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 '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

False, the market price will not rise to the monopoly level.

Step-by-step solution

Understand the Pricing Function

First, take a look at the given pricing function, \(P=30-Q\). This tells that the price \(P\) decreases as the total output \(Q=Q_{1}+Q_{2}\) by both firms increases. The ultimate price that consumers get for the product is determined by this pricing function.

Analyze Firm 1

Firm 1's marginal cost remains constant at zero. This means that the firm does not have any additional cost for producing additional units.

Analyze Firm 2

Due to change in environmental regulations, Firm 2's marginal cost is $15. Meaning, Firm 2 will incur $15 for each unit it produces.

Analyze situation at Monopoly Level

The monopoly price is the price at which single supplier sells the goods. The monopoly supplier will set marginal cost equal to marginal revenue to maximize profits. If there were to be a monopoly for this good, the marginal cost would be compared to the derived demand, which is the demand as a function of \(Q_2\).

Compare Monopoly Situation and Current Situation

We can now compare the monopoly situation, where a potential monopoly (in this case Firm 2) would produce where marginal cost equals marginal revenue. Due to changes in regulation, Firm 2's marginal cost is now $15. If Firm 2 were a monopoly, it would produce where $15 equals marginal revenue leading to a price strictly greater than $15. But in the duopoly market, Firm 1 can still produce at zero cost and could lower its price if Firm 2 chooses a price above $15. Hence, the market price won't rise to the monopoly level because the other firm (Firm 1) would have an incentive to reduce its price.

Key concepts

Marginal Cost

In economics, the marginal cost is the change in the total cost that arises when the quantity produced is incremented by one unit. It's essentially the cost of producing one additional unit of a good or service. Calculating marginal cost involves taking the derivative of the total cost with respect to quantity, which, put simply, means looking at how the cost changes as you produce more.

In our exercise, Firm 1's marginal cost is zero, meaning it doesn't cost them anything extra to produce another widget. Firm 2, however, now incurs a $15 increase in total cost for each additional widget due to new environmental regulations. This discrepancy in costs will affect how the firms compete and price their products. Marginal cost is a crucial concept in determining the supply side of market equilibrium, as it influences firms' decisions on how much to produce.

Demand Curve

The demand curve is a graphical representation of the relationship between the price of a good and the quantity demanded by consumers. Generally, it is downward sloping, reflecting the inverse relationship between price and demand – as the price decreases, the demand typically increases, and vice versa.

In the context of our duopoly situation, the demand curve is defined by the equation \( P = 30 - Q \), wherein \( P \) is the price that consumers are willing to pay, and \( Q \) is the total quantity of widgets supplied by both Firm 1 and Firm 2. The curve gives us a visual framework to predict consumer behavior and market dynamics. It can help determine the equilibrium price and quantity in the market, where the amount consumers wish to buy equals the amount the firms are willing to sell.

Monopoly Pricing

Monopoly pricing refers to the behavior of a single seller in a market, a monopolist, who has considerable control over the price because they can adjust the supply to meet their desired price level. In such a scenario, a monopolist will typically produce at the quantity where the marginal cost of production equals marginal revenue to maximize profits, a state known as the profit maximization condition.

The monopoly price is typically higher than in a competitive market because, in the absence of competitors, the monopolist can set higher prices. However, in our exercise regarding a duopoly, even if Firm 2's marginal cost increases to a level where it might wish to set monopoly-like prices, Firm 1 has the ability to keep prices lower due to its zero marginal cost, thus preventing the price from reaching the monopoly level.

Environmental Regulations

Environmental regulations are rules and standards set by governments to protect the environment. These regulations can impact businesses significantly, often increasing costs due to added measures for pollution control, waste management, and use of sustainable resources.

In our exercise, Firm 2 experiences an increase in marginal cost directly because of new environmental regulations. These increased costs can change the competitive dynamics of a market. While such regulations are essential for protecting environmental health, they can also reshape the competitive landscape by creating cost burdens that may alter production decisions and market prices. It's an example of how non-market forces, like regulations, can have profound effects on market outcomes.