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+ 2000-202

Solution

Profit Q = - 50 + 200Q - 2Q^2

On differentiating profit function and equating it with Zero:

dProfit /dQ = 200 - 4Q ......(1)

200 - 4Q = 0

4Q = 200

Q = 200/4

=50

Profit maximizing Level of output (Q) = 50

Second Order Condition:

differentiating equation (1)

d^2 Profit / d^2Q = -4

Second differentiating is negative, Hence Proved.

Profit Q = - 50 + 200(50) - 2(50)^2

= - 50 + 10,000 -5,000

= 4950

Profit = $ 4,950