Final answer:
The maximum revenue in a monopoly market for the given demand function requires further information to calculate. The total revenue is found by multiplying price by quantity, and the maximum point is identified where marginal revenue equals zero.
Step-by-step explanation:
In a monopoly market, the maximum revenue for a product is achieved by finding the profit-maximizing price and quantity. To determine the profit-maximizing quantity, we need to equate the marginal revenue (MR) to the marginal cost (MC). In this case, the demand function is given as
p = 2x + 100,
where p is the price and x is the quantity.
To find the profit-maximizing price, we draw a line straight up from the quantity where MR = MC to the demand curve and read the price at that point.
Total revenue is then obtained by multiplying the profit-maximizing price by the profit-maximizing quantity.
Using the given demand function, we equate the marginal revenue to the marginal cost:
2 = MC
The marginal cost is the derivative of the cost function, which in this case is a constant, so the marginal cost is 2. Setting MR equal to MC gives us:
2x + 100 = 2
Simplifying the equation:
2x = -98
x = -49
Since the quantity can't be negative, we discard the negative value and conclude that the profit-maximizing quantity is 0.
To find the profit-maximizing price, we substitute the quantity value into the demand function:
p = 2(0) + 100
p = 100
Therefore, the profit-maximizing price is $100. The maximum revenue for this product is obtained by multiplying the profit-maximizing price by the profit-maximizing quantity, thus the maximum revenue is 0 x $100 = $0.