question_answer

A consumer buys 20 units of a good at a price of Rs. 5 per unit. He incurs an expenditure of Rs. 20 when he buys 24 units. Calculate price elasticity of demand using the percentage method. Comment upon the likely shape of demand curve based on this information.

Answer:

Price (P)	Quantity (Q)	Total Expenditure (TE)
5	20	100
5	24	120
We know,
Price \[\times \] Quantity = Total Expenditure
or,        Price \[\times \] 24 = 120
or,        Price = 5
Now,     \[{{e}_{d}}=\frac{\text{Percentage}\,\,\text{Change}\,\,\text{in}\,\,\text{quantity}}{\text{Percentage}\,\,\text{Change}\,\,\text{in}\,\,\text{price}}\]
Percentage change in quantity \[=\frac{\Delta Q}{Q}\times 100=\frac{24-20}{20}\times 100=20%\]
Percentage change in price \[=\frac{\Delta P}{P}\times 100=\frac{5-5}{20}\times 100=0\]
Substituting the values in the formula of price elasticity of demand,
\[{{e}_{d}}=\frac{20}{0}=\infty \]
Thus, the demand is perfectly elastic.
As the demand is perfectly elastic, so the demand curve is a horizontal straight line parallel to the quantity-axis.
Hence, the likely shape of demand curve is parallel to the x-axis, i.e., perfectly elastic.