In: Economics
There is a single seller in a market which faces market demand: P=85-2Q. The monopolist has total costs TC=5Q and MC=5. What is the profit of the monopolist?
The demand function is given as:
P = 85 - 2Q
The total revenue function is:
TR = 85Q - 2Q²
The marginal revenue function is calculated below:
MR = d(TR)/dQ = 85 - 4Q
The marginal cost is given as 5.
The monopolist maximizes the profit when the marginal revenue equals marginal cost.
Equating MR and MC:
85 - 4Q = 5
4Q = 80
Q = 80/4 = 20
The profit-maximizing level of output is 20 units. The profit is calculated by the following formula:
Profit = TR - TC
Profit = 85Q - 2Q² - 5Q
Profit = 80Q - 2Q²
Putting Q = 5:
Profit = 80(5) - 2(5)² = 400 - 2(25) = 400 - 50 = 350
So, the profit of the monopolist at the profit-maximizing level is $350.