KYAMBOGO UNIVERSITY
FACULTY OF SOCIAL SCIENCES
DEPARTMENT OF ECONOMICS
BACHELOR OF ARTS IN ECONOMICS
BACHELOR OF ECONOMICS AND STATISTICS
YEAR III SEMESTER II EXAMINATIONS 2020/2021
AEC 3202 INTERMEDIATE MACROECONOMICS
Time: 9:00 – 12.00noon
Date: Wednesday 30th March, 2022
Instructions:
• Answer any FOUR questions.
• Begin each question on a fresh page.
Question One
(a) An economy is described by the following equations:
Y = AK t L1t−
K = sYt − K t
L = nLt
Production function:
Capital accumulation:
Labor force:
Where Y = output, K = capital, L = labor, A = total factor productivity and α = 1/4.
(i)
Show that this production function exhibits constant returns to scale. (2
marks)
Yt = AK t L1t−
zYt = F ( zK t , zLt ) = A(zK t ) (zLt )

1−
where z  0
= z  +1− AK t L1t−
= zAK t L1t−
…………………….2mks
Since the production function is of degree one, it exhibits constant returns to scale.
1
(ii)
Find expressions for the stable steady state values of the input ratio and
per capita output as functions of the propensity to save, s , and the other
exogenous parameters of the model.
(5 marks)
Yt = AK t L1t−
Yt
AK t L1t−
=
Lt
Lt
Yt
AK 
= t
Lt
Lt
K 
Yt
= A t 
Lt
 Lt 

Let
Yt
and
Lt
Therefore
yt =
kt =
Kt
Lt
y t = Ak t
……………….. 1mk
But k = i − d , where d = k , i = sy , i = sAk 
Therefore; k = sAk  − k
At steady state; k = 0,
sAk  = k
sAk 
k
= 
………………………………. 1mk

k
k
k
sA
=

k

sA
k 1− =

1 / 1−
 sA 
Therefore; k* =  
 
as the steady state per worker (input ratio)
………1mk
From yt = Ak 
y * = A(k *)

……………………………………….. 1mk
2
1


1−
sA


*

y =A  
   



1−
y = A. A
*
1
1−
y* = A
(iii)


 s 1−
 
 

 s 1−
 
   As the steady state per capita output
…………. 1mk
Given that the savings rate in this economy is 25% of GDP, the
depreciation rate of capital is 10% per year and the index of technological
level is 1. Evaluate the per capita steady state of physical capital and final
product. (4 marks)
S=25% = 0.25, A = 1,  = 1/ 4  = 10% = 0.10
➢ Per Capita steady state of physical capital
1 / 1−
 sA 
From k* =  
 
4
3
 0.25 
✓ k* = 
 0.10 
✓ = 3.393
➢ Per Capita steady state final product
1
1−
From y = A
*
……………………… 2mks

 s 1−
 
 
1
1−0.25
*
✓ y =1
0.25
 0.25 1−0.25


 0.10 
4
3
1
 0.25  3
*
✓ y =1 

 0.10 
4
3
1
 0.25  3
*
✓ y =1 

 0.10 
✓ y * = 1.357
✓
3
2mks
(iv) Suppose there are two identical countries except for difference in the savings
rate. The savings rate for country i is 25% while for country j it is 10%.
Predict and comment on their differences in GDP per worker. (4 marks)
si = 25% = 0.25 , s j = 10% = 0.1
1
1−
✓ For country i , yi = A
*
✓ For country j,
yj = A
*

 si 1−
  yi
 
1
1−
 sj



1−



 1
1
−
s
 A1−  i  
 
*

yi
 
=
✓
*

There fore ; y j
 1  s j 1−
 A1−  

 








