Three Oligopolists A, B, And C Produce An Identical Product

three Oligopolists A B And C Produce An Identical Product Q Q I

Three oligopolists, A, B, and C, produce an identical product, Q. Q is produced under conditions of constant costs, with average cost (AC) and marginal cost (MC) both equal to $100. The market demand schedule for Q is provided, with a price of $1 for the corresponding quantity demanded. The specific demand function is not explicitly given in the prompt, but for the purpose of this analysis, we assume a linear demand curve that aligns with the data provided.

The scenario involves several strategic behaviors among the firms, including collusion (cartel formation), cheating, and retaliation, which influence their profits and market outcomes. The key questions focus on the cartel’s profit-maximizing output and price, the effects of cheating by one firm, the retaliatory actions of the other firms, and the implications for cartel stability.

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In oligopolistic markets where a few firms dominate, strategic interactions significantly influence market outcomes. The scenario involving three firms—A, B, and C—producing an identical product illustrates the core challenges of collusion, cheating, and stability within such markets. This analysis explores the intricacies of cartel behavior and the impact of deviations from collusive agreements, providing insights into the sustainability of collusions in oligopolistic settings.

Initially, the firms decide to act as a cartel, aiming to maximize collective profits by dividing the market equally and setting an optimal price and output level. Assuming the demand schedule indicates that the market price is $1 at a certain quantity, and considering the constant costs, the firms’ goal is to find the profit-maximizing quantity and price for the entire cartel.

Under cartel behavior, the firms effectively behave like a monopolist, seeking to maximize total industry profit. To determine this, we need to establish the total revenue (TR) and total cost (TC) for the industry. The total revenue is given by TR = P × Q, where P is the price and Q is total quantity. Given the demand schedule, the total profit (π) for the cartel is the difference between total revenue and total cost:

π = TR – TC = (P × Q) – (AC × Q).

Given AC = MC = $100, the total cost is 100 × Q. To maximize profits, the firms set MR (marginal revenue) equal to MC. As the demand curve declines, the MR is also derived accordingly. The equilibrium quantity and price depend on the demand function, but assuming linear demand and the available data indicating a price of $1 at a particular demand level, the cartel chooses an output where MR = MC.

However, since the demand schedule is not explicitly provided, for this scenario, suppose the demand curve is linear with a maximum quantity at zero price and decreasing to a point where the demand equals the total quantity supplied at the cartel's chosen price. Based on typical assumptions, the cartel chooses the quantity that maximizes total profit, which, due to the constant costs, occurs at the point where marginal revenue equals marginal cost.

Under perfect collusion, the firms agree to produce a total quantity Q that maximizes profit. For simplicity, if the demand curve is such that when the price is $1, the total quantity demanded is Qd, then the cartel sets the output to Qd and the price is set at $1. The total profit for the industry is:

Profit = (Price – Cost) × Quantity = ($1 – $100) × Qd = negative in this case, indicating the need for a re-examination of demand assumptions or a different demand slope.

In real-world scenarios, the demand would be structured so that the price at the profit-maximizing output would be above the marginal/average cost for profits to be positive. For illustrative purposes, assume the demand schedule implies a decline such that the cartel's profit is maximized at an output level Q, with a corresponding price P>$100, making profits positive.

Assuming this, each firm in the cartel agrees to produce Q/3 units, and the total industry profit is shared equally. The profit for each firm is then the total profit divided by three. The critical insight is that collusive behavior allows firms to earn supra-competitive profits, but this stability is fragile.

In the second scenario, firm A cheats by increasing its output by 25 units. The new market equilibrium then depends on how this increase affects the total supply and consequently the market price. Typically, increasing output causes the market price to fall because of the downward-sloping demand curve. As the price drops below the cartel’s agreed-upon price, the profitability of cheating depends on whether the additional units sold at the lower price compensate for the reduction in market price.

Calculating the new market price involves understanding the demand elasticity. Assuming linear demand, an increase in supply shifts quantity upward and reduces price. The precise new equilibrium price can be estimated by substituting the increased total supply into the demand function and solving for P.

For example, if the initial cartel output was Q, and A increases output by 25 units, the new total is Q + 25 units. Plugging this into the demand function yields a lower price, which diminishes the marginal profit per unit, often leading A to earn less or even incur losses. Meanwhile, B and C maintain their original outputs, potentially suffering from decreased market share and reduced profits.

The overall impact on the industry’s total profits depends on the extent of price reduction and the remaining market demand. Typically, cheating destabilizes the cartel by decreasing total profits and incentivizing more firms to cheat, leading to a breakdown of collusion.

In retaliation, B and C may increase their outputs to defend their market share, leading to a further decline in the market price and profits for all firms. The explicit actions could include B and C increasing their outputs or engaging in price wars. As a result, the market price drops further, and industry profits diminish or become negative, threatening cartel stability.

The entire analysis underscores the core challenge in maintaining collusive agreements. The temptation to cheat for short-term gains ultimately erodes the cartel’s profitability, illustrating the instability of such arrangements over time. This aligns with the economic theory of collusion stability, which states that unless monitored and enforced, collusive agreements are inherently unstable because individual firms have incentives to defect.

In conclusion, the dynamics of oligopolistic collusion hinge on the delicate balance of incentives. While cartels can temporarily increase industry profits, the temptation for individual firms to cheat and the retaliatory actions of competitors tend to prompt cartel breakdown. Effective enforcement mechanisms or regulations are essential to sustain collusive behavior and prevent market abuses associated with oligopoly power.

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