# If pq+5p=q+95  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. 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) +...

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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)`

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