### Question 2

The tables below show the prices and quantities demanded of some commodities.
Use the information to answer the questions that follow.

Table 1.0

 Price of W       \$ Quantity demanded         of X (kg) 20 500 30 300

Table 2.0

 Price of Y        \$ Quantity demanded          Of Z (kg) 30 200 40 300

(a)        Calculate the cross elasticity of demand for commodities:
(i)         W and X;
(ii)        Y and Z.

(b)        What type of demand relationship exists between commodities:
(i)         W and X;
(ii)        Y and Z.

### Observation

This was the alternative data response to question (1) and was largely attempted. The question required candidates to calculate the cross elasticity of demand for two groups of commodities and state the demand relationship that exists in each group with reasons. Most of the candidates could state the formula but had problems in their substitution as most of them ignored the negative sign in (a)(i). Secondly some candidates wrongly stated the degrees of elasticity instead of demand relationships that exists between the commodities in the (b) part of the question. This made them to score below average marks.

The candidates were expected to provide the following answers to obtain maximum marks.

(a)        (i)         CED    =         Percentage change in quantity demanded of X
Percentage change in the price of W

Percentage change in the quantity demanded of X     =       300 – 500100
500           1
OR
=      - 200  x    100                                                                                                                                  500          1

=      - 40 %

Percentage change in the price of W         =         30 – 20   x   100
20            1

OR

=         10 x   100
20        1

=         50 %

CED    = - 40 %
50 %

=   - 0.8

(a)        (ii)        Percentage change in the quantity demanded of   Z
Percentage change in the price of Y

% ∆ Qty of Z         =         300 – 200  x    100
200              1

OR

=         100    x 100
200         1

=         50 %

% ∆ price of Y       =         40 – 30  x   100
30             1

OR
=         10  x   100
30        1

=         33.33 %

CED    =         50 %                                                                                                                            33.33%

=         1.5

Q. 2     NB      Alternative Formula

(a)(i)    % ∆ Qx = 300 – 500        - 200           - 200  x 20  = - 4      or  – 0.8
% ∆ Pw         500          =   500   =       500    10        5
30 – 20              10
20                 20

(a)(ii)     % ∆ Qz = 300 – 200          100            100  x 30      =   3   or  1.5
% ∆ Py         200          =   200   =       200    10           2

40 – 30              10
30                 30

(b) (i)         Complementary demand.
(ii)        Competitive demand.

(c)              Complementary demand in (b) (i) because the coefficient of cross elasticity of demand is negative, i.e. as the price of W increases, the quantity demanded of X decreases.
It is competitive demand in b (ii) because the coefficient of cross elasticity of demand is positive i.e. when the price of Y increases, quantity demanded of Z increases.