Question

The equation for a supply curve is P = 3Q – 8. What is the elasticity in moving from a price of 4 to a price of 7?

Short answer

The supply curve is inelastic at this point.

Step-by-step solution

Definition

Price Elasticity: Elasticity is a metric for calculating the percentage change in one variable as a result of a percentage change in another. The elasticity of demand is calculated by looking at how the price of goods changes over time.

Explanation

The supply curve is

P=3Q-8

At P=4, Q=4

At P=7, Q=5

The quantity offered increases as the price rises. Let's use the average formula to compute supply price elasticity.

% Change in quantity =$\frac{Qfinal-Qinitial}{averagequantity}\times 100\%=\frac{5-4}{4.5}\times 100\%=22.2\%$

% Change in price =

$\frac{Pfinal-Pinitial}{averageprice}\times 100\%=\frac{7-4}{5.5}\times 100\%=54.5\%$

Price elasticity of demand =$\frac{\%Changeinquantity}{\%Changeinprice}=\frac{22.2\%}{54.5\%}=0.41$

The elasticity of supply is $0.4$thus inelastic.