Question

Two firms compete in selling identical widgets. They choose their output levels \(Q_{1}\) and \(Q_{2}\) simultaneously and face the demand curve $$P=30-Q$$ where \(Q=Q_{1}+Q_{2}\). Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm \(2^{\prime}\) s marginal cost to \(\$ 15 .\) Firm \(1^{\prime}\) s marginal cost remains constant at zero. True or false: As a result, the market price will rise to the monopoly level Suppose that two identical firms produce widgets and

Short answer

Given the available information, it is unclear if the market price will rise to the monopoly level. Though increase in marginal cost of one firm might lead to an increment in market price, whether this will reach the monopoly level is uncertain without knowing the actual monopoly price.

Step-by-step solution

Understanding the concepts

Firms choose their output levels \(Q_{1}\) and \(Q_{2}\) simultaneously and face the given demand curve \(P=30-Q\), where \(Q=Q_{1}+Q_{2}\). Marginal cost is the cost added by producing one additional unit of a product or service. Here, Firm \(2^{\prime}\) s marginal cost has increased to \$15 due to environmental regulations while Firm \(1^{\prime}\) s marginal cost remains zero. The problem requires to state if the market price will rise to the monopoly level - a market structure characterized by a single seller, selling a unique product in the market with no close substitutes.

Analyze the demand function

The given demand function \(P=30-Q\) suggests that as the quantity \(Q\) increases, the price \(P\) will decrease. This is characteristic of demand in many markets where the price of an item falls as the quantity available increases.

Analyze the effect of marginal cost on output and price

Marginal cost plays a major role in economic decision-making processes of firms. In this case, an increase in the marginal cost of Firm 2 may cause it to reduce its output, \(Q_{2}\). This reduction in output may cause a rise in the market price, as the overall supply \(Q=Q_{1}+Q_{2}\) decreases.

Final step: Compare the resulting market price to monopoly price

A monopoly price is a price set by a monopolist due to lack of competition. However, the problem did not disclose the level of monopoly price. It is important to note that while the price in this market scenario might increase with the rise of marginal cost for Firm 2, whether it will reach the monopoly level or not, cannot be ascertained without the data for monopoly price level.

Key concepts

Marginal Cost

Marginal cost is a critical concept in economics that relates to the cost of producing one extra unit of a product. It's often abbreviated as MC.
For firms in competitive markets, understanding marginal cost helps determine the level of output that maximizes profit.
In our exercise, Firm 2's marginal cost has risen to $15 while Firm 1 retains a marginal cost of zero.
Here’s how it affects decision-making:

• Firm 2, faced with a higher marginal cost, may produce fewer units since each additional unit costs more to produce.
• Firm 1, with a marginal cost of zero, can produce more as it incurs no extra cost for additional units.

Marginal cost influences pricing and production strategies, influencing overall market dynamics by changing the supply equilibrium.

Market Price

Market price is the prevailing price at which goods are sold in the market. It is determined by the intersection of supply and demand.
In an oligopoly, where few firms dominate the market, like in our example, strategic interactions between the firms significantly influence the market price.
If Firm 2 reduces its output due to a higher marginal cost, the supply decreases, potentially raising the market price if Firm 1 does not compensate by increasing its output.

• The balance between firms' production levels will directly alter the market price.
• With a reduced total output by Firm 2, market scarcity can induce higher prices, but the price may not reach monopoly levels without further data.

The interaction of supply and demand, adjusted by firms' production decisions, continues to play a pivotal role in setting the market price.

Demand Curve

A demand curve represents the relationship between the price of a good and the quantity demanded by consumers. In this context, the demand curve is given by the equation \(P=30-Q\), where \(Q\) is the total output of both firms.
This indicates that as supply increases, the price tends to fall, following the general law of demand.
The impact of changes in output levels from Firm 1 and Firm 2:

• If total output \(Q\) decreases due to higher marginal costs driving Firm 2 to reduce its production, the demand curve suggests the price \(P\) will rise.
• The slope also tells us how sensitive price is to changes in output quantity.

Scripts of supply and demand in oligopolistic markets thus dictate such fluctuating prices. Understanding how the demand curve operates aides firms in making smart production choices to optimize profits.