Test exercise 1b
1 If the following system of equations
has infinitely many solutions, find the value
of the constant, k.
2 5 1
2 3 4
4 3 7
x y z
x y z
x y z k
[8]
What can you say about the nature of
the solution for other values of k? [2]
2 Consider the national income model:
50
24
20
d
d
Y C I
C aY
I
Y Y T
T
Show that the equilibrium level of
national income is given by
74 20
1
Y a
a
[5]
Transpose this equation to express a
in terms of Y.[5]
Hence, or otherwise, find the value of
afor which Y =155 and find the value of C.[2]
3 (a) Simplify
31 8 14
(2 1)( 2) 2
x
x x x
[7]
(b) Solve the equation
1 3 1
8 4 2
x x
[3]
(c) Simplify the inequality
(2×1)(x5) 2(x2)(x
4)[4]
4 The demand and supply functions of a
good are given by
3 60
2 40
D
S
P Q
P Q
respectively. If the government
decides to impose a tax of $tper good, show that
the equilibrium quantity is given by
Jacques: Mathematics for Business
and Economics, 5th edition, Instructors
Manual
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© Pearson Education Limited 2006
4 1
5
Q t
and write down a similar expression
for the equilibrium price. [6]
(a) If it is known that the
equilibrium quantity is 3, work out the value of t.[2]
How much of this tax is paid by the
firm? [4]
(b) If, instead of imposing a tax, the
government provides a subsidy of $5 per
good, find the new equilibrium price
and quantity. [2]
Jacques: Mathematics for Business
and Economics, 5th edition, Instructors
Manual
13
