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 0.4.

Step-by-step solution

Step 1: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 has a price elasticity larger than one, whereas inelastic demand is defined as demand for which price elasticity is less than one.

Calculation

As the price goes up, the quantity supply increases.

Let's calculate using the price elasticity of supply using the average formula.

The supply curve is,

P=$3Q-8$

At,$P=4,Q=4$

At,$P=7,Q=5$

% Change in quantity=$\frac{Qfinal-Qintial}{averagequantity}\times 100\%$

$\%changeinquantity=\frac{5-4}{4.5}\times 100\%=22.2\%$

$$\begin{gathered} \%Changeinprice=\frac{Pfinal-Pintial}{averageprice}\times 100\% \\ \%Changeinprice=\frac{7-4}{5.5}\times 100\%=54.5\% \end{gathered}$$$\%Priceelaticityofdemand=\frac{\%changeinquantity}{\%changeinprice}=\frac{22.5}{54.5}=0.41$

Conclusion

Thus, price elasticity of supply=$0.41$

The elasticity of supply is 0.4, thus inelastic.