Two firms produce luxury sheepskin auto seat covers: Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by $$C(q)=30 q+1.5 q^{2}$$ The market demand for these seat covers is represented by the inverse demand equation $$P=300-3 Q$$ where \(Q=q_{1}+q_{2},\) total output. a. If each firm acts to maximize its profits, taking its rival's output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm? b. It occurs to the managers of \(\mathrm{WW}\) and \(\mathrm{BBBS}\) that they could do a lot better by colluding. If the two firms collude, what will be the profit-maximizing choice of output? The industry price? The output and the profit for each firm in this case? c. The managers of these firms realize that explicit agreements to collude are illegal. Each firm must decide on its own whether to produce the Cournot quantity or the cartel quantity. To aid in making the decision, the manager of WW constructs a payoff matrix like the one below. Fill in each box with the profit of \(\mathrm{WW}\) and the profit of BBBS. Given this payoff matrix, what output strategy is each firm likely to pursue? d. Suppose WW can set its output level before BBBS does. How much will WW choose to produce in this case? How much will BBBS produce? What is the market price, and what is the profit for each firm? Is WW better off by choosing its output first? Explain why or why not.

An oligopoly is a market structure characterized by a small number of firms that dominate the market, where each firm must take into account the reactions of its rivals when making decisions. This setup is highly strategic, as companies can observe and react to the actions of their competitors, which in turn affects market outcomes.

In an oligopoly, pricing and output decisions are interdependent, making the analysis more complex than in perfect competition or monopoly. Unlike a perfectly competitive market, where firms are price takers, or a monopoly, where one firm dictates the price, oligopolistic firms have a degree of market power but their decisions are closely tied to one another.

Dynamic Interactions

In an oligopolistic market, such as the one involving Western Where (WW) and B.B.B. Sheep (BBBS) producing luxury auto seat covers, firms are engaged in a strategic game. They need to consider how changing their output will affect the overall market price and what reaction it will elicit from the other firm. The Cournot model, as described in the exercise, encapsulates this situation where each firm determines its output based on the expected output of the other, leading to the Cournot Equilibrium.

Market Influence

The influence oligopolists have on market conditions means they can implement strategies like price setting and output manipulation to maximize profits. However, these strategies must be done with caution to avoid aggressive responses from competitors that could lead to price wars or reduced market shares. It’s essential for firms in such a market to predict rival responses accurately to maintain a favorable position within the oligopoly.

Collusion occurs when firms in an oligopoly secretly agree to take actions that increase their profits at the expense of consumers. By forming a cartel, firms can agree on prices, outputs, or market shares, essentially acting as a monopoly and avoiding the uncertainty that comes with competition.

Collusive agreements are typically illegal as they are anti-competitive and lead to higher prices and lower product quantities, which harm consumers. However, even without explicit agreements, there can be tacit collusion where firms implicitly understand to maintain higher prices. In the example with WW and BBBS, the firms realize they could earn higher profits if they collude rather than competing as Cournot oligopolists.

Difficulties in Sustaining Collusion

While collusion can lead to higher profits, sustaining such agreements can be very challenging. Each firm has an incentive to cheat on the agreement to capture a larger market share, leading to potential breakdowns in the collusion. Additionally, legal constraints make explicit collusion risky and punishable.

Within the exercise, the firms are considering the profits they could earn by colluding to act as a monopoly. They must weigh the potential increased earnings against the risks of being caught and the temptation to defect for immediate gains, showcasing the delicate balance that must be achieved for successful collusion.

The first-mover advantage is a strategic benefit a firm gains by being the first to act in a market or in a particular strategic move. In the context of oligopolies, if one firm can set its output or prices before its rivals, it can potentially capture a larger market share and set the competitive landscape in its favor.

WW's consideration of setting its output before BBBS is an example of trying to leverage the first-mover advantage. By deciding first, WW aims to secure a profit-maximizing quantity that BBBS must react to, potentially leading to a more favorable outcome for WW.

Anticipating Rivals' Responses

For a first-mover to be successful, it must anticipate the possible reactions of its rival. In the example provided, WW would assess the possible quantities BBBS could produce in response to their initial output and select a level that maximizes its profits, taking into account BBBS's subsequent reaction function.

Although being a first-mover can be advantageous, it's not without risks. If the second-mover can observe and adjust to the first-mover's action, it might mitigate the first-mover's advantage or even use the information to its benefit. Therefore, WW must carefully analyze if moving first will indeed result in a significant advantage, as strategic missteps can lead to suboptimal outcomes when rivals counteract effectively.