Question

Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 – Q where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2's marginal cost to $15. Firm 1's marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level.

Short answer

The statement is true.

Step-by-step solution

Determination of monopoly market price

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.

Price when marginal cost increases to $15

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.