elasticity of demand

**lilwayne** · November 9th 2010, 04:26 PM

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!

**skeeter** · November 9th 2010, 04:36 PM

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" ?

**lilwayne** · November 9th 2010, 04:40 PM

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..

**skeeter** · November 9th 2010, 04:49 PM

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?

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

solve for what?

**lilwayne** · November 9th 2010, 04:54 PM

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)

**scherz0** · November 9th 2010, 05:07 PM

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.

**skeeter** · November 9th 2010, 05:11 PM

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.

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

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

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

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

$\frac{-500}{p} = \frac{dq}{dp}$