3. Consider a product that can be purchased for price p = 5 and fails with probability f. If the product fails, the consumer experiences a loss of f = 60, but each consumer obtains a gross benefit of & = 100 from consuming the product. Assume that consumer decisions are made by calculating the expected net benefits of consumption (i.e., what remains from the gross benefit after subtracting the purchase price and the expected value of losses, 6 - p - ff). Suppose initially that f = 0.2: then the consumer's expected net benefit of consuming the product is 100 -5 - (0.2)60 = 83.a) Suppose that the producer can reduce the probability of product failure from f = 0.2 to f' = 0.1. What is the impact of this safety improvement on consumer's net benefit from consumer the product? b) Suppose that the product safety improvement costs $5 per unit. Would a fully informed consumer be willing to pay an additional $5 for the safer product? Will it be socially beneficial for the firm to undertake this safety improvement? Explain. c) Suppose now that the probability a consumer will have the product fail is determined by both the product failure probability, f, but also by the consumer's level of care or recklessness (r) when using the product. If the consumer behaves carefully, r = 1, and if the consumer behaves recklessly, r = 2. Now, the consumer's expected net benefit is given by 6 -p - fre. If f = 0.2, what is the consumer's net benefit from consuming the product carefully versus recklessly? d) Supposing that f = 0.2 still, if using the product carefully has a cost to the consumer of c = 10 in lost utility (using it recklessly has no such cost), what is the consumer's net benefit from consuming the product carefully versus recklessly now? e) Suppose the cost of using the product carefully is the same as in part d), but improvements made to the product have cut the probability of failure in half (i.e., f = 0.1 ) while increasing the price to p = 10. In this setting, will the consumer behave carefully or recklessly? Demonstrate and explain your answer. f) Would your answer to part e) change if the price remained at p = $5 rather than increasing to $10? Demonstrate and explain your