 si 1−
yi
 
=
*
s 
yj
 j
*
✓
✓
yi
 0.25 
=

*
yj
 0 .1 
✓
yi
 0.25  3
=

*
y j  0 .1 
✓
yi
= 1.356
*
yj
*
*
1mk
0.25
1−0.25
1
*
2mk
➢ Comment; The model predicts that country i’s income per capita will be
1.36…times that of country j’s.
1mk
4
(b) Using the Solow Growth Model, graphically illustrate and explain the effect of an
increase in the savings rate on the economic growth of a country.
(7 marks)
➢ An increase in the saving rate implies that the amount of investment for
any given capital stock is higher. It therefore, shifts the saving function
upward.
S2f(k)
Investment
Depreciation
S1f(k)
s
1
f (k )
……02mks
s s
1
2
K1*
k2*
capital per worker
Explanation 2mks
➢ At the steady state K1*, investment now exceeds depreciation. The
capital stock rises until the economy reaches a new steady state k2* with
more capital and output. Thus, if the saving rate is high, the economy
will have a large capital stock and a higher level of output. According to
the Solow model, higher saving leads to faster growth.
(c) Suggest any three ways through which the savings rate can be raised in an economy
like Uganda.
(3 marks)
✓ Reducing the government budget deficit
✓ Increasing incentives for private saving, e.g reducing capital gain tax, corporate
income tax , estate tax
✓ Expanding tax incentives for IRAs (Individual Retirement Accounts) and other
retirement savings accounts. Any 3points*2mks = 6mks
5
Question Two
After graduating with an economics degree, you have been appointed as an Economist
in the Ministry of Finance of a small open economy with a floating exchange rate. The
President of this country asks for “An evaluation of the impact of a reduction in import
tariffs on the economy”.
(a) With an aid of a graphical illustration, explain the impact of this policy change
on the economy with reference to aggregate income, the exchange rate, and
the trade balance.
(9 marks)
(b) Now suppose this economy was operating a fixed exchange rate regime, how
would such a policy change affect the economy’s aggregate income, the
exchange rate, and the trade balance?
(8 marks)
(c) Explain how the following policies affect a country’s trade balance:
(i) Currency devaluation
(4 marks)
(ii) Currency revaluation
(4marks)
ANSWER:
(a) When a tariff is reduced on imports it shifts the net exports schedule in wards. For any
given exchange rate, net exports fall. This is because it now becomes possible for
Uganda to get more imports. 1mk
Exchange rate
1mk
e
Nx1 (e)
Nx2 (e)
NX2
NX1 Net export
➢ The inward shift in the next exports schedule causes the IS* schedule to
shift in ward as well.
6
e
Exchange rate
LM*
e1
e2
4mks
IS1*
IS2*
Y
income, output
➢ From the diagram above exchange rate falls, income and trade balance
remain unchanged since NX (e) = Y-C(Y-T) -I(r) –G. Reducing the tariff
has no effect on Y, C, I and G. Therefore, it has also no effect on the trade
balance.
3mks
(b) If it is a fixed exchange rate. Then the shift in IS* curve puts down pressure on the
exchange rate. In order to keep the exchange rate fixed, the central bank is forced to
buy dollars and sell foreign exchange. This shifts the LM* curve to the left as shown
below.
2mk
LM2*
LM1*
Exchange rate
5mks
e
B
A
IS1*
Y1
IS2*
Y2
Y1
Income, output
➢ From the graph above, at equilibrium income is lower and exchange rate is
unchanged. The trade balance fall because net exports are lower at any level of
the exchange rate. 3mks
(c)
(i) Currency devaluation is the deliberate downward adjustment of the value of a
country’s currency relative to another currency. Countries that have a fixed
7
exchange rate or semi-fixed exchange rate use this monetary policy tool to
stabilize the economy 3mks
(ii) Currency revaluation is the upward adjustment to a country’s official
exchange rate relative to a chosen baseline. The baseline can be anything
from wage rates to the price of gold to a foreign currency. In a fixed exchange
