Question

Andrina always spends 30 % of her income on thingamabobs. Assume that her income increases by some percentage while the price of thingamabobs remains constant (and that all thingamabobs cost the same). What is her income elasticity of demand for thingamabobs?

Answer 1

Answer

What is Income Elasticity of Demand?

Income elasticity of demand is the ratio of percentage change in quantity of a product demanded to percentage change in the income level of consumer. It is a measure of responsiveness of quantity demanded to changes in consumers income.

Income elasticity of demand indicates whether a product is a normal good or an inferior good. When the quantity demanded of a product increases with an increase in the level of income and decreases with decrease in level of income, we get a positive value for income elasticity of demand. A positive income elasticity of demand stands for a normal (or superior) good. When the quantity demanded of a product or service decreases in response to an increase and increases in response to decrease in the income level, the income elasticity of demand is negative and the product is an inferior good.

Formula

Income Elasticity of Demand Ei%\ Change in Quantity Demanded%\ Change in Consumers Income

Percentages are calculated using the mid-point formula, i.e. by dividing the change in quantity by average of initial and final quantities, and change in income by the average of initial and final values of income. Therefore:

Income Elasticity of Demand - Ei = Qf - Qi ÷ Qf + Qi ÷ 2  ÷ If - Ii / If + Ii ÷2

Income Elasticity of Demand - Ei = % Change in Quantity Demanded ÷ % change in consumer Income

Where:

Qf - is the final initial quantities demanded of the product,

Qi - is initial quantities demanded of the product,

If -  is the final incomes of consumer

Ii - is the initial incomes of consumer.

∴

Question

What is her income elasticity of demand for thingamabobs?

Solution:

From the Problem, it can be deduced that -

Qf   -  assume it to be 60 since it is not given

Qi  -  assume it to be 50 thingamabobs?

If -  assume it to be 40% since it is not given

Ii -  30%

Assume the % increase in Income to be                  

∴

Ei = 60 -50/ 60 + 50 ÷ 2  ÷  40 - 30 / 40 + 30 ÷ 2    

Ei = 10/110 /2  ÷ 10/70 ÷ 2

Ei = 10/11 X 70/10 ÷ 2

Ei = 10/55 x 14

Ei = 28/11 = 0.73%    

Therefore the Income elasticity of demand for Adrina is 0.73 %