1. Consider a monopolist that produces a single good whose quality is either high or low. Quality is exogenously given and the monopolist knows it. The marginal cost of production is if the quality is high, and is if the quality is low, where . There are N consumers, each of whom is interested in buying at most one unit in each of two periods. Each consumer is willing to pay H for high quality and L for low quality. However, consumers cannot tell the product's quality before they consume it in the first period. They believe that each quality is equally likely. If a consumer buys the good in the first period, then she learns the good's true quality; so, she will possess complete information before the second period.

1. Suppose that the firm can signal its quality through an introductory price. Can the first-period signal reveal the quality? If so, find the introductory price it needs to set to achieve separation. [15 pts]

2. Now, suppose that the firm can spend on advertising the good on TV before the first period, though advertising itself does not convey any direct information about the good's quality. However, consumers may infer the actual quality from the amount of money spent on advertising. Can the high-quality firm signal its quality by advertising? If so, find the minimum amount it needs to spend to achieve separation. [15 pts]

3. Does the firm prefer to signal its quality through introductory price or advertising expenditure? Do consumers prefer introductory price or advertising expenditure? [10 pts]

4. Explain how advertisement as a signal is different from persuasive and informative advertisement? [10 pts]