# Please see belowIf pq+5p=q+95 defines the demand curve of a firm, where p is price and q is quantity demanded.   Derive an expression for the rate of change in the price of the firm with respect...

If pq+5p=q+95 defines the demand curve of a firm, where p is price and q is quantity demanded.   Derive an expression for the rate of change in the price of the firm with respect to quantity.

Asked on by april1980

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to form the price function, hence you need to isolate the term containing p to the left side.

Notice  that you need to factor out p to the left side such that:

`p(q+5) = q+95`

You need to express p in terms of q, hence you need to divide by q+5 both sides such that:

`p = (q+95)/(q+5)`

You need to find the rate of change of price with respect to quantity, hence you need to differentiate the price function with respect to q using the quotient rule such that:

`(dp)/(dq) = ((q+95)'*(q+5) - (q+95)*(q+5)')/((q+5)^2)`

`(dp)/(dq) = (q + 5 - q - 95)/((q+5)^2)`

`(dp)/(dq) = -90/((q+5)^2)`

Hence, evaluating the expression that expresses the rate of change of price with respect to quantity yields `(dp)/(dq) = -90/((q+5)^2).`

We’ve answered 317,755 questions. We can answer yours, too.