5 For the following the profit function below compute the pr

5. For the following the profit function below, compute the profit maximizing level of output Q*, and verify from the second order conditions that this is indeed a profit maximum. Also, compute the maximum level of profits, * (Q) =-50 + 2000-20

Solution

Profit is maximized when dP/dQ = 0

P = -50 +200Q -2Q²

dP/ dQ = 200 -4Q = 0

Q^* = 50

The second derivative d²P/dQ² = - 4

This means that rate of change of slope is decreasing, this means that the point obtained is a maxima.

Pmax = -50 +200 x 50 -2 x 50² = 4950