# Question on Elasticity of Demand.

• Jan 27th 2011, 08:08 AM
k101
Question on Elasticity of Demand.
How do we find the value of q, where demand is elastic?
The demand equation is:

p = 21 - 2√q

for 10 >= q =< 90

BOTH SIGNS ARE LESS THAN OR EQUAL AND GREATER THAN OR EQUAL.

The first part of the question is to find the elasticity of demand, which I did get to be:

n = [-2√q (21-2√q)]/(q)

The second part of the question is trying to find the value of q between 10 and 90, for which demand is elastic.

And the third part is computing the total revenue r when the demand has unit elasticity, and 10 >= q =< 90

Thank you for anyone who helps.
• Jan 27th 2011, 08:51 AM
Amer
I think this question is about physics, "elasticity of demand" u mean diamond ??
physics forum
http://www.physicshelpforum.com/physics-help/
chemistry forum
http://www.chemistryhelpforum.com/chemistry-help/
• Jan 27th 2011, 09:23 AM
HallsofIvy
No, "elasticity of demand" (more correctly "price elasticity of demand") is an economics term. It refers to the way demand for a good changes in response to changes in its price. If demand for a good increases only slightly, as say for water, which is required to live no matter what it costs, the "elasticity of demand" will be small. If it is a luxury, that people can easily give up if the price goes up, the "elasticity of demand" will be large (in absolute value).

Of course, the elasticity of demand varies, perhaps in very complicated ways, with the price. The elasticity of demand, at a specific price, depends upon the derivative: $\displaystyle \frac{P}{Q}\frac{dQ}{dP}$. Normally, of course, demand declines as price increases so that elasticity of demand is negative. Some authors multiply that by -1 just to make "elasticity of demand" a positive number. Without that multiplication by "-1", demand for a good is said to be "elastic" if the elasticity of demand is negative, "inelastic" if it is not.

Here, P is given as a function of Q: $\displaystyle P= 21- 2Q^{1/2}$ to find the derivative dQ/dP, we can do either of two things:
1) Solve that equation for P: $\displaystyle 2Q^{1/2}= 21- P$ so $\displaystyle Q^{1/2}= \frac{21}{2}-\frac{1}{2}P$ and then $\displaystyle Q= (\frac{21}{2}- \frac{1}{2}P)^2$ so that $\displaystyle dQ/dP= 2(\frac{21}{2}- \frac{1}{2}P)^1(-\frac{1}{2})= -\frac{21}{2}+ \frac{1}{2}P$

2) Differentiate P with respect to Q, then invert: $\displaystyle dP/dQ= -Q^{-1/2}$ so that $\displaystyle dQ/dP= -Q^{1/2}$. That's simpler but gives the derivative in terms of Q rather than P. If you replace Q with $\displaystyle Q= (\frac{21}{2}- \frac{1}{2}P)^2$ you see that they are the same. Since Q/P is always positive, demand will be "elastic" when that derivative is negative.

"$\displaystyle 10\ge q\le 90$" makes no sense. The first, $\displaystyle 10\ge q$, says that q is less than or equal to 10. If that is true, then it is not necessary to say "$\displaystyle q\le 90$" because if q is less than or equal to 10, it must be less than 90. I suspect you meant $\displaystyle 10\le q\le 90$, which says that q is between 10 and 90.