# Math Help - price elasticity of demand

1. ## 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.

2. 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

3. ## 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?

4. 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

5. i dont see how you get -1 for dQ/dP

6. $Q_d=100-P-4P_A+3Y$

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

$\frac{dQ_d}{dP} = -1$

7. 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

8. 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 $\frac{dQ_d}{dY}$

9. dQ/dl =3
(dQ / dI) (I/Q) = 3( 60/244) = 180/244

thanks

10. thats right