In terms of reputation for quality, imagine that we have a firm that can produce a good at any quality level in the interval [0, 1], where 0 means a good of low quality, and 1 means a good of exceptionally high quality. Demand for the good depends on consumer perceptions of the good's quality. If consumers anticipate that the good is of quality q, their demand is given by · P. = 4 + 6q - X, where X is the quantity demanded. Costs of manufacture depend on the quality level of the good being produced; it costs a constant marginal 2 + 6q2 to produce a unit of quality level q. Consider the repeated setting described in section 14.5: In each period, the firm chooses a quality level and price. Consumers see the price but not (until after they have bought) the quality level. But consumers do know the level of qualities the firm has produced previously. Assume the firm discounts profits with a discount factor a = .9. For which levels of quality q is there a viable reputational equilibrium, that is, an equilibrium where (along the path) the firm produces in each period at quality level q?
In terms of reputation for quality, imagine that we have a firm that can produce a good at any quality level in the interval [0, 1], where 0 means a good of low quality, and 1 means a good of exceptionally high quality. Demand for the good depends on consumer perceptions of the good's quality. If consumers anticipate that the good is of quality q, their demand is given by · P. = 4 + 6q - X, where X is the quantity demanded. Costs of manufacture depend on the quality level of the good being produced; it costs a constant marginal 2 + 6q2 to produce a unit of quality level q. Consider the repeated setting described in section 14.5: In each period, the firm chooses a quality level and
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