|Question||Advertising as Quality Signal: In the text, we have discussed two possible motives for advertising, one focused on providing information (about the availability of goods or the prices of goods) and another focused on shaping the image of the product. Another possible motive might be for high quality firms to signal that they produce high quality goods to consumers who cannot tell the difference prior to consuming a good. Consider the following game that captures this: In each of two periods, firms get to set a price and consumers get to decide whether or not to buy the good. In the first period, consumers do not know if a firm is producing high or low quality goods—all they observe is the prices set by firms and whether or not firms have advertised. But if a consumer buys from a firm in the first period, she experiences the quality of the firm’s product and thus knows whether the firm is a high or low quality firm when she makes a decision of whether to buy from this firm in the second period. Assume throughout that a consumer who does not buy from a firm in the first period exits the game and does not proceed to the second period.
A: Notice that firms and consumers play a sequential game in each period, with firms offering a price first and consumers then choosing whether or not to buy. But in the first period, firms also have the option to advertise in an attempt to persuade consumers of the product’s value.
(a) Consider the second period first. Given that the only way a consumer enters the second period is if she bought from the firm in the first period, and given that she then operates with the benefit of having experienced the good’s quality, would any firm choose to advertise in the second period if it could?
(b) Suppose that both firms incur a marginal cost of MC for producing their goods. High quality firms produce goods that are valued at vh >MC by consumers and low quality firms produce goods that are valued at v? >MC (with vh > v?). In any sub game perfect equilibrium, what prices will each firm charge in the second period — and what will consumer strategies be (given they decide whether to buy after observing prices)?
(c) Now consider period 1. If consumers believe that firms who advertise are high quality firms and firms that don’t advertise are low quality firms, what is their sub game perfect strategy in period 1 (after they observe prices and whether a firm has advertised)?
(d) What is the highest cost ah (per output unit) of advertising that a high quality firm would be willing to undertake if it thought that consumers would interpret this as the firm producing a high quality good?
(e) What is the highest cost a? that a low quality firm would be willing to incur if it thought this would fool consumers into thinking that it produced high quality goods (when in fact it produces low quality goods)?
(f) Consider a level of advertising that costs a?. For what levels of a? do you think that it is an equilibrium for high quality firms to advertise and low quality firms to not advertise?
(g) Given the information asymmetry between consumers and firms in period 1, might it be efficient for such advertising to take place?
(h) We often see firms sponsor sporting events— and it is difficult to explain such sponsorships as “informational advertising” in the way we discussed such advertising in the text. Why? How can the model in this exercise nevertheless be rationalized as informational advertising (rather than simply image marketing)?
B: Suppose that a firm is a high quality firm h with probability ? and a low quality firm ? with probability (1??). Firm h produces an output of quality that is valued by consumers at 4 while firm ? produces an output of quality 1 (that is valued by consumers at 1), and both incur a marginal cost equal to 1 per unit of output produced. (Assume no fixed costs.)
(a) Derive the level of a? of advertising (as defined in part A) that could take place in equilibrium.
(b) The most efficient such equilibrium is one where a? = 3. (c) Do your answers thus far depend on ??
(d) The equilibria you have identified so far are separating equilibria because the two types of firms behave differently in equilibrium — thus allowing consumers to learn from observing advertising whether or not a firm is producing a high or low quality good. Consider now whether both firms choosing (p, a) — and firms thus playing a pooling strategy — could be part of an equilibrium. Why is period 2 large irrelevant for thinking about this?
(e) If the firms play the pooling strategy (p, a), what is the consumer’s expected payoff from buying in period 1? In terms of ?, what does this imply is the highest price p that could be part of the pooling equilibrium?
(f) Suppose consumers believe a firm to be a low quality firm if it deviates from the pooling strategy. If one of the firms has an incentive to deviate from the pooling strategy, which one would it be? What does this imply about the lowest that p can be relative to a in order for (p, a) to be part of a pooling equilibrium?
(h) In equilibrium, consumers will see (p, a) from both types of firms — and will thus not be able to update their beliefs from the initial ? with which high quality was assigned (by Nature) to the firm. Thus, when the time comes to buy or not to buy in period 1, the consumer believes she is facing a high quality firm with probability ? and a low quality firm with probability (1??). Beliefs about what type the firm is if it does not play (p, a) in the first stage of the game are “out-of-equilibrium” in the sense that they do not happen in equilibirum. Bayes rule therefore does not tell us anything about how consumers would update their beliefs—and any beliefs can therefore be equilibrium beliefs. But the equilibrium requires that consumers interpret a deviation from the pooling strategy as the actions of a low quality firm. (i) Can advertising in a pooling equilibrium ever be efficient?
(i) Can advertising in a pooling equilibrium ever be efficient?