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A risk-neutral consumer is deciding whether to purchase a homogeneous product from one of two firms. One firm produces an unreliable product and the other a reliable product. At the time of the sale, the consumer is unable to distinguish between the two firms' products. From the consumer's perspective, there is an equal chance that a given firm's product is reliable or unreliable. The maximum amount this consumer will pay for an unreliable product is $0, while she will pay $250 for a reliable product.
a. Given this uncertainty, what is the most this consumer will pay to purchase one unit of this product?
b. How much will this consumer be willing to pay for the product if the firm offering the reliable product includes a warranty that will protect the consumer?
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