Question

Using arc method calculate the elasticity of demand for oranges when the price rises from $2 to $3 Price per orange, its demand reduces from 80 thousands oranges to 70 thousands oranges. Interpret your answer in term of the farmer’s revenue

Answer 1

Solution:

The arc elasticity of demand formula = $\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

The arc elasticity measures elasticity at the midpoint between two selected points on the demand curve by using a midpoint between the two points. The arc elasticity of demand can be calculated as follows:

Arc E_d = $= \frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 } \times 100$

% change in quantity demanded =$=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \times 100 = \frac{70,000 -80,000}{(70,000+80,000)/2 } \times 100$

$=\frac{-10,000}{75,000} \times 100 = -13.33\%$

 

% change in price = $\frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 } \times 100 = \frac{3 -2}{(3+2)/2 } \times 100 = \frac{1}{2.5} \times 100 =40\%$

 

Arc E_d = $\frac{-13.33\%}{40\%} = -0.33$

Arc E_d = 0.33

The arc elasticity of demand is less than 1, which means that oranges are inelastic and a normal good.

Since the PED of oranges is inelastic, this means that a price increase will result in a smaller percentage decrease in the number of oranges sold. Therefore, the farmer should raise the price of the oranges which will ultimately increase the total revenue.