3. Consider a monopoly that sells a product to consumers with a constant marginal cost of $5. There are two potential consumers. As a prior belief, each consumer thinks that the product is worth either $25 or $15 with equal probability, and he/ she learns the true value of the product after trying it out. Each consumer may have a different perception of the value of the product, and these perceptions are independent events. The product is nondurable. Suppose there are two periods, and each consumer demands at most one unit of the product in each period. After the rst period, a company named InfoteX could conduct an online marketing survey to learn consumers\" perceptions of the product. By purchasing the survey from InfoteX, the monopolist knows whether a consumer is happy with the product (i.e., he/ she thinks the product is worth $25 instead of $15 after trying out) or not, and can offer personalized prices to customers in the second period. Then the monopolist should charge 35 _______ in the rst period, and will be willing to pay up to $ ________ to buy the survey from InfoteX. 4. Suppose there are two operating systems: Mac and Windows, and it people are contemplating which system to purchase (each buys one or the other). The payoff of using a Mac is assumed to be 41 + 3m, where m is the number of Mac users. The payoff of choosing Windows is 221, where u is the number of Windows users. Then everyone buys Windows is a Nash equilibrium when n is greater than or equal to __________