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# How Is Profit Maximized in a Monopolistic Market?

## What Is a Monopolistic Market?

In a monopolistic market, there is only one firm that produces a product. There is absolute product differentiation because there is no substitute. One characteristic of a monopolist is that it is a profit maximizer.

Since there is no competition in a monopolistic market, a monopolist can control the price and the quantity demanded. The level of output that maximizes a monopoly's profit is calculated by equating its marginal cost to its marginal revenue.

### Key Takeaways

• A monopolistic market is where one firm produces one product.
• A key characteristic of a monopolist firm is that it's a profit maximizer.
• A monopolistic market has no competition, meaning the monopolist controls the price and quantity demanded.
• The level of output that maximizes a monopoly's profit is when the marginal cost equals the marginal revenue.
• In a competitive market, on the other hand, competitors will tend to drive down the marginal cost and erode profitability.

## Marginal Cost and Marginal Revenue

The marginal cost of production (MC) is the change in the total cost that arises when there is a change in the quantity produced. In calculus terms, if the total cost function is given, the marginal cost of a firm is calculated by taking the first derivative with respect to the quantity.

The marginal revenue is the change in the total revenue that arises when there is a change in the quantity produced. The total revenue is found by multiplying the price of one unit sold by the total quantity sold. For example, if the price of a good is $10 and a monopolist sells 100 units of a product per day, its total revenue is$1,000.

The marginal revenue (MR) of producing 101 units per day is $10. With 101 units produced and sold, the total revenue per day increases from$1,000 to 1,010. The marginal revenue of a firm is also calculated by taking the first derivative of the total revenue equation. Economists sometimes refer to marginal revenue as marginal product (MP). ## Calculating the Maximized Profit in a Monopolistic Market In a monopolistic market, a firm maximizes its total profit by equating marginal cost to marginal revenue and solving for the price of one product and the quantity it must produce. For example, suppose a monopolist's total cost function is \begin{aligned}&P = 10Q + Q ^ 2 \\&\textbf{where:} \\&P = \text{Price} \\&Q = \text{Quantity} \\\end{aligned} Its demand function is $P = 20 - Q$ and the total revenue (TR) is found by multiplying P by Q: $TR = P \times Q$ Therefore, the total revenue function is: $TR = 25Q - Q^2$ The marginal cost (MC) function is: $MC = 10 + 2Q$ The marginal revenue (MR) is: $MR = 30 - 2Q$ The monopolist's profit is found by subtracting total cost from its total revenue. In terms of calculus, the profit is maximized by taking the derivative of this function: \begin{aligned}&P = TR - TC \\&\textbf{where:} \\&P=\text{Profit} \\&TR=\text{Total revenue} \\&TC=\text{Total cost} \\\end{aligned} Then you set it equal to zero. Therefore, the quantity supplied that maximizes the monopolist's profit is found by equating MC to MR: $10 + 2Q = 30 - 2Q$ The quantity it must produce to satisfy the equality above is 5. This quantity must be plugged back into the demand function to find the price for one product. To maximize its profit, the firm must its of the product for20 per unit. The total profit of this firm is then $25, or: $TR - TC = 100 - 75$ ## What Is a Profit Maximizer? In economics, a profit maximizer refers to a firm that produces the exact quantity of goods that optimizes the profits received. Any more produced, and the supply would exceed demand while increasing cost. Any less, and money is left on the table, so to speak. ## What Is a Monopolist's Profit-Maximizing Level of Output? All firms maximize profits when their marginal cost is equal to the marginal product. This dollar amount should also be the selling price that maximizes profits. ## How Is Total Revenue Calculated? Total revenue is arrived at simply by multiplying the number of units sold by the selling price. So if 100 widgets are sold at$100 each, the total revenue is \$10,000. Note that revenue does not account for costs or expenses, so revenue will be higher than net income or profit.

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