Answer:
A. 25.5
Explanation:
The monopolist's profit function is:
Profit = Price*Q(Price) - marginal cost
Since the marginal cost is $1 for each unit produced, profit is given by:
Profit = Price*Q(Price) - 1*Q(Price)
Since the Q(p) function is given, profits are given by:
[tex]Profit= p*(100-2*p) - (100-2*p)\\Profit = -2p^2 +102p - 100[/tex]
The maximum value for the profit function occurs at the point in which the function's derivative equals zero, therefore:
[tex]\frac{d(Profit)}{dp}=\frac{d(-2p^2 +102p - 100 )}{dp}\\\frac{d(Profit)}{dp}= -4p +102 = 0\\p=\frac{102}{4} \\p=25.5[/tex]
The price that the monopolist will set to maximize its profits is 25.5.