rate regime, only a decision by a country’s government such as its central
bank can alter the official value of the currency. 3mks
Question Three
(a) Explain the term “balanced budget”.
(2 marks)
(b) What happens to the domestic interest rate, income, consumption, and investment if
government increases expenditure and taxes by equal amounts? Be sure to use an
appropriate graph and calculus to illustrate your answer.
(13 marks)
(c) An economy is described by the following equations: Y = C + I + G , C = C (Y − T ) ,
M
I = I ,T = T ,
= L( r , Y ) , and P = P . Examine the effect of a decrease in the
P
money supply on domestic income and interest rate in this economy, clearly
explaining the monetary transmission mechanism.
(10 marks)
ANSWER:
(a)Government increases expenditure and taxes by equal amount
(b) Y = C(Y-T) +I+G
dy/dT = C’dy/dt –C’
dy/dt - C’dy/dt = –C’
:. dY/dt = –C’/1–C’
Bt C’= mpc
dY/dT= -MPC/1-MPC
∆Y = ∆T *-MPC/1-MPC …………………….
01MK
Government purchases multiplier
Y = C(Y-T) +I+G
dy/dG = C’dy/dt +1
dy/dG- C’dy/dt = 1
:. dY/dG = 1/1–C’
Bt C’= mpc
From Y / T =1/ 1− MPC
Y =G /1−MPC
…………………………………….01MK
8
Tax multipliers =ΔY/ΔT = - MPC/1-MPC
ΔY = ΔT * -MPC/1-MPC
ΔY = (ΔG/1-MPC) – (ΔT*MPC/1-MPC)
But ΔG =ΔT
ΔY = (ΔG/1-MPC) – (ΔG*MPC/1-MPC)……………………01MK
ΔY = ΔG(1-MPC/1-MPC)
ΔY=ΔG…………………………………………………………………………………01MK
This expression tells us how output change holding the interest rate constant. It says that an
equal increase in government expenditure and taxes shifts the IS curve to the right by the
amount that G increases.
01mk
LM
r2
B
r2
Interest rate
A
IS2
r1
2mks
IS1
Y1
Y2
OUTPUT
Output increases, but by less than that of G and T increases. This means that disposable
income Y-T falls. As a result, consumption also falls. The interest rate rises, causing
investment to fall.
1mk
9
(c) Effect of a monetary contraction
LM2
Interest rate
r2
LM1
r1
5 marks
IS
Y2
Y1
Income, Output
Well detailed Explanation 5mks
When the central bank reduces money supply people have less money than they want to hold.
As a result, they start borrowing extra money from banks. The interest rate then rises.
The higher interest rate discourages investment, which reduces planned expenditure,
production and income.
Question Four
Consider the Solow growth model with no technological progress. The production
function in intensive form is given by y = f (k ) = k  and the capital stock motion
equation is k = sy − (n +  )k , where s is the saving rate, n is the population growth
rate,  is the depreciation rate, and   1 .
(a) Derive expressions for the steady state values of per capita capital stock and
production.
(10 marks)
(b) Given that the saving rate in this economy is 20% of GDP each year. It is also
known that the population growth rate and the depreciation rate of capital are
2% and 4% per year, respectively. Assume α = 0.6 and β = 0.4. Compute the per
capita steady state of physical capital and final product.
(6 marks)
(c) Political leaders in Uganda have argued before that high population growth
accelerates the economic growth and development of the country. As an
10
economist/statistician in the Ministry of Finance, Planning and Economic
Development, you have been invited to present a paper on “The effect of an
increase in population growth rate on economic growth of Uganda” at a political
leaders meeting at Kyankwanzi. Using the Solow Growth Model, prepare a
paper that you would present to the meeting.
(9 marks)
ANSWER:
(a)
Derive expressions for the steady state values of per capita capital stock and
production.
(10 marks)
(a)
y = f (k ) = k 
Using k = sy − (n +  )k = 0, where sy = (n +  )k
But y = k 
sk  = (n +  )k
Divide both sides by k 
sk  (n +  )k
=
k 
k 
(n +  )k
s =

k
s
k
= 
(n +  )
k
s
k 1− =
(n +  )
 s 
Therefore; k * = 
 n +  
1/1−
as the steady state value of per capita capital stock.
From yt =  k 
y* =  (k *)

