School of Management Sciences
Department of economics
BASIC MACROECONOMICS .
ECO 1641.
Memo Mathematical note. 2019
1. Calculate the equilibrium level of income if C = R100 million + 0,8Y and Ī = R125 million.
Y = A = C + I = 100m + 0,8Y + 125m
Y
 Y–0,8Y
 0,2Y
Y
= 225m + 0,8Y
= 225m
= 225m
= 225m/0,2 = 225m x 5 = 1 125m
2. Consider the following numerical example of the simple Keynesian model with no government
spending, taxes or a foreign sector (all figures in R millions):
C = 100 + 0,9Y
I = 50
Answer the following questions.
(a)
(b)
(c)
(d)
What is the value of the marginal propensity to consume (MPC) in this model?
Use a graph to illustrate the equilibrium level of output.
Calculate the equilibrium level of output.
In equilibrium, what is the value of consumption spending? Use this number to verify that the
sum of C and I in equilibrium equals the value for equilibrium output you obtained above.
(e) What is the value of the multiplier in this economy?
(f) Suppose the level of output that creates full employment in the economy is 1 800. Using the
multiplier, determine the level of investment spending that would create full employment in
this economy.
(a) The MPC or c = 0,9
(b)
Y = A = C + I = 100 + 0,9Y + 50 = 150 + 0,9Y
First method: you can start by
the multiplier

0,1Y
=150
= 1500
Y
(d) C = 100 + 0,9Y = 100 + 0,9 (1500) = 100 + 1350 = 1450
C + I = 1450 + 50 = 1500
(e) α =1/(1–c) = 1/(1–0,9) = 1/0,1 = 10
(f) Y0 = 1500, Yf = 1800; gap thus 300
Multiplier = 10; thus additional I required = 300/10 = 30
Investment should thus increase from 50 to 80
3. Explain how the inflation rate, that is usually reported every month in the media, is obtained.
It is obtained by comparing the value of the consumer price index (CPI) for the latest month with
the value of the CPI for the same month of the previous year. For example, if the CPI for March
2013 is 126 and the CPI for March 2012 was 120, then the inflation rate is reported as (126/1201) x 100 = 5%.
4. a. Unemployment rate
Unemployment= Number of unemployed x100
Labour force
=452 6000/17 948 000 x100
= 25,2 %
b. The absorption rate= Number of people/ working age population x 100
=13 422 000/ 32 786 000 x 100
=40,9%
c. LPFR= Labour force/ working age population x 100
=179 498 000/327 860 00x100
=54,7%
5. CPI pre basket
2009
2010
juice
60x2=120
juice
60x4=240
cloth
30x5=150
cloth
30x6=180
Total
$270
$480
a. CPI= Cost of CPI per basket at current price $270.
CPI= Cost of CPI per basket at constant price $480
b. Inflation rate
CPI this year- CPI last year/CPI last year X100
480-270/270x 100
= 77,7%
6.a. Economic growth= GDPc- GDPb/GDPb
=
£1 434 – 1 360/1 360 X 100
=0,054 X 100
= 5,4%
c. Growth rate of real GDP per person
2009
1 360/191.5= 7,10
2010
1 434/193.3= 7,42
Real GDP per person= 7.42 -7,10 / 7,10 X 100
= 4,5.
d. The answer to this question is found in Parkin: page 500, an example only.
Rule of 70 applies. This rule applies to any variable, so it applies to real GDP per person.
Answer will be 70/ 4, 5 = 15.5. This is how economists predict the future economic
growth rate give the current growth rate.