Question

a firm has the following demand function P=60-0.5Q and its total cost are defined by TC=13+Q. find the maximum revenue

Answer 1

The revenue function is given as follows:

$$R(Q) = Q\cdot P(Q) = Q\cdot (60-0.5Q)=-0.5Q^2 +60Q$$

In order to find its maximum, let's set its derivative to 0 and solve for $Q^*$ :

$$R'(Q^*)=-Q^*+60=0\\ Q^*=60$$

The value of maximum revenue is obtained by plugging $Q^*$ into $R(Q)$:

$$R(Q^*)=-0.5\cdot 60^2 + 60\cdot 60=1800$$

Answer. 1800.