD; consumption of households - 380 USD;
deficit of trade balance (excess of imports over exports) – 10 USD.
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
To define:
а) savings and net investments;
b) state charges;
c) sum of direct taxes, if the deficit of state budget equals 10 USD.
4
The rate of consumption in GDP of the state "А" is 20 %. GDP is equal to 300 USD.
The consumption function is defined as:
С = 40 + 0,6 (У-Т), where Т is taxes
The investments equal to 50 USD. What are the equilibrium state taxes?
5
What should be the volume of production equal to if independent consumption equals
30 USD, the propensity to consume of households is 0.4, the demand for investments
in 80 USD and for government spending in 40 USD was satisfied?
6
In the country “Оmegia” the base size of consumption is 120 USD. Annual rate of a
gain consumption is equal 4 %. The size of state charges is fixed and is equal to 38
USD. Investment function is defined in the following way: I = 15 + 100/r (r is
measured in percents).
What is the size of current annual GNP, if r = 20 %?
7
GNP= 10.000, consumption С=2000 +0,5 (У-Т), investment I=1800 - 60 r, where r real interest rate, Т=1200, Q = 2100. Find the equilibrium interest rate, individual
savings, state savings and national savings.
Zrinka Kvesic
1
Determine the rate of inflation 2000-2001 if GDP deflator in year 2000 was 0,9 and
real and nominal GDP in 2001 was 24 billion MU, respectively 25 billion.
Valery Chernooky
1
Secrets of Belarussian economic "miracle": GDP growth and inventories. The
flow description of GDP presumes that all produced goods are sold. In fact some are
stocked as additions to inventories. Many large Belarussian firms receive from
government production plans and are forced to produce planned volume despite of
impossibility to sell it. How do national accounts treat changes in inventories and
which conclusion could be reached about adequacy of using GDP growth as a
measure of economic growth in Belarus?
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
Balance of Payments
Valery Chernooky
1
How would be recorded the following transactions in the balance of payments of
Belarus:
a) a Belarussian resident buys a 10 tons of oil in Russia,
b) a Belarussian concern Beltransgas serves gas transit through pipe line
"Yamal-Europa",
c) a Belarussian worker in Russia sends money to his family in Brest,
d) a Russian mobile operator MTS supplies equipment as share in joint
Belarussian-Russian firm in Minsk,
e) a Russian banker sends money to his bank account in Belarussian
Priorbank,
f) Gazprom remits the debt of Belarussian government.
2
Which important condition is violated in any financial bubble? Give several
examples.
3
Is current account deficit good or not for transition economies? Explain its role in the
process of "catching up".
Budget Deficit
Almagul Zhumabekova
1
Government of the country “A” reduces budget with deficit at the rate of 500 peso per
year. For its financing the government sells to the central bank the exchequer bill. The
exchange rate is fixed at the level of 20 peso for 1 dollar. Let's assume, that the level
of world prices is fixed and the central bank has large volumes of currency reserves:
а) Calculate annual change of volume of currency reserves of the central bank.
Is it possible to expect, that this process will run smoothly? Why?
b) Describe dynamics of a price level, exchange rate and real money balances
before and after an exhaustion of currency reserves of the central bank.
2
Explain, why the government with large budget deficit, can select devaluation of
currency, and how the central bank will exhaust currency reserves.
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
3
The size of budget deficit in country “A” equals 2% of GDP. The real demand for
money also grows at the rate of 2 % per year. Government covers deficit.
а) Describe dynamics of currency reserves of the central bank at fixed
exchange rates;
b) What will be rate of inflation in the country “A” at floating exchange rates?
4
Government of the country “A” has budget deficit, financed totally with the help of
printing money, at a rate of 6 % of GDP. The exchange rate is floating, world rate of
inflation is equal to 3 % per year and the volatility of money is fixed at the level of 4.
а) What should be the rate of inflation to meet this deficit?
b) What is the rate of depreciation of currency?
Investment
Almagul Zhumabekova
1
Investment function is given by the following equation: I =1000 - 30 r, where r is real
interest rate. The nominal interest rate equals 10 %, the rate of inflation is 2 %.
Calculate the volume of investments.
