91Ó°ÊÓ

The monopoly market represents a market where only one seller operates the market and controls the price. The monopolist producer operates at the level where marginal revenue is equal to marginal cost.

The price and quantity are calculated below:

$$\begin{gathered} P=30-Q \\ TR=30Q-Q^2 \\ MR=30-2Q \\ MC=\$0 \\ MR=MC \\ 30-2Q=0 \\ 2Q=30 \\ Q=15 \\ P=30-15 \\ =\$15 \end{gathered}$$

The price will be $15, and the quantity will be 15 units.

Two firms are operating in the market; the marginal revenue and marginal cost are equated with generating each firm's reaction curve.

Assuming that both firms know about the other firm's marginal cost and that they know that the other firm knows this:

Firm 1's reaction curve is calculated below:

$$\begin{gathered} P=30-Q_1-Q_2 \\ T{R}_1=30Q_1-Q_1^2-Q_1{Q}_2 \\ M{R}_1=30-2Q_1-Q_2 \\ M{C}_1=\$0 \\ M{R}_1=M{C}_1 \\ 30-2Q_1-Q_2=0 \\ {Q}_1=\frac{30-Q_2}{2}....................i \end{gathered}$$

Firm 2's reaction curve is calculated below:

$$\begin{gathered} P=30-Q_1-Q_2 \\ T{R}_2=30Q_2-Q_2^2-Q_1{Q}_2 \\ M{R}_2=30-2Q_2-Q_1 \\ M{C}_2=\$15 \\ M{R}_2=M{C}_2 \\ 30-2Q_2-Q_1=15 \\ {Q}_2=\frac{15-Q_1}{2}....................ii \end{gathered}$$

From i and ii,

$$\begin{gathered} Q_1=\frac{30-\left(\frac{15-Q_1}{2}\right)}{2} \\ {Q}_1=\frac{60-15+Q_1}{4} \\ 4Q_1-Q_1=45 \\ {Q}_1=\frac{45}{3}=15 \\ {Q}_2=\frac{15-15}{2}=0 \end{gathered}$$

The output for firm 1 will be 15 units, and for firm 2 will be 0.

The price is calculated below:

P = 30 - 15 - 0

=$15

The price will be $15. Thus, the price is equal to the monopoly price.