Questions: Consider a hypothetical demand schedule for monosodium glutamate (MSG). Suppose that Ajinomoto holds 50% of the market, Jiali holds 30% of the market, and Quingdao holds 20% of the market. Suppose the three firms agree to form a cartel to fix production of monosodium glutamate. Assume marginal cost equals zero, and the output is split equally across the firms. What quantity maximizes the cartel's profit? 20 million pounds Price of MSG ( per pound) Quantity of MSG demanded (millions of pounds) 8 0 7 20 6 30 5 40 4 60 3 90 2 110 1 180 0 300 90 million pounds 110 million pounds 300 million pounds Suppose Ajinomoto's marginal cost remains equal to zero, but for Jiali and Quingdao, marginal costs rise above zero. How would this affect the incentive of Ajinimoto to act noncooperatively and change its output?

To determine the quantity that maximizes the cartel's profit, we need to consider the demand schedule and the fact that the marginal cost is zero for all firms initially. The goal of the cartel is to maximize total profit, which is the total revenue minus total cost. Since the marginal cost is zero, the total cost is zero, and the profit is simply the total revenue.

The total revenue is calculated as the price multiplied by the quantity demanded. We need to find the price-quantity combination that maximizes this product.

Let's calculate the total revenue for each price point:

• At \$8 per pound, quantity demanded is 0, so total revenue = \$8 * 0 = \$0.
• At \$7 per pound, quantity demanded is 20 million pounds, so total revenue = \$7 * 20 = \$140 million.
• At \$6 per pound, quantity demanded is 30 million pounds, so total revenue = \$6 * 30 = \$180 million.
• At \$5 per pound, quantity demanded is 40 million pounds, so total revenue = \$5 * 40 = \$200 million.
• At \$4 per pound, quantity demanded is 60 million pounds, so total revenue = \$4 * 60 = \$240 million.
• At \$3 per pound, quantity demanded is 90 million pounds, so total revenue = \$3 * 90 = \$270 million.
• At \$2 per pound, quantity demanded is 110 million pounds, so total revenue = \$2 * 110 = \$220 million.
• At \$1 per pound, quantity demanded is 180 million pounds, so total revenue = \$1 * 180 = \$180 million.
• At \$0 per pound, quantity demanded is 300 million pounds, so total revenue = \$0 * 300 = \$0.

The maximum total revenue, and thus the maximum profit, occurs at a price of \$3 per pound with a quantity demanded of 90 million pounds. Therefore, the quantity that maximizes the cartel's profit is 90 million pounds.

Now, considering the second part of the question, if Ajinomoto's marginal cost remains zero while Jiali and Quingdao's marginal costs rise above zero, Ajinomoto would have an incentive to act noncooperatively. Since Ajinomoto can produce at a lower cost, it might increase its output to capture a larger market share and increase its own profit, especially if the other firms are constrained by higher costs. This could lead to Ajinomoto producing more than its agreed share in the cartel, potentially destabilizing the cartel agreement.