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

Expert Answers

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You need to isolate the variables p and q, hence you should factor out p to the left side such that:

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

You need to isolate p to the left side such that:

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

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

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

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

Reducing like terms yields:

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

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

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