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