Question 6.41: Show that a demand function of the form Q = a/P^c , where a ......

General expression

Step 1:

Q = $\frac {a}{P^c} = a P^{−c}$

Step 2:

= $-\frac {ca P^{−c−1}}{1} \frac {P}{Q}$

= $\frac {−ca P^{−c}}{Q}$  adding indices on P

= $-\frac {c Q}{Q}$    since Q = a $P^{−c}$

= −c     Qs cancel

Example

Step 1:

Q = $\frac {200}{P^2} = 200 P^{−2}$

Step 2:

= $\frac {−2(200)P^{−3}}{1}  \frac {P}{Q}$

= $\frac {−2(200)P^{−2}}{Q}$  adding indices on P

= $\frac {(−2)Q}{Q}$    since Q = 200 $P^{−2}$

= −2        Qs cancel