It is given that pq + 5p = q + 95 where p is the price and q is the quantity demanded. The expression for the rate of change in the price with respect to the quantity demanded is the derivative `(dp)/(dq)`

Using implicit differentiation gives:

`p + q*(dp)/(dq) +...

## Unlock

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

It is given that pq + 5p = q + 95 where p is the price and q is the quantity demanded. The expression for the rate of change in the price with respect to the quantity demanded is the derivative `(dp)/(dq)`

Using implicit differentiation gives:

`p + q*(dp)/(dq) + 5*(dp)/(dq) = 1`

=> `(dp)/(dq)(5 + q) = 1- p`

=> `(dp)/(dq) = (1- p)/(5 + q)`

**The required rate of change in the price with respect to the quantity demanded is **`(dp)/(dq) = (1- p)/(5 + q)`