MathRocks' question at Yahoo Answers regarding price elasticity of demand

[MarkFL]

Here is the question:

Calc price elasticity problem and demand?

Suppose that 50000 people take city buses each day and pay for a ticket. A regression model suggests that the number of people taking city buses at price p dollars per ticket is given by

x=50000*sqrt(6−p)(a) Evaluate the price elasticity of demand at \$5 per ticket.

E(5)=

(b) For what value of p is the demand unitary?
p=

Here is a link to the question:

Calc price elasticity problem and demand? - Yahoo! Answers

I have posted a link there to this topic so the OP can find my response.

 

[MarkFL]

Re: MathRocks' quation at Yahoo! Answers regarding price elasticity of demand

Hello MathRocks,

In our problem, the point-price elasticity of demand is:

$$E_d=\frac{p}{x}\cdot\frac{dx}{dp}$$

Using the given $$x=50000\sqrt{6-p}$$ we find:

$$E_d=\frac{p}{50000\sqrt{6-p}}\cdot\frac{-25000}{\sqrt{6-p}}=\frac{p}{2(p-6)}$$

(a) Evaluate the price elasticity of demand at \$5 per ticket.

Letting $p=5$, we find:

$$E_d(5)=\frac{5}{2(5-6)}=-\frac{5}{2}$$

At this price, we may say demand is relatively elastic.

(b) For what value of p is the demand unitary?

For this, we want to set:

$$E_d=-1$$

$$\frac{p}{2(p-6)}=-1$$

Now we solve for $p$:

$$p=2(6-p)$$

$$p=12-2p$$

$$3p=12$$

$$p=4$$

Thus, we find that elasticity is unitary at a price of \$4.

To MathRocks and any other guests viewing this topic, I invite and encourage you to register and post other price elasticity of demand problems in our http://www.mathhelpboards.com/f18/ forum.

Best Regards,

Mark.