Question

The equation for a demand curve is P = 48 – 3Q. What is the elasticity in moving from a quantity of 5 to a quantity of 6?

Short answer

The price elasticity of demand is $1.91$

Step-by-step solution

Definition

The elasticity of Demand: Elasticity refers to the responsiveness of the quantity required by consumers in response to variations in the price of the good. Elastic demand is defined as demand that is larger than one, whereas inelastic demand is defined as demand that is less than one.

Explanation

The demand curve is: P = 483Q

$$\begin{gathered} AtQ=5,P=48-15=33 \\ AtQ=6,P=48-18=30 \end{gathered}$$

The quantity demanded reduces as the price rises. Let's use the average formula to calculate price elasticity:

% change in quantity=$\frac{Qfinal-Qintial}{Averagequantity}\times 100\%$

% Change in quantity =$\frac{6-5}{5.5}\times 100\%=18.18\%$

% Change in price =$\frac{Pfinal-Pintial}{Averageprice}\times 100\%$

=$\frac{30-33}{31.5}\times 100\%=-9.52\%$

% Price elasticity of demand =

$\frac{\%changeinquantity}{\%changeinprice}=-\frac{18.18}{9.52}=-1.91$