Question

If the cost of Production given by C=50+Q+Q and the demand function is P=40-Q, then what is the profit maximizing level of production for the monopolist

Answer 1

The marginal cost of production:

$C^{\prime}=(50+2Q)^{\prime}=2$

The profit-maximizing level of production for the monopolist can be find from the equation:

$P*Q=40Q-Q^2=2$

$Q^2-40Q+2=0$

$D=1600-4*2=1592$

$Q_1=(40-\sqrt{1592})/2=-0.05$ (it cannot be negative)

$Q_2=(40+\sqrt{1592})/2=39.94$

So, the profit maximizing level of production is 39.94