Consider a monopolist who sells a product that contains two attributes A and B. Each of these attributes can be of high or of low quality. Low quality gives utility u_i = 0 and high quality utility u_i = 1/2, i = A, B. The willingness to pay for the product is the sum of the ‘attributes’ utilities plus some small, positive fixed value, u₀ > 0- i.e., u₀ + u_A + u_B. Nature draws high and low quality with probability 1/2 each, independently across attributes. The cost of production is equal to zero. The realization of the two qualities is private information of the firm. The firm can advertise that the product exists at zero costs. The firm chooses its marketing strategy, consisting of its advertising strategy and its price.

1. Suppose that the monopolist can reveal the quality of both attributes at zero cost. What is the equilibrium outcome?

2. Suppose that the monopolist can at most truthfully advertise the quality of one of the two attributes. What is the equilibrium outcome of such a game?

3. Consider the situation in (2), but suppose that, after the advertising decision,  consumers can search at cost z to receive noisy information about the quality of one of the attributes. Clearly, consumers may only search for the quality of an attribute whose quality has not been discloses. Specifically, suppose that consumers learn with probability 3/4 that a low-quality attribute  is indeed low quality. With the remaining probability 1/4 they obtain the same signal that they receive if the attribute is of high quality. Show that there exists a semi-separating equilibrium in the which a product  with two high-quality attributes pools with a product with two low-quality  attributes by not revealing any attribute information. By contrast, products (H, L) and (L, H) inform consumers through advertising about the high quality of one of the attributes.

•  Characterize the equilibrium search behavior of the consumers.

•  Characterize the maximal equilibrium prices and profits that can be supported along the equilibrium path.

•  Show that none of the firms has an incentive to deviate.

•  Give a condition on the level of the search cost such that the equilibrium exists.

4. Discuss your result obtained in (3) with respect to the informativeness of ads depending on product quality.