Monopoly Profit Maximization: How Monopolists Maximize Profit

What Is a Monopolistic Market?

In a monopolistic market, there is just one agency that produces a product. There may be absolute product differentiation as a result of there is no such thing as a substitute. One attribute of a monopolist is that it’s a revenue maximizer.

Since there is no such thing as a competitors in a monopolistic market, a monopolist can management the worth and the amount demanded. The extent of output that maximizes a monopoly’s revenue is calculated by equating its marginal value to its marginal income.

Marginal Value and Marginal Income

The marginal value of manufacturing (MC) is the change within the complete value that arises when there’s a change within the amount produced. In calculus phrases, if the whole value perform is given, the marginal value of a agency is calculated by taking the primary spinoff with respect to the amount.

The marginal income is the change within the complete income that arises when there’s a change within the amount produced. The entire income is discovered by multiplying the worth of 1 unit bought by the whole amount bought. For instance, if the worth of is $10 and a monopolist sells 100 items of a product per day, its complete income is $1,000.

The marginal income (MR) of manufacturing 101 items per day is $10. With 101 items produced and bought, the whole income per day will increase from $1,000 to $1,010. The marginal income of a agency can be calculated by taking the primary spinoff of the whole income equation.

Calculating the Maximized-Revenue in a Monopolistic Market

In a monopolistic market, a agency maximizes its complete revenue by equating marginal value to marginal income and fixing for the worth of 1 product and the amount it should produce.

For instance, suppose a monopolist’s complete value perform is

$beginaligned&P = 10Q + Q ^ 2 &textbfwhere: &P = textPrice &Q = textQuantity endaligned$​P=10Q+Q2the place:P=WorthQ=Amount​

Its demand perform is

$P = 20 – Q$P=20−Q

and the whole income (TR) is discovered by multiplying P by Q:

$TR = P instances Q$TR=P×Q

Due to this fact, the whole income perform is:

$TR = 25Q – Q^2$TR=25Q−Q2

The marginal value (MC) perform is:

$MC = 10 + 2Q$MC=10+2Q

The marginal income (MR) is:

$MR = 30 – 2Q$MR=30−2Q

The monopolist’s revenue is discovered by subtracting complete value from its complete income. When it comes to calculus, the revenue is maximized by taking the spinoff of this perform:

$beginaligned&P = TR – TC &textbfwhere: &P=textProfit &TR=textTotal income &TC=textTotal value endaligned$​P=TR−TCthe place:P=RevenueTR=Complete incomeTC=Complete value​

Then you definately set it equal to zero. Due to this fact, the amount provided that maximizes the monopolist’s revenue is discovered by equating MC to MR:

$10 + 2Q = 30 – 2Q$10+2Q=30−2Q

The amount it should produce to fulfill the equality above is 5. This amount should be plugged again into the demand perform to seek out the worth for one product. To maximise its revenue, the agency should its of the product for $20 per unit. The entire revenue of this agency is then $25, or:

$TR – TC = 100 – 75$TR−TC=100−75