Valery Chernooky
1
Secrets of Belarussian economic "miracle": wear-out of production capital. Very
bad financial condition of the state Belarussian firms is one of the reasons of
significant physical and moral wear-out of their equipment. Which effect does it exert
on their capitalisation?
Money, Exchange Rate and Inflation
Almagul Zhumabekova
1
We assume, that the rate of inflation is higher than the rate of growth of nominal
money balances:
a) What happens to the real money balances?
b) What is greater: inflation tax or seigniorage? Why?
2
Let us assume, that the government needs to receive by means of seigniorage the sum
of 1,5 % of GDP. The demand for money is given by expression 3М=PQ, where Q =
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
12. Calculate the rate of inflation, which is in accordance with such level of
seigniorage.
3
Some economists maintain, that a number of countries should not have national
currency to interfere with inflationary financing of the budget. Instead of that they
should use the currency of a country with long history of stable prices. What are the
reasons for and against this assumption?
Valery Chernooky
1
Secrets of Belarussian economic "miracle": money supply growth and
monetisation. In 1996 National bank of Belarus initiated new "grandiose" idea of
Belarussian "miracle". It has been asserted that monetisation (ratio of money supply
to nominal GDP) of Belarussian economy is very low and it should be improved by
increasing money supply. Money aggregate M2 rose 100 times in 1996-2001, but
monetisation didn't change and in 1999 even decreased. Comment.
2
What is the effect on the real exchange rate of:
g) growth of housing prices,
h) nominal exchange rate devaluation,
i) terms of trade improvement,
j) capital account liberalisation.
3
Secrets of Belarussian economic "miracle": real exchange rate misalignment and
industry growth. After sharp nominal depreciation of Belarussian ruble in August
1998 Belarussian firms accelerated their growth. Why? What can you say about
quality of this growth and its effect on households welfare?
4
What are the costs of inflation in Belarus? Are there any advantages of inflation?
IS-LM
Almagul Zhumabekova and Maria Dubovskaya
1
Consider the economy described by the following equations:
С=170+0.6(Y-T)
(M/P)d=0.75Y-6r
T=200
(M/P)s=735
I=400-4r
P=1
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
G=350
a) Write down the equations for the IS and LM curves and calculate their
slopes;
b) Determine the equilibrium level of real income, interest rate, planned
investment and consumption;
c) Calculate budget surplus at the equilibrium level of real income;
d) Government spending increase to 386. Define new IS and LM curves.
Calculate new equilibrium level of real income, interest rate, planned
investment and consumption;
e) Central bank decided to increase real output to the value you defined in
part d). Determine necessary increase in money supply. Calculate new
equilibrium level of real income, interest rate, planned investment and
consumption;
f) Compare equilibrium levels of main macroeconomic variables in parts d)
and e). Using these data explain why some economists prefer the fiscal
policy while the others prefer monetary one.
Maria Dubovskaya
1
Countries A and B differ by the level of marginal propensity to consume so that
MPCA is greater than MPCB. Draw the IS and LM curves for each country. Compare
the shape of the curves if money demand and money supply are the same in both
countries. In which country monetary policy will be more effective?
2
Suppose that planned investments increase with the increase of output. It can happen
if planned investments depend on the expected profit or expected sales, which change
in the same direction with the output. Draw the graph of planned investments in the
case of linear model. Define the changes in
a) slope of the planned expenditure line;
b) government spending multiplier;
c) slopes of the IS and LM curves.
3
Analyse the following modifications of the linear IS-LM model:
a) Consider the economy with the money demand determined as in the quantity
theory of money. Draw the LM curve. Calculate government spending
multiplier for this case. How the changes in government spending will
influence on the aggregate demand?
b) Suppose that investment expenditures don’t depend on interest rate. Draw
the IS curve. Calculate the money multiplier. Can changes in money supply
shift the aggregate demand curve?
c) Consider the case, when the money demand is infinitely large at a certain
interest rate below r* and it is equal to zero for r<r*. Draw the LM curve on
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
the graph. Calculate the money multiplier. Draw the aggregate demand
curve. Can changes in money supply shift the aggregate demand curve?
d) Suppose that investment demand is infinite at a certain interest rate below
r** and it is equal to zero for r<r**. Draw the IS curve for this case.
