Q3) (Fill in the black and show working out):

Consider a monopoly that sells a product to consumers with a constant marginal cost of $13. There are two potential consumers. As a prior belief, each consumer thinks that the product is worth either $29 or $19 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 non-durable. Suppose there are two periods, and each consumer demands at most one unit of the product in each period. After the first 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 $29 instead of $19 after trying out) or not, and can offer personalized prices to customers in the second period.

Then the monopolist should charge $_______ in the first period, and will be willing to pay up to $________ to buy the survey from InfoteX.