elasticity of demand

• Nov 9th 2010, 05:26 PM
lilwayne
elasticity of demand
The demand equation for a certain product is given by p =18e^−0.002q ,

where p is
the price in dollars and q is the quantity in units.

a) Find the elasticity of demand when 1000 units are produced.

b) Interpret your result from part a) by analyzing the revenue when the unit price
is increased.

Can someone help get me started please? I'm quite unsure about how to do this, thanks!
• Nov 9th 2010, 05:36 PM
skeeter
Quote:

Originally Posted by lilwayne
The demand equation for a certain product is given by p =18e^−0.002q ,

where p is
the price in dollars and q is the quantity in units.

a) Find the elasticity of demand when 1000 units are produced.

b) Interpret your result from part a) by analyzing the revenue when the unit price
is increased.

Can someone help get me started please? I'm quite unsure about how to do this, thanks!

what is the definition of "elasticity of demand" ?
• Nov 9th 2010, 05:40 PM
lilwayne
Responsiveness of the demand for a good or service to the increase or decrease in its price. Normally, sales increase with drop in prices and decrease with rise in prices. As a general rule, appliances, cars, confectionary and other non-essentials show elasticity of demand whereas most necessities (food, medicine, basic clothing) show inelasticity of demand (do not sell significantly more or less with changes in price).

lol I just dont know how to solve p =18e^−0.002q..
• Nov 9th 2010, 05:49 PM
skeeter
Quote:

Originally Posted by lilwayne
Responsiveness of the demand for a good or service to the increase or decrease in its price. Normally, sales increase with drop in prices and decrease with rise in prices. As a general rule, appliances, cars, confectionary and other non-essentials show elasticity of demand whereas most necessities (food, medicine, basic clothing) show inelasticity of demand (do not sell significantly more or less with changes in price).

lol I just dont know how to solve p =18e^−0.002q..[/QUOTE]

sorry ... I'm not an economist, so that entire paragraph definition is Greek to me. the question wants to know what elasticity of demand is for q = 1000

do you happen to have a formula to calculate this?

Quote:

lol I just dont know how to solve p =18e^−0.002q..
solve for what?
• Nov 9th 2010, 05:54 PM
lilwayne
E(P) = -p/x * dx/dp

that's the formula, but i dont know how to differentiate p =18e^−0.002q (dunno why i said solve lol)
• Nov 9th 2010, 06:07 PM
scherz0
Hello there,

Actually, since quantity in your case is expressed with $q$, and not $x$, elasticity of demand is as follows:

$\displaystyle \epsilon_D = \frac{-p}{q} \times \frac{dp}{dq}$,

where $\displaystyle \frac{dp}{dq} = \frac{d}{dq} 18e^{-0.002q}$.

You are given a function $p$ which is in terms of $q$. So after differentiating, simply substitute the derivative and your function $p(q)$ into the elasticity definition above to arrive at an expression in terms of only $q$.

I hope that this helps.
• Nov 9th 2010, 06:11 PM
skeeter
Quote:

Originally Posted by lilwayne
E(P) = -p/x * dx/dp

that's the formula, but i dont know how to differentiate p =18e^−0.002q (dunno why i said solve lol)

first of all, note that you have p as a function of q ... I'm assuming x in your formula is q ... that would mean to find dq/dp , you are going to have to solve for q in terms of p and then take the derivative of that function w/r to p.

$\frac{p}{18} = e^{-.002q}$

$\ln\left(\frac{p}{18}\right) = -.002q$

$-500 \ln\left(\frac{p}{18}\right) = q$

$-500 \ln(p) + 500\ln(18) = q$

$\frac{-500}{p} = \frac{dq}{dp}$
• Nov 9th 2010, 06:19 PM
skeeter
Quote:

Originally Posted by scherz0
$\displaystyle \frac{dq}{dp} = \frac{d}{dq} 18e^{-0.002q}$.

no ... that would be $\frac{dp}{dq}$ , not $\frac{dq}{dp}$