# price elasticity of demand

• Jul 19th 2010, 02:08 PM
arslan
price elasticity of demand
1. Given the demand function:

Qd=100-P-4PA+3Y

where P = the price of the good, PA = the price of an alternative good and Y = income

If P=4, PA=8 and Y=60 find:

a. the price elasticity of demand
b. the cross-price elasticity of demand
c. the income elasticity of demand

If income increases by 5%, calculate the corresponding change in the quantity demanded.
Is the good inferior or superior?

thank you all for your help.
• Jul 20th 2010, 04:42 AM
SpringFan25
i find it difficult to believe you would have been set this question without being told the formula to use.

Do you know the formula?

If so, post as much of the solution as you can
• Jul 20th 2010, 04:53 AM
arslan
no formula
i havent been given a formula with this question all i no by google is that

Price elasticity of demand: = (dQ / dP)*(P/Q)

Price elasticity of income: = (dQ / dI)*(I/Q)

Cross-price elasticity of demand = (dQ / dP')*(P'/Q)

should i post this in the calculus section perhaps?
• Jul 20th 2010, 05:24 AM
SpringFan25
its in the right section and you have the right formula (did your teacher really not tell you that?!)

Here is the price elasticity of demand

$\epsilon_{xx} = \frac{dQ_x}{dP_x} * \frac{P_x}{Q_x}$
$\epsilon_{xx}= -1 * \frac{4}{Q_x}$

The quantity of X when the price is 4 is 100-4-4*8+3*60 = 244

$\epsilon_{xx}= -1 * \frac{4}{244}$

Try (b) and (c) yourself
• Jul 20th 2010, 07:34 AM
arslan
i dont see how you get -1 for dQ/dP
• Jul 20th 2010, 08:35 AM
SpringFan25
$Q_d=100-P-4P_A+3Y$

$\frac{dQ_d}{dP} = 0 ~~-1 ~- 0~~~ + 0$

$\frac{dQ_d}{dP} = -1$
• Jul 20th 2010, 09:01 AM
arslan
thanks for your help i understand that one now, but cant solve the others im no good at this could u solve the rest for me?

many thanks
• Jul 20th 2010, 02:12 PM
SpringFan25
Cross elasticity of demand
$\frac{dQ_d}{dP_a} * \frac{P_a}{Q_d}$

$= -4 * \frac{P_a}{Q_d}$
$= -4 * \frac{8}{244}$

income elasticity of demand:
$\frac{dQ_d}{dY} * \frac{Y}{Q_d}$

try finishing. start by finding the value of the derivative $\frac{dQ_d}{dY}$
• Jul 21st 2010, 03:12 PM
arslan
dQ/dl =3
(dQ / dI) (I/Q) = 3( 60/244) = 180/244

thanks
• Jul 22nd 2010, 01:45 AM
SpringFan25
thats right :)