Calculate the government spending multiplier. Can changes in government
spending shift the aggregate demand curve?
Zrinka Kvesic
1
The following macroeconomic model is given:
C= 1.600+0,6(Y-T)
I= 40+0,2Y-r
T=G=1.000
M=20.000
L=0,2Y-129r
If assumed price level P=20
a) Explain this national economy, by using IS-LM model
b) At which point is there an equilibrium at both goods and money markets?
c) If the natural level of output is 10.500 MU, is there GDP gap? If yes, what
change in fiscal policy could be made to maintain the equilibrium at the
natural level of output on goods and money markets?
2
Use the IS-LM model to explain briefly:
a) the effects of increase of government spending (G). What effects it will have
on the IS curve and LM curve?
b) What effects will this increase have on i and Y?
c) What effect will this increase in G have on consumption and savings?
d) What will be the effect on investment?
Valery Chernooky
1
Illustrate by means of IS-LM-BP model short-run effect of direct financing of
government program of house-building by National bank of Belarus.
Test on IS-LM – Maria Dubovskaya
1
If investment, taxes, and government spending are held constant, the planned
expenditure curve:
a. slopes upward and its slope is equal to the MPC;
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
b. slopes downward and its slope is equal to the MPC.;
c. is a 45-degree line;
d. is a vertical line.
2
In the Keynesian cross model, the 45-degree line indicates that:
a. GNP rises whenever consumption rises;
b. actual expenditures always equal to income;
c. the equilibrium level of income increases whenever actual income
increases;
d. all of the above.
3
At the equilibrium level of income:
a. unintended inventory accumulation is equal to zero;
b. planned expenditures equal to actual expenditures;
c. there is no tendency for GNP to change;
d. all of the above.
4
If income exceeds planned expenditures, firms will cut back production because
unplanned inventory accumulation will be:
a. positive;
b. negative;
c. zero;
d. indeterminate.
5
If the consumption function is C = 100 + 0.8(Y - T) and taxes decrease by $1,
equilibrium level of income will:
a. decrease by $5;
b. decrease by $4;
c. increase by $5;
d. increase by $4.
6
Which of the following statements is FALSE?
a. A decrease in the interest rate increases planned investment;
b. A decrease in the interest rate shifts the planned expenditures curve
upward;
c. A decrease in the interest rate shifts the IS curve to the right;
d. As the interest rate falls, planned expenditures equal to actual expenditures
at a higher level of income.
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
7
If the consumption function is C = 100 + 0.8(Y - T) and both taxes and government
spending increase by $1, the equilibrium level of income will:
a. remain constant;
b. increase by $3;
c. increase by $1;
d. decrease by $4.
8
If the consumption function is C= 100 + 0.8 (Y - T), the government spending
multiplier is
a. 0.8;
b. 1.25;
c. 4;
d. 5.
9
An increase of $1 in government spending will:
a. shift the planned expenditures curve upward by $1;
b. shift the IS curve to the right by $l/(1 - MPC);
c. not shift the LM curve;
d. all of the above.
10
According to the loanable funds interpretation of the IS curve:
a. firms want to invest more as their income rises;
b. banks want to lend more as the interest rate rises;
c. an increase in income raises savings and lowers the interest rate that
equilibrates the supply of and demand for loanable funds;
d. all of the above.
11
A decrease in taxes will:
a. shift the planned expenditures curve upward and the IS curve to the left;
b. shift the planned expenditures curve upward and the IS curve to the right;
c. shift the planned expenditures curve downward and the IS curve to the
left;
d. shift the planned expenditures curve downward and the IS curve to the
right.
12
A smaller marginal propensity to consume leads to:
a. a steeper planned expenditures curve;
b. a smaller government spending multiplier;
12
Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
c.
d.
a flatter IS curve;
all of the above
14
As we move along a stationary aggregate demand curve, one factor that is held
constant is:
a. real income;
b. the aggregate price level;
c. the (nominal) money supply;
d. real money balances.
15
All of the following will shift the aggregate demand curve to the right EXCEPT:
a. an increase in government spending;
b. a reduction in transfer payments;
c. an increase in the (nominal) money supply;
d. a reduction in taxes.
