Consider a game between a firm and a consumer. The firm's product may be of either...

 

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Consider a game between a firm and a consumer. The firm's product may be of either high or low quality (H or L). A prior, the probability of the product being a high-quality one is (0, 1). In addition, the firm incurs a cost CH (CL) when it supplies a high-quality (low-quality) product. The consumer, who is risk-neutral, desires to buy at most one unit of the product but cannot observe the quality of the product before purchase. The con- sumer's valuation for high- and low-quality products are v and v, respectively. Finally, the price of the firm's product is regulated and is set at p. Throughout the exercise, we assume that vH > P > VL > CH > CL > 0. (i) For a fixed price p, under what condition will the consumer buy the product? Suppose that before the consumer decides whether to buy, the firm (which knows the quality of its product) can advertise. Advertising conveys no information directly. How- ever, the consumer can observe the total amount of money that the firm is spending on advertising. (ii) Can there be a separating Perfect Bayesian Equilibrium (PBE), that is, an equilibrium in which the consumer rationally expects firms with different quality levels to pick different levels of advertising? (iii) Can there be a pooling PBE, that is, an equilibrium in which the consumer rationally expects firms with different quality levels to pick the same level of advertising? Consider a game between a firm and a consumer. The firm's product may be of either high or low quality (H or L). A prior, the probability of the product being a high-quality one is (0, 1). In addition, the firm incurs a cost CH (CL) when it supplies a high-quality (low-quality) product. The consumer, who is risk-neutral, desires to buy at most one unit of the product but cannot observe the quality of the product before purchase. The con- sumer's valuation for high- and low-quality products are v and v, respectively. Finally, the price of the firm's product is regulated and is set at p. Throughout the exercise, we assume that vH > P > VL > CH > CL > 0. (i) For a fixed price p, under what condition will the consumer buy the product? Suppose that before the consumer decides whether to buy, the firm (which knows the quality of its product) can advertise. Advertising conveys no information directly. How- ever, the consumer can observe the total amount of money that the firm is spending on advertising. (ii) Can there be a separating Perfect Bayesian Equilibrium (PBE), that is, an equilibrium in which the consumer rationally expects firms with different quality levels to pick different levels of advertising? (iii) Can there be a pooling PBE, that is, an equilibrium in which the consumer rationally expects firms with different quality levels to pick the same level of advertising?

Answer rating: 100% (QA)

i The consumer will buy the product if their expected utility from purchasing the product at price p is higher than their utility from not purchasing ... View the full answer