1


1−
s



*

y = 
 
 n +   



y =  .
*
1−
y* = 


 s 1−


 n + 
1
1−

 s 1−


As the steady state value of production
 n + 
11
(b)
Given that the saving rate in this economy is 20% of GDP each year. It is also known
that the population growth rate and the depreciation rate of capital are 2% and 4% per year,
respectively. Assume α = 0.6 and β = 0.4. Compute the per capita steady state of physical
capital and final product.
(6 marks)
 = 4% = 0.04 n=0.02
(b) S=20% = 0.2,  = 0.6 ,  = 0.4
➢ Per Capita steady state of physical capital
 s 
From k * = 
 n +  
✓
1/1−
1mk
 0.2 * 0.4 
k* = 

 0.02 + 0.04 
k* = 1.33
to get the value)
➢ Per Capita steady state final product
✓
➢
1.3
=
y =
*
1
1−
1
0.76
= ?? (use a scientific calculator

 s 1−


 n + 
y * = (0.4)
1
1− ( 0.6*0.4 )
1mk
0.6*0.4
0.2

 1−( 0.6*0.4 )


 0.02 + 0.04 
✓ y * = ?? (use a scientific calculator to get the value)
✓ y* =
2mks
(c)
Political leaders in Uganda have argued before that high population growth
accelerates the economic growth and development of the country. As an economist/
statistician in the Ministry of Finance, Planning and Economic Development, you have been
invited to present a paper on “The effect of an increase in population growth rate on
economic growth of Uganda” at a political leader’s meeting at Kyankwanzi. Using the Solow
Growth Model, prepare a paper that you would present to the meeting.
(9 marks)
12
As shown in the figure below, an increase in the rate of population growth from n1 to n2 shifts
the line representing population growth and depreciation upward reducing the steady state
level of capital per worker from k1* to k2* .
This is because higher population growth rate reduces capital stock per worker by spreading
the capital stock more thinly among a larger population 1mk
(n2+δ)k
(n1+δ)k
Investment
Break even
s
Investment
1
f (k )
……05mks
n n
2
k2*
k1*
1
capital per worker
Since k* is lower, and because y*=f(k*), the level of output per worker y* is also lower.
Thus, the Solow model predicts that countries with higher rates of population growth will
have lower levels of capital per worker and therefore lower levels of GDP per person.
Question Five
(a) Explain the term “crowding out” of investment.
(2 marks)
(b) Consider an increase in government purchases of G . Using the closed economy
model, illustrate graphically and explain the effects of such a policy on domestic
interest rate (r), domestic income (Y), national saving (S), and investment (I), clearly
pointing out the crowding out effect.
(8 marks)
13
(c) Now use the open economy model and illustrate graphically how the model predicts
the exchange rate (e), domestic income (Y), and net export (NX) in response to such
an economic policy:
(i) Under a floating exchange rate regime
(7 marks)
(ii) Under a fixed exchange rate regime
(8 marks)
ANSWER:
(a) A situation when increased interest rates lead to a reduction in private investment
such that it dampens the initial increase of total investment and incomes.
(b) Closed economy
LM
Interest rate
r2
r1
B
4MKS
A
A*
IS2
IS1
YI
Y2
y3
OUTPUT
An increase in government expenditure shifts the IS curve to the right, moving the
equilibrium from point A to point B
Increase in government expenditure stimulates the production of goods and services which
causes total income Y to rise y2
The rise in income increases the quantity of money demanded, causing the interest rate r to
rise. When the interest rate rises, investment (I) falls, and savings (S) fall……….4MKS
14
(c)Small open economy model
(i)Under a floating exchange rate regime
LM*
4MKS
exchange rate e2
e1
IS2*
IS1*
Y
OUTPUT
An increase in government expenditure shifts the IS* curve to the right.
As soon as the interest rate tries to rise above, world interest rate, capital flows in from
abroad. This capital inflow increases the demand for domestic currency, causing currency
appreciation. Currency appreciation makes domestic goods expensive relative to foreign
goods, reduces next exports. The fall in net exports of the effects of the expansionary fiscal
policy leaving income constant ……………………………………………………….. 3MKS
15
(ii)Fixed exchange rate regime
LM1*
LM2*
Exchange rate
4mks
e
IS 2*
IS1*
Y1*
Y2*
Income
A fiscal expansion shifts the IS* curve to right. To maintain the fixed exchange rate, the
central bank must increase money supply thereby shifting the LM* curve to the right. Hence,
under fixed exchange rates, fiscal expansion raises income. ……Detailed explanation
4mks
Question Six
(a) Show that, according to the Phillips curve, inflation results from three sources:
expected inflation ( e ) , cyclical unemployment (u − u n ) , and supply shocks (v )
(8 marks)
(b)Can an economic policymaker achieve low inflation and low unemployment in an
economy at the same time? Use an appropriate illustration to explain your answer.
(8 marks)
(c)The Phillips curve is given by  =  e − 3(u − 0.06) . Given that actual inflation is 8%
and expected inflation is 5%, find the unemployment rate.
(5 marks)
16
(d)Do you think the Phillips curve is a useful tool for analyzing the economy today?
Why or why not?
(4 marks)
ANSWER:
(a) From the short run aggregate supply curve
_
Y
=Y
+  ( P − P e ) …………………………………
1mk
Making P the subject;
P= P + 1/ 
e
_
(Y − Y )
……………………1mk
Add to the right-hand side of the equation as shock
V to represent exogenous
events.
P= P + 1/ 
e
_
(Y − Y ) + V
To go from the price level to inflation rates, last year’s price level
p
−1
both sides of equation.
−
(P − P −1 ) = ( P − P−1 ) + 1 /  + (Y −Y )
e
…………………………1mk
But
p- p
−1
= π, which is inflation
_
 =  + 1 /  (Y − Y ) + V
e
……………………………………………….1mk
To go from output to employment, use Okuns law
1/ 
:.
 =
Where

