Question

Suppose that a monopolist faces linear demand given by Q(p)-100-2*p The monopolist also pays a marginal cost of $1 for each unit produced. What is the price that the monopolist will set to maximize its profits? A. 25.5 B. 51 C. 50.5 D. 24.5

Answer 1

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:

$Profit= p*(100-2*p) - (100-2*p)\\Profit = -2p^2 +102p - 100$

The maximum value for the profit function occurs at the point in which the function's derivative equals zero, therefore:

$\frac{d(Profit)}{dp}=\frac{d(-2p^2 +102p - 100 )}{dp}\\\frac{d(Profit)}{dp}= -4p +102 = 0\\p=\frac{102}{4} \\p=25.5$

The price that the monopolist will set to maximize its profits is 25.5.