16
The Pigou-effect stipulates:
a. falling prices expand income;
b. falling prices depress income;
c. expanding income leads to a higher price level;
d. falling income leads to a lower price level.
17
Which of the following statements is FALSE?
a. The classical assumption that output reaches its natural rate is best used to
describe the long run;
b. In the short run, output may deviate from its natural rate;
c. In the IS-LM model, the price level is assumed to be sticky in the short
run;
d. In the IS-LM model, aggregate demand never equals the natural level of
output even in the long run.
18
If income is initially less than the natural rate of output:
a. the price level will gradually fall, shifting the LM curve downward (to the
right);
b. the price level will gradually rise, shifting the LM curve upward (to the
left);
c. the price level will fall, shifting the IS curve to the right;
d. the price level is stuck at this level even in the long run.
13
Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
19
According to adherents of the money hypothesis, the Great depression was caused by:
a. a sharp decline in money supply;
b. a decline in business confidence;
c. a decline in consumer confidence.;
d. a sharp decline in real money balances.
20
According to the debt-deflation theory, unexpected deflation hurts debtors and
benefits creditors. Consequently, national income will fall if:
a. both groups have the same spending propensities;
b. debtors have a higher propensity to spend than creditors;
c. creditors have a higher propensity to spend than debtors;
d. the MPC for both groups is less than 1.
21
The aggregate demand curve will be relatively flat if:
a. the MPC is large;
b. the multiplier is small;
c. investment is not very sensitive to changes in the interest rate;
d. all of the above.
22
If real income rose and the interest rate fell following an increase in government
spending:
a. the IS curve must be vertical;
b. the LM curve must be vertical;
c. the Fed must have increased the money supply at the same time;
d. the Fed must have decreased the money supply at the same time.
23
If the Fed decreases the money supply at the same time as taxes increase:
a. the interest rate will definitely rise;
b. the interest rate will definitely fall;
c. the equilibrium level of income will definitely rise;
d. the equilibrium level of income will definitely fall.
24
If people suddenly wish to hold more money at each interest rate:
a. the money demand curve will shift to the right;
b. the LM curve will shift upward (to the left);
c. real income will fall;
d. all of the above.
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
AD-AS
Zrinka Kvesic
1
If AD equilibrium is set at AD=Y= 1.000+ 20P and AS equilibrium is set as AS=Y=
520 – 40P, determine the point of macroeconomic equilibrium!
2
Explain the increase of the oil price in the terms of:
a. IS-LM model
b. AD-AS model, if we assume that the initial equilibrium was set at the
natural (long term) rate of output.
International Economics
Svetlana Golovina
1
Why in the Mundell-Fleming model is the LM* curve a vertical line?
2
Suppose that, in the Mundell-Fleming model, the equilibrium exchange rate is above
the level e' at which the central bank wishes to keep the currency. Suppose that the
central bank takes steps to peg the exchange rate to e'. Which curves shift: the IS*, the
LM*, or both, and why?
3
What must be true about elasticity of demand for imports and exports, if net exports
are to be a decreasing function of the real exchange rate?
4
Suppose exchange rates are fixed: is the imposition of a tariff expansionary or
contractionary? Suppose exchange rates are flexible. Is the answer the same? Why?
5
In the Mundell-Fleming model under flexible exchange rates what happens to
production, exchange rate, and trade balance if the world interest rate r* suddenly
rises?
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
6
In the Mundell-Fleming model under fixed exchange rates what happens to
production, exchange rate, and trade balance if the world interest rate r* suddenly
falls?
Final exam
Part I. Multiple Choice (15 minutes; 30% of exam)
1
The broadest measure of the economy's price level, the GDP deflator, is calculated by:
a) Dividing nominal GDP by real GDP;
b) Multiplying nominal GDP by real GDP;
c) Subtracting real GDP from nominal GDP;
d) Adding real GDP to nominal GDP.
2
In the national income accounting investment does NOT necessarily include:
a) The purchase of new plants and machinery by businesses;
b) The purchase of new houses by families and by landlords;
c) The purchase of stocks on the New York Stock Exchange;
d) Increases in businesses' inventories of goods.
3
All of the following statements about national savings are true EXCEPT:
a) National saving is the sum of private and public savings;
b) National saving equals private saving minus the government deficit;
c) National saving is the total amount of savings deposits in banks;
d) National saving equals investment at the equilibrium interest rate.
