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 of elasticity 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,

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

As the price increases, quantity demand increases.

Calculation

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

Step 4:Conclusion

Therefore the price elasticity of demand is $1.91.$