Question

Solve the following problems on Price elasticity of demand and classify the nature of

elasticity and good.

1) The demand for a CDs is 1000 units and the price is Rs. 20/- per CD. Later on the price rises

to Rs.22/- per CD as result the demand falls to 870 units.

2) The demand for a commodity is 80 units and the price is Rs. 14 /- per unit. In the next month,

the price falls to Rs.10/- per unit and the demand rises to 88 units.

Answer 1

Solution:

1.). Price elasticity of demand (PED) $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

PED = $=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

Where: Q₁ = 1000                   P₁ = 20

            Q₂ = 870                     P₂ = 22

PED = $\frac{870 -1000}{(870+1000)/2 } \div\frac{22 -20}{(22+20)/2 }$

= $\frac{-130}{935} \div\frac{2}{21} = \frac{-0.139}{0.095} = -1.46$

PED = 1.46

The good is price elastic since PED is greater than 1, indicating high responsiveness of quantity demanded to changes in price. The good is a normal good.

2.). Price elasticity of demand (PED) $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

PED = $=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

Where: Q₁ = 80                   P₁ = 14

             Q₂ = 88                  P₂ = 10

PED = $\frac{88 -80}{(88+80)/2 } \div\frac{10 -14}{(10+14)/2 }$

= $\frac{8}{84} \div\frac{-4}{12} = \frac{0.095}{-0.33} = -0.29$

PED = 0.29

The good is price inelastic since PED is below 1, indicating low responsiveness of quantity demanded to changes in price. The good is a normal good.