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(Solved): 9. Consider a firm facing three consumers, 1,2 and 3 , with the following valuations for two go ...
9. Consider a firm facing three consumers, 1,2 and 3 , with the following valuations for two goods, and (All consumers consume at most 1 unit of and 1 unit of .) The firm can produce both goods at a cost of zero. Suppose the firm can supply both goods at a constant per unit price of for , and for . It can also supply the two goods as a bundle, for a price of . The optimal vector of prices is given by A. . B. . C. D. None of the above.
Expert Answer
To find the demand for goods X and Y, we need to determine how much each consumer is willing to pay for each unit of the goods. This can be calculated as the difference between the consumer's valuation of the good and the price that the firm charges for it.For example, if the firm charges a price of p for good X, then the demand for good X from consumer 1 is:D1(X) = 1 if p ? 7, and 0 otherwise.Similarly, the demand for good X from consumer 2 and 3 can be calculated as:D2(X) = 1 if p ? 4, and 0 otherwise.D3(X) = 1 if p ? 1, and 0 otherwise.Using the same approach, we can calculate the demand for good Y from each consumer.Once we have the demand functions for goods X and Y, the firm can determine the profit-maximizing prices for these goods. The optimal prices are those that maximize the firm's total revenue, which is equal to the product of the price and the quantity sold.However, since we do not know the costs of production, we cannot determine the exact profit-maximizing prices for goods X and Y. The firm's optimal pricing strategy will depend on its costs and other factors such as competition in the market, elasticity of demand, and market power.