4
When economists say "money", they mean:
a) The stock of assets that can be used to pay for purchasing of goods and
services;
b) The number of dollars in the hands of the public;
c) A store of value, a unit of account, and a medium of exchange;
d) All of the above.
5
The money supply necessarily increases when:
a) There is an increase in government spending;
b) The Federal Reserve buys Treasury bonds from the public;
c) A private citizen buys a bond issued by General Motors;
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
d) Silicon Graphics sells stock to the public, and uses the proceeds to buy
a new factory.
6
During periods of unexpected inflation, lenders are hurt while borrowers gain
because:
a) The ex-post real interest rate is higher than the ex-ante real interest
rate;
b) The ex-post real interest rate is lower than the ex-ante real interest rate;
c) The real interest rate falls;
d) The nominal interest rate falls.
7
At the intersection of the IS and LM curves:
a) Actual expenditures equal planned expenditures;
b) The real money supply equals real money demand;
c) The levels of Y and r satisfy goods-market and money-market
equilibrium conditions;
d) All of the above.
8
If people suddenly wish to hold more money at any given interest rate:
a) The money demand curve will shift out and to the right;
b) The LM curve will shift upward and to the left;
c) Unless countervailing steps are taken, real incomes will fall;
d) All of the above.
9
If investment is very sensitively dependent on the interest rate:
a) The IS curve is steep;
b) The IS curve is flat;
c) The LM curve is steep;
d) The LM curve is flat.
10
According to the Phillips curve, the inflation rate depends on:
a) Expected inflation and the level of aggregate demand relative to
potential output;
b) The money supply and the real interest rate;
c) The stocks of labour and capital ready for use in production;
d) Menu costs and staggered wage and price setting.
Part II. Short answers (15 minutes; 30% of exam; about 3 sentences on each)
Identify and briefly discuss each of the following concepts:
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
1
"Inside lags" and "outside lags" in conducting macroeconomic policy.
2
Automatic stabilisers and the sensitivity of GDP to shocks in spending.
3
The policy rule that the Federal Reserve should try to keep the rate of growth of the
moneys supply very stable.
4
Based on the discussion in the textbook and during classes, do you think the Great
Depression was caused primarily by a monetary shock on the LM curve or a spending
shock on the IS curve? Why?
Part III: Debt-Deflation and the Great Depression (20 minutes; 40% of exam)
a. Suppose the economy has the following determinants of aggregate demand (with
all numbers in billions):
 Y = C + I + G (national income identity)
 G = $20 is constant (determinants of government spending)
 T = $20 is constant (determinants of taxes)
 C = $50 + 0.5(Y - T) (consumption function)
 I = $90 - 10r (investment; where an interest rate of 5% means r=5)
Derive this economy's IS curve, that is, solve for Y as a function of r given the values
of the other parameters and variables.
b. Suppose r=5; what is the value of Y? What is the value of Y if r = 10? What is the
value of Y if r = 0?
c. Suppose that the Phillips curve in the economy is such that:
 the inflation rate p = 0.1(Y-$200), so that (for example) a real GDP
level Y = $190 is associated with an inflation rate p = -1 percent per
year.
At what value should the Federal Reserve set the real interest rate r so as to maintain a
stable price level, i.e. to set the inflation rate p = 0?
d. Suppose that everyone in the economy expects inflation to be -10%, that is,
everyone expects prices to fall, expects deflation. And suppose the Federal Reserve
does everything it can to stimulate the economy and expand the money supply, and
pushes the nominal interest rate i down to zero. Recalling that
r = i - E(p)
the real interest rate [r] equals the nominal interest rate [i] minus expectations of
inflation [E(p)]:
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg


What is the equilibrium level of GDP (of Y)?
What is the corresponding level of inflation? Are the expectations of
inflation held by decision makers in the economy in fact accurate?
Discuss, very briefly, what your results suggest on the ability of
monetary policy to stop deep depressions associated with deflation all
by itself.

