(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