Instructor’s Manual Mathematics for Economics and Business

Test exercise 1a

1 Simplify the following algebraic expressions:

(a)3x4x22 5x8x2[2]

(b)x(3×2) 3x(x5)[2]

(c)2

4 2x

x y y

[2]

2 A consumption function is given byC aY b.

It is known that when Y= 10, the value of Cis 28, and that when Y= 30, the value

of Cis 44.

By solving a pair of simultaneous equations, find the values of aand b, and deduce

that the corresponding savings function is given by

S0.2Y20[6]

Determine the equilibrium level of income when planned investment I= 13. [4]

3 A demand equation of a certain good is given by

20 0.04 4 3rQ P Y T P

where Qand Pdenote the quantity and price of the good, Yis income, Tis taste,

andrPis the price of a related good.

(a) Calculate Qwhen P= 8, Y =1000, T= 15 and30rP. [2]

(b) Is the related good, substitutable or complementary? Give a reason for

your answer. [2]

(c) Find the value of Pwhen Q =235, Y= 8000, T= 30 andrP= 25. [3]

(d) The exogenous variables are now fixed at Y= 2000, T= 10 and5rP. State

the values of the slope and vertical intercept when the demand equation is

sketched with

(i) Pon the horizontal axis and Qon the vertical axis [2]

(ii) Qon the horizontal axis and Pon the vertical axis. [4]

Jacques: Mathematics for Business and Economics, 5th edition, Instructor’s Manual

10

© Pearson Education Limited 2006

4 (a) Solve the equation

6(2 x) 5(1 4x)[3]

(b) Solve the inequality

3×6 5×14[3]

(c) Make xthe subject of the formula

y3 2

x

[3]

5 (a) Copy and complete the following table of values for the supply function

1 20

2

P Q[3]

Q 0 50

P 25

Hence, or otherwise, draw an accurate sketch of this function using axes with

values of Qand Pbetween 0 and 50. [2]

(b) On the same axes draw the graph of the demand function

P50 Q

and hence find the equilibrium quantity and price. [5]

(c) The good under consideration is superior. Describe the effect on the

equilibrium quantity and price when income rises. [2]

Jacques: Mathematics for Business and Economics, 5th edition, Instructor’s Manual

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