Question

A consumer’s demand curve for X is given by the equation P=100-squarerootofQ.

Calculate his point Price elasticity of demand when the price of Xi s 60.

Answer 1

The price elasticity of demand can be found as follows:

$$\epsilon=\dfrac{p}{q}\dfrac{dq}{dp}.$$

Let's write the direct demand function:

$$\sqrt{q}=100-p,$$ $$q=p^2-200p+10000.$$

Then,

$$\dfrac{dq}{dp}=2p-200.$$

Finally, we get:

$$\epsilon=\dfrac{p}{p^2-200p+10000}(2p-200),$$ $$\epsilon=\dfrac{60}{60^2-200\cdot60+10000}\cdot(2\cdot60-200)=-3.0.$$