Theory of Economic Growth and Business Cycles
Oleg Mariev
Class Work
1
Suppose a one-member family will live T years. Time is continuous. It begins and
ends with zero assets, can borrow and lend freely at constant interest rate r. It
consumes one good, and receives a wage of w per hour worked, and the price of the
good is always 1. The family inelastically supplies ls units of labour at age s. Its flow
u ( s )  e   s  ln( c s ),
of utility for age s is:
where  is its subjective discount rate.
a) Write down the family’s dynamic optimisation problem, including its budget
constraint.
b) Convert the family’s problem into the classical calculus of variations form.
c) Write down the first-order conditions for the family’s optimisation problem.
What does the time path of the family’s lifetime consumption look like?
d) Solve the calculus of variations problem algebraically and graphically.
2
(Version of problem #1 from HW#2, Ramsey model). Add labour-augmenting
technical progress at rate g. Use the notation EtLt*eg*t and ctCt/Et and ktKt/Et,
where С is aggregate consumption. Then the utility flow in the criterion should
depend on Ct/Lt=ct*eg*t:

max  e   t  u (ct  e g t )dt ,
ct
0
The problem will no longer be tractable unless we require homothetic preferences (as
well as additivity). That implies:
c
u(c) 
,   1.

Making this specification, derive the first-order conditions.
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
Exam
1
Consider a Solow growth model in continuous time. Physical capital depreciates at a
rate δ(0,1). The average propensity to save (ie, gross saving as a fraction of gross
output) is s(0,1). The aggregate production function is:
Qt=[Kt] α  [Lt] 1-α,
α(0,1)
There is no population growth or technological progress, and the labour supply
is always 1.
(a) Receive the equation of changes in stock of physical capital Kt, show the
steps.
(b) Derive the steady-state value of K.
(c) What does it mean for the economy to reach a “golden rule” steady state?
(d) Show that if the economy here reaches a golden rule steady state growth
path, then on that path the gross-of-depreciation factor payments to capital
just equal gross investment spending in the economy.
2
Suppose GDP is homogeneously divisible into private investment, private
consumption, and government consumption. Government consumption per worker is
gt. It enters private utility functions in an additive and separable way. We have an
optimal growth model:

max  e   t   u (ct )  v( g t ) dt ,
ct , g t
0
s.t. kt  f (kt )  ct  g t  n  kt ,
k0=given, (implicitly): kt≥0 all t≥0
Assume there is no physical depreciation of capital.
(a) Write down the first-order conditions for the optimal growth model.
(b) Can you interpret the Euler equation for gt?
3
Consider an optimal growth model with «А-К» technology:
T
max  e   t  u (Ct )dt ,
Ct
s.t.
0
K t  A  K t  C t    K t ,
K 0 , _ K T _ are _ given
Output here is Qt=A*Kt. There is no exogenous technological change, and the
population is always 1.
(a) Derive the Euler equation applicable to this problem.
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
(b) Draw the relevant phase diagram for this problem putting К on the
horizontal axis and С on the vertical axis.
Home Work №1
1
Consider Solow growth model. Omit technological progress for simplicity. Let the
production function be a Cobb-Douglas one (1): F ( K , L)  A  K   L1
a) Let kt=Kt/Lt , and solve algebraically for an expression for the stationary state
k*0.
b) Solve algebraically for an expression for the stationary state capital-to-output
ratio.
c) Suppose we can permanently raise the efficiency of the economy, say, by
reducing government regulation or eliminating monopolies, and that this raises
А. Find the comparative static multiplier  ln( k * ) /  ln( A).
d) Let the per capita income be qt=F(Kt,Lt)/Lt. Find the comparative static
multiplier  ln( q* ) /  ln( A). Explain why it comes out bigger than 1.
2
Rewrite Solow growth model in discrete time. Let Lt=L0*(1+n)t , and Et=Lt*(1+g)t .
Derive an equation describing the dynamics of kt. What can you say about the
existence of a stationary solution?
3
Assume a continuous-time Solow growth model with no technological progress. The
labour supply and population are both given by Lt=en*t. The physical capital stock is
Kt. It has depreciation rate δ(0,1). The average propensity to save out of after-tax
gross income is s(0,1). GDP is given by Cobb-Douglas aggregate production
function:
Qt=A*[Kt] α  [Lt] 1-α, α(0,1)
where А is a constant. Government spending on goods and services is Gt=G0*Lt,
where G0 is a positive constant. There is no government debt or money at any time.
