Question

1. Find the maximum of the following total revenue function (TR) by finding out (a) the output ?∗ value where the first order condition is satisfied; and (b) the maximum total revenue.

??(?)=32?−?2

2. Find the maximum of the following profit function by finding out (a) the output ?∗ value where the first order condition is satisfied; and (b) the maximum profit.

?(?)=−?33−5?2+2000?−326.

3. Find the minimum of the average cost function given following total cost function by finding out (a) the output ?∗value where the first order condition is satisfied; and (b) the minimum average cost.

??(?)=?3−21?2+500?

4. Given the following total revenue function ??(?) and the total cost function ??(?), maximize profit ?(?) by following steps

(a) set up the profit function

?=??(?)−??(?)

(b) the output value where the profit is at a relative extremum; and

(c) the maximum profit value.

??(?)=4350?−13?2

??(?)=?3−5.5?2+150?+675.

(please answer all)

Answer 1

The total revenue (T R) received from the sale of Q goods at price P is given by T R = P Q. Based on the total revenue we can obtain another key concept: marginal revenue. Marginal revenue (MR) can be defined as the additional revenue added by an additional unit of output. In other words marginal revenue is the extra revenue that an additional unit of product will bring a firm. It can also be described as the change in total revenue divided by the change in number of units sold. This brings us back to the idea of differentiation and rates of change. More formally, marginal revenue is equal to the change in total revenue over the change in quantity when the change in quantity is equal to one unit. It is possible to represent marginal revenue as a derivative; MR = d(T R) /dQ . Marginal revenue is the derivative of total revenue with respect to demand.

This sets the limit of questions to be asked to first question only.