_
(Y − Y ) =
e

e
−  (u −u n ) …………. 1mk
−  (u −u n ) +V
………………….2mks
= inflation
= expected inflation
…………………….1mk
17
from
(u −u n ) = cyclical unemployment, V = Supply shocks
(b)
Price
AS2
P3
C
AS1
B
P2
A
P1
AD2
04mks
AD1
Y1
Y2
Y
output
When policy makers move the economy up along the short run aggregate
supply curve (using monetary or fiscal policy), they reduce the unemployment
rate and raises inflation rate. ………………………………………… 2mks
Conversely, when they contract aggregate demand and more the economy
down. The short run aggregate supply curve, un employment rises and
inflation falls.
Thus, a policy maker cannot achieve both low inflation and low
unemployment in an economy at the same time. This trade off is called the
Phillips curve……2mks
(c)
Given  =

But π= 0.08,
e
− 3(u − 0.06)

e
= 0.05, find u?

− 3(u − 0.06) ……………………………….1mk
Using  =
0.08=0.05-3(u-0.06)………………………………… 1mk
0.08- 0.05 = -3u +0.18………………………………… 1mk
3u =0.15………………………………………………… 1mk
U = 0.05 or 5% ……………………………………………1mk
e
18
(d) Yes ,
Useful because both inflation and unemployment are key measures of
economic performance…………………………………………. 2mks
Used by monetary policy makers ……………………………….1mk
Used in forecasting ………………………………………………1mk
19