(a) What is income elasticity of demand? The table below shows the various incomes and demand for different commodities.
| Income (N) | Quantity Demanded (kg) |
| A 20,000 | 120 |
| B 36,000 | 96 |
| C 40,000 | 160 |
| D 44,000 | 200 |
| E 45,000 | 240 |
| F 47,000 | 252 |
(b) Calculate the income elasticity between
(i) A and B
(ii) C and D
(iii) E and F
(c) What kind of good is between
(i) A and B?
(ii) C and D?
Explanation
(a) Income elasticity of demand is the degree of responsive-ness of the quantity demanded of a commodity to a little change in income. Income elasticity of demand can be expressed as: % change in quantity dd
% change in income
(b)(i) Income elasticity between A and B
= Change in quantity dd 96 - 120 = -24
%Change in quantity dd = \(\frac{-24}{120} \times \frac{100}{1}\) = - 20%
Change in income = N36,000 - N20,000 = N16,000
% change in income = \(\frac{16000}{20000} \times \frac{100}{1}\) = 80%
Income elasticity of dd = \(\frac{20}{80}\) = 0.25
(ii) Calculation of Income Elasticity between C and D
Change in quantity = 200 - 160 = 40 %
% change in quantity = \(\frac{40}{160} \times \frac{100}{1}\) = 25%
Change in income = 44000 - 40,000 = 4,000
% Change in income = \(\frac{4000}{40000} \times \frac{100}{1}\) = 10%
Income elasticity of dd = \(\frac{25}{10}\) = 2.5
(iii) Calculation of Income Elasticity between E and F
Change in quantity = 252 - 240 = 12
% Change in quantity = \(\frac{12}{240} \times \frac{100}{1}\)% = 5%
Change in income = 47,000 - 45,000 = 2000
% Change in income = \(\frac{2000}{45000} \times \frac{100}{1} = \frac{40}{9}\) = 4.4%
Income elasticity of dd = \(\frac{5}{4.4}\) = 1.1
Alternative method of solving Question 2(b)
Ey = dd x y
dy q
where dq = change in quantity
dy = change in income
y = old income
q = old quantity
(i) Elasticity between A and B
change in quantity = 96 - 120 = 24
change in quantity = N36,000 - N20,000 = N16,000
old income = 20,000
old quantity = 120
= \(\frac{24}{16000} \times \frac{20,000}{120}\) = 0.25
(ii) Between C and D
dq = 160 - 200 = 40
dy = N40,000 - N44,000 = 4,000
y = 40,000
q = 160
= \(\frac{40}{4000} \times \frac{40,000}{160}\) = 2.5
(iii) Between E and F
2q = 240 - 252 =12
2y = 45,000 - N47,000 = 42,000
y = N45,000, q = 240
= \(\frac{12}{2000} \times \frac{45,000}{240}\) = 1.1
(c)(i) Inferior or giffen good
(ii) Normal good and luxury good