Taxes are lump-sum, with total tax collection Tt at time t. There are no government
transfer payments. The economy is closed.
a) The endogenous variables are Qt, Lt, Kt, It, St, Gt and Tt , where I is gross
investment and S is gross private saving. Write down seven equations for this
seven variables.
b) Let kt=Kt/Lt. Show each step leading to the equation describing the dynamics
of kt
kt  s  A  [kt ]  s  G0  (n   )  kt
c) Using diagrams, find all of the stationary values of k. If G0 is very large, how
many stationary equilibria are there? What can you say about the local
stability of each of the stationary equilibria that you found?
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
d) If k*>0 is a stationary equilibrium, what can you say about the sign of the
comparative static multiplier k * / G0 ? Show your steps.
e) What does it mean for kGR to be the “golden rule” value of k? Derive the
interest rate for this model when the economy has settled to its golden rule k,
show your steps.
Home Work №2
1
Consider central planner’s model with infinite time horizon:

max  e   t  u (ct )dt ,
ct
0
s.t. kt  f (kt )  ct  (n   )  kt ,
k0=A,
(implicitly): kt≥0 all t≥0
Let (k*,c*) to be the “turnpike” stationary solution. Computing linearisations of the
model’s equations of motion at (k*,c*), can you show that eigen values lead to saddle
point?
2
A central planner might care about more than per capita consumption, possibly about
the number of people enjoying a given level of consumption. Thus, we might want to
restate the above problem as:

max  e   t  e nt  u (ct )dt ,
ct
0
s.t. kt  f (kt )  ct  (n   )  kt ,
k0=A,
(implicitly): kt≥0 all t≥0
Let (k*,c*) be the “turnpike”.
a) How do you think the new k* will change in comparison to the one from
problem 1? Explain briefly.
b) Work out the conditions for the new k*.
c) Is k*GR≥k* here if ρ>0?
3
Suppose government spending enhances production but does not directly raise
consumer utility. Suppose the aggregate production function is:
Qt=F(Kt,Gt,Lt),
where Gt is government spending. Suppose F(.) has constant returns to scale. Dividing
through by Lt, Qt/Lt=F(Kt,Gt,Lt)/Lt=F(Kt/Lt,Gt/Lt,1)=F(kt,gt,1)=f(kt,gt).
We have an optimal growth model

max  e  t  u (ct )dt ,
ct , g t
0
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
s.t. kt  f (kt , gt )  ct  gt  n  kt ,
k0 given, and kt≥0 all t≥0 implicit.
a) Write down the first-order equations for an optimal solution.
b) Provide an interpretation of the Euler equation for gt.
Home Work №3
1
Consider two different growth models, each assuming a closed economy with no
population change. The first is the Solow model. Use it with an aggregate production
function:
Qt=A*[Kt] α  [Et] 1-α, α(0,1)
where Q is GDP, Е is effective labour (ie, natural labour augmented by technical
progress), К is physical capital. The rate of labour augmenting technical progress is γ
(Et=E0*eγt); the rate of depreciation for К is δ; and the average propensity to save is
s(0,1).
The second model is the so-called «А-К» model. It has aggregate production function:
Qt=A*Kt.
There is no technological progress. Depreciation and savings are as in the Solow
model.
a) Write down the equilibrium conditions for the Solow model. Analyse for this
model the growth in per capita GDP over time.
b) Repeat step а for the «А-К» model.
c) Early empirical evidence for a handful of European countries showed: (i) all
had lower output per capita levels immediately after World War II than the US
but (ii) virtually all exhibited faster growth rates of per capita output in the
ensuing decades than the US. It was easy to project that all would converge to
the same per capita output level as the US over time.
Explain whether this is consistent with the Solow model. What is implied
about parameter combinations (γ, s, A) across countries? Explain whether the
same evidence is consistent with the «А-К» model.
d) Subsequent empirical evidence on larger sample of countries seemed to show
differences in growth rates of per capita output for different countries which
(i) were independent of initial output levels and (ii) were persistent for a very
long time.
