3. Warranties as a signal of quality

Consumers wish to buy a product and get a utility 10 if the product is of high quality and is working, and a utility of 4 if the product is of low quality and is working. If a product does not work, then the utility from having it is 0 irrespective of its quality. Ex-ante, only the firm knows the quality of its product (but cannot choose it). Consumers expect that the product is of high/low quality with equal probabilities. The likelihood that a high quality will not work is 1/5 and the likelihood that a low quality product will not work is 4/5. The cost for the firm of replacing a product that does not work is c (this cost is independent of the product's quality)

1. Suppose the firm does not offer a warranty. What is the price that consumers will pay for the product?
2. Suppose that the firm does offer a warranty. What are the conditions on c such that offering a warranty can serve as a signal of high quality?
3. What happens if the conditions you found in (b) are violated?
4. Compare the profits of firms in (b) and in (c). Comment on your findings.