3. (18 points) You are the manager of a firm that produces products X and Y at 0 marginal cost. You know that different types of consumers value your two products differently, but you are unable to identify these consumers individually at the time of the sale. In particular, you know there are three types of consumers (1000 of each type) with the following valuations Consumer 1: Good X- $90, Good Y- $60…..Consumer 2: Good X- $70, Good Y- $140…Consumer 3: Good X- $40, Good Y- $160a. (4 points) What are your firm’s profits if you charge $40 for product X and $60 for product Y? b. (4 points) What are your firm’s profits if you charge $90 for product X and $160 for product Y?c. (4 points) What are your firm’s profits if you charge $150 for a bundle containing 1 unit of product X and 1 unit of product Y?d. (6 points) What are your firm’s profits if you charge $210 for a bundle containing 1 unit of product X and 1 unit of product Y but also sell the products individually at a price of $90 for product X and $169 for product Y?

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