Explain whether this is consistent with the «А-К» model. What is implied
about parameter combinations (s, A) across the countries? Explain whether the
same evidence is consistent with the implications of the Solow model?
e) A recent empirical paper argues that while per capita GDP varies enormously
across countries, the ratio of per capita GDP for rich countries to the same for
poor countries does not seem to change much over time.
Is this consistent with either of the models? And in case of affirmative answer,
under what assumptions about parameter combinations across countries?
2
23
Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
The following model is a paraphrase of Kenneth Arrow’s famous paper on learning
by doing. The labour force, Lt, grows exponentially at a positive percentage rate n:
Lt=en*t, n>0.
(1)
The average propensity to save out of GNP, Qt , is s(0,1). Physical capital, Kt, does
not depreciate; and there is no government or foreign sector:
K  s  Qt , s(0,1)
(2)
The “effective” labour supply is Et, and the aggregate production function is CobbDouglas:
Qt=A*[Kt] α  [Et] 1-α, α(0,1) (3)
Over time the economy’s knowledge base expands. Knowledge accumulates from
experience as physical capital is built. In fact, the effective labour supply is Lt times a
function of the total amount of capital ever built (ie, a function of Kt):
Et=[Kt]  Lt, (0,1) (4)
We then have four equations for the four endogenous variables: L, K, Q и E.
a) In general, in the Arrow model will the economy’s equilibrium growth path be
Pareto efficient? Explain briefly.
b) Define a new variable kt=Kt/Et. Using the equations above, derive an dynamic
equation of changes in kt over time. Show all your steps. (Hint: note that
E t / Et  ( Lt / Lt )    ( K t / K t ) from (4) and k t  K t / K t  K t / Et )
c) Using algebra or graphic analysis, show that kt has one or more stationary
solutions. What can you say about the determinacy and stability of each of
your stationary solutions? Explain briefly.
d) If the model follows a stationary solution k*>0, what happens over time to
consumption per worker (ie, Ct/Lt)? Show your work.
e) How does your answer to part d) depend on n? Show your steps and explain
the intuition of your answer briefly.
Home Work №4
1
(35%) Consider a modified Solow growth model. The aggregate production function,
that is, GNP, is
F(K,L)=A*[K] α  [L] 1-α,
α(0,1)
i.e. constant-returns-to-scale Cobb-Douglas function. There is no government or
foreign sector. Private gross savings is a constant, s, times GNP. Capital, К,
depreciates at rate δ(0,1). Hence,
K t    K t  s  F ( K t , Lt ).
There is no technological progress. The price of output is 1 at every date. Use the
notation k=K/L and f(k)=F(k,1). The labour force at time 0 is L0=1. The percentage
growth rate of labour, L t / Lt , depends on the wage:
L / L    w  w ,
t
t
t
where  and w are positive constants, and wt is the current wage rate. (this is a simple
“Malthusian model”).
a) We have f(k)=kα here. Show that f’(kt) equals the gross (of depreciation)
interest rate. Given that, show that with competitive factor pricing wt will
equal (1-α)*(kt)α.
b) Differentiating kt with respect to time,
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Workshop “Teaching Modern Theoretical and Applied Macroeconomics”
European University at St. Petersburg
K
L
kt  t  t  k t .
Lt Lt
Using the elements of the model, derive an dynamic equation showing changes
in kt over time in the model. Show your steps.
c) What does it mean for a model to have a “stationary solution” in kt?
d) Can you prove that the model has a stationary solution k*>0? Show your
steps.
e) Suppose the model has a positive stationary solution k*. Let the corresponding
stationary percentage rate of population growth be n*. What can you say about
the sign of comparative static multiplier n * / s ? Show your steps.
Home Work №5
1
(40%) Discuss the following pseudo-quotation in an analytical essay:
«Small costs of changing nominal prices (menu costs) can explain only small output
fluctuations in response to changes in the money supply. In order to explain large
output changes, one needs to add a variety of “real rigidities” to these models. But
then it is these real features of the model, not menu costs, that are the key to
explaining large fluctuations in output over the business cycle”.
Make sure your essay includes (but do not limit it to) a discussion of the evidence for
monetary non-neutrality, an analysis of menu cost models with and without real
rigidities, and the evidence for or against specific real rigidities you consider
important.
25