Question

A monopoly firm faces two markets where the inverse demand curves are

Market A: Pₐ = 140 - 2.75Qₐ.
Market B: PB = 120 - QB.
The firm operates a single plant where total cost is C = 20Q + 0.25Q², and marginal cost is m = 20 + 0.5Q. Suppose the firm sets a single price for both markets Using the information above, the profit maximizing price is $86.18 and the profit maximizing quantity is 53.37 units. Given the information, you determine that the firm will earn a profit of $ _____.

Answer 1

The monopoly firm will earn an approximate profit of $2819.79 by deducting the total cost from the total revenue for the provided profit-maximizing price and quantity.

Step-by-step explanation:

To calculate the profit earned by the monopoly firm, we need to subtract the total cost from the total revenue. The profit-maximizing price has been given as $86.18, and the profit-maximizing quantity is 53.37 units. Therefore, the total revenue (TR) can be calculated as the price multiplied by the quantity, which would be $86.18 × 53.37.

Total Revenue (TR) = Price (P) × Quantity (Q)

Using the provided total cost (C) function C = 20Q + 0.25Q², we can calculate the total cost for the quantity of 53.37 units.

Total Cost (TC) = 20Q + 0.25Q²

Finally, to find the profit, we subtract the total cost from the total revenue:

Profit = Total Revenue - Total Cost

Now let's compute the actual values:

• TR = $86.18 × 53.37 = $4599.79 (approximately)
• TC = 20 × 53.37 + 0.25 × 53.37² = $1067.4 + $712.6 = $1780 (approximately)
• Profit = $4599.79 - $1780 = $2819.79 (approximately)

Therefore, the firm will earn a profit of approximately $2819.79.