Given a table showing price and quantity demanded, calculate the price elasticity of demand using the arc…

Question

Given a table showing price and quantity demanded, calculate the price elasticity of demand using the arc elasticity method.

ScanSolve AI Tutor · Accepted Answer

The table shows the relationship between the price of a commodity and its quantity demanded. Since no specific question is asked, I will calculate the price elasticity of demand using the arc elasticity method, which is common for discrete changes in price and quantity.

I will use the first two distinct data points from the table:

When Price ( $P_1$ ) = N20, Quantity Demanded ( $Q_1$ ) = 500 kg
When Price ( $P_2$ ) = N30, Quantity Demanded ( $Q_2$ ) = 300 kg

The formula for arc price elasticity of demand (PED) is:

PED = \frac{\frac{Q_2 - Q_1}{(Q_2 + Q_1)/2}}{\frac{P_2 - P_1}{(P_2 + P_1)/2}}

Calculate the change in quantity demanded and the average quantity.
$Q_2 - Q_1 = 300 \text{ kg} - 500 \text{ kg} = -200 \text{ kg}$ $\frac{Q_2 + Q_1}{2} = \frac{300 \text{ kg} + 500 \text{ kg}}{2} = \frac{800 \text{ kg}}{2} = 400 \text{ kg}$
Percentage change in quantity demanded:
$\frac{-200 \text{ kg}}{400 \text{ kg}} = -0.5$
Calculate the change in price and the average price.
$P_2 - P_1 = \text{N}30 - \text{N}20 = \text{N}10$ $\frac{P_2 + P_1}{2} = \frac{\text{N}30 + \text{N}20}{2} = \frac{\text{N}50}{2} = \text{N}25$
Percentage change in price:
$\frac{\text{N}10}{\text{N}25} = 0.4$
Calculate the price elasticity of demand.
$PED = \frac{-0.5}{0.4}$ $PED = -1.25$
The absolute value of the price elasticity of demand is 1.25. Since $|PED| > 1$ , the demand for this commodity is elastic between these two price points.

The price elasticity of demand is $-1.25$ .

Given a table showing price and quantity demanded, calculate the price elasticity of demand using the arc elasticity method.

Answer

Step-by-step solution

Calculate the change in quantity demanded and the average quantity.

Calculate the change in price and the average price.

Calculate the price elasticity of demand.

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