Assuming the generic form from class, show algebraically that when consumers misperceive risk associated with products, the equilibrium outcome will differ from the efficient outcome. What is a solution to this?

(1) Assuming the generic form from class, show algebraically that when consumers misperceive risk
associated with products, the equilibrium outcome will differ from the efficient outcome. What is a
solution to this?
(2) Suppose the inverse demand and supply curves for Coca Cola are given by 𝐷=60−2𝑄 and 𝑆=𝑄.
There is .001 chance that a can of Coke will explode, causing $30,000 in damages. (a) If there is no
liability, what will be the market clearing price and quantity? If there is a strict liability rule, what will
be the market clearing price and quantity? What is the difference? Explain. (b) Suppose consumers
misperceive the damages of a can of coke exploding by $15,000. If there is no liability, what will be
the market clearing price and quantity? If there is a strict liability rule, what will be the market
clearing price and quantity? What is the difference? Explain.
(3) Suppose that there are two consumers who derive benefits from consuming one unit of a
dangerous product. Consumer A derives total benefits of $200; consumer B derives total benefits of
$100. The risk of an accident from consuming the product is .01, and the damages from an accident
are $5,000. Finally, the firm’s cost of producing the product is constant at $75 per unit. (a) Is it
efficient for the firm to produce and sell the product to consumer A? What about consumer B? (b)
Suppose that both consumers (and the firm) correctly perceive the risk of an accident. What is the
price of the product, and which consumer(s) purchases it under a rule of no liability? Under strict
liability? Which rule (or rules) yields the efficient outcome? (Assume the firm is competitive and sets
the price equal to its full expected cost per unit.) (c) Now suppose that both consumers misperceive
the risk of an accident to be .001. How does this change your answer to (b)? (Assume the firm
continues to perceive the risk correctly.)
(4) Workplace accident laws have been becoming stricter for employers. What are some inefficient
outcomes resulting from this change? Liability rules have become stricter for environmental
accidents, too. What are some of the negative consequences here?