Suppose Tim and Alyssa form a cartel and behave as a monopolist. The profit-maximizing price is $\qquad$ per gallon, and the total output is $\qquad$ gallons. As part of their cartel agreement, Tim and Alyssa agree to split production equally. Therefore, Tim's profit is $\qquad$ , and Alyssa's profit is $\qquad$ - Suppose that Tim and Alysa have been successfully operating as a cartel. They each charge the monopoly price and sell half of the monopoly quantity. Then one night before going to sleep, Tim says to himself, "Alyssa and I aren't the best of friends anyway. If I increase my production to 45 gallons more than the cartel amount, I can increase my profit even though her profit goes down. I will do that starting tomorrow." After Tim implements his new plan, the price of water $\qquad$ to $\qquad$ per gallon. Given Alyssa and Tim's production levels, Tim's profit becomes $\qquad$ 5 and Alyssa's profit becomes $\qquad$ . Because Tim has deviated from the cartel agreement and increased his output of water to 45 gallons more than the cartel amount, Alyssa decides that
Answer (2)
Tim and Alyssa formed a cartel to maximize their water profits, initially setting a price of $3.00 per gallon and each earning $405.00. When Tim breaks the cartel by increasing his output to 180 gallons, the market price drops to $2.50, reducing Alyssa's profit to $337.50. This scenario exemplifies the instability of cartels as individual incentives can lead to conflicts and further price declines.
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The profit-maximizing price is $3.00 per gallon, and the total output is 270 gallons.
Tim's initial profit is $405.00 , and Alyssa's initial profit is $405.00 .
After Tim increases his production, the price decreases to $2.50 per gallon.
Tim's profit becomes $450.00 , and Alyssa's profit becomes $337.50 .
Explanation
Finding the Monopoly Price and Output First, we need to determine the profit-maximizing price and total output when Tim and Alyssa form a cartel. Looking at the table, the maximum total revenue is $810.00, which occurs when the price is $3.00 per gallon and the total output is 270 gallons.
Calculating Initial Profits Since Tim and Alyssa split production equally, each produces half of the total output. So, Tim's output is 2 270 = 135 gallons, and Alyssa's output is also 135 gallons. Their profits are also split equally, so Tim's profit is $\frac{{$810.00}}{2} = $405.00, and Alyssa's profit is also $405.00.
Calculating Tim's Increased Output Next, Tim increases his production by 45 gallons, so his new output is 135 + 45 = 180 gallons. Alyssa's output remains at 135 gallons. The new total output is 180 + 135 = 315 gallons.
Determining the New Price Looking at the table, when the total output is 315 gallons, the price per gallon is $2.50.
Calculating New Profits Tim's new revenue is his output multiplied by the new price: $180 \times $2.50 = $450.00. Alyssa's new revenue is her output multiplied by the new price: $135 \times $2.50 = $337.50.
Alyssa's Reaction Because Tim has deviated from the cartel agreement and increased his output, Alyssa will likely react by also increasing her output to try to regain some of her lost profit. This could lead to a further decrease in price and potentially a price war.
Examples
Cartels are often formed to control prices and maximize profits, but they are inherently unstable because each member has an incentive to cheat on the agreement. This scenario illustrates how individual incentives can undermine a cartel agreement, leading to lower prices and profits for all members. Understanding these dynamics is crucial in economics and business strategy, as it highlights the challenges of maintaining cooperation in competitive environments. For example, OPEC (Organization of the Petroleum Exporting Countries) faces similar challenges in managing oil production quotas among its member countries. The calculations performed here help to quantify the impact of such decisions on individual profits and overall market outcomes.
