# 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...

Please see below

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.

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### 1 Answer

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).` **