Question

At a price of $\backslash (25,000$, producers of midsized automobiles are willing to manufacture and sell $75,000$cars per month. At a price of $\backslash )35,000$, they are willing to produce and sell $125,000$a month. Using the same type of calculation method used to compute the price elasticity of demand, what is the price elasticity of supply? Is supply elastic, unit-elastic, or inelastic?

Short answer

The supply is elastic considering $1.5$price elasticity of supply.

Step-by-step solution

Introduction.

Producers of midsized automobiles willing to manufacture and sell $75,000$cars at a price of$\$25,000$per month and $125,000$cars at a price of $\$35,000$per month.

To find price elasticity of supply.

Calculation of price elasticity of supply.

The price elasticity of a supply is calculated by taking into account the rate of change in supply and the rate of change in price. Below is a measure of the price elasticity of supply.

$E_{\mathrm{p}}=\frac{\text{Percentage change in Quantity Supplied}}{\text{Percentage change in Price}}$

The percentage change in quantity is divided by the percentage change in price while measuring the price elasticity of supply.

Calculation of mid-point elasticity:

The formula used to calculate mid-point price elasticity of demand is:

Mid point elasticity$=\frac{Q_2-Q_1}{Q_2+Q_1/2}÷\frac{P_2-P_1}{P_2+P_1/2}$

To calculate price elasticity of demand:

${\mathrm{E}}_d=\frac{Q_2-Q_1}{Q_2+Q_1/2}÷\frac{P_2-P_1}{P_2+P_1/2}$

$=\frac{125000-75000}{125000+75000/2}÷\frac{35000-25000}{35000+25000/2}$

$=\frac{100,000}{200,000}÷\frac{20,000}{60,000}$

$=\frac{100,000}{200,000}\times \frac{60,000}{20,000}$

$=1.5$

Hence, considering the rate of change in price and shipment quantity, the price elasticity of supply is $1.5$. If the price elasticity is greater than $1$, the supply is elastic. Therefore, the supply is elastic considering that the price elasticity ofthe supply is$1.5.$