There is a single seller in a market which faces market demand: P=85-2Q. The monopolist has...

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?

Solutions

Expert Solution

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.

Rahul Sunny answered 1 year ago

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