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?

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.

The demand curve,

$$\begin{gathered} P=48-3Q \\ AtQ=5,P=48-15=33 \\ AtQ=6,P=48-18=30 \end{gathered}$$

As the price increases, quantity demand increases.

Price elasticity using the average formula,

$$\begin{gathered} \%changeinquantity=\frac{Qfinal-Qintial}{averagequantity}\times 100\% \\ \%changeinquantity=\frac{6-5}{5.5}\times 100\%=18.18\% \end{gathered}$$

localid="1644829435917" $$\begin{gathered} \%Changeinprice=\frac{Pfinal-Pintial}{averageprice}\times 100\% \\ \%Changeinprice=\frac{30-33}{31.5}\times 100\%=-9.52\% \\ \%Priceelasticityofdemand=\frac{\%changeinquantity}{\%changeinprice} \\ \%Priceelasticityofdemand=-\frac{18.18}{9.52}=-1.91 \end{gathered}$$

Therefore the price elasticity of demand is $1.91.$