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Question 2. (30 points). The recognition that information problems can unravel markets is well-established. Here is another example, applied to a possible Coasian solution of the polluting firm problem. A polluting firm must decide whether to adopt a new cleaner technology, at some fixed cost cF, or do nothing. The technology has no other effect on the firm's profits, besides the fixed cost of adoption. The cost is higher the cleaner the technology, but only the firm knows the one technology it can really adopt. Thus the firm knows cF, but the rest of the world only knows that cF can take any value between 0 and some ceiling c?F, all with equal probability. In this problem, the counterpart to the firm is the village, represented by a single actor (for example, the mayor). The benefit of the new technology to the village depends on how clean it is, but in any case it is a multiple of its cost to the firm. The village's total benefit is: bV = rcF where r is a known parameter larger than 1. 1. (5 points). Is it socially efficient for the Firm to adopt the new technology? Does you answer depend on cF? 2. (3 points). What is the Village's expected benefit from the new technology? The firm has the legal right to remain with its current technology. However, it can be induced to change technology by receiving a transfer ?? from the Village. 3. Suppose first that a proposed transfer ??M is set by an external mediator. As everyone else, the mediator only knows that cF can take any value between 0 and some ceiling c?F, all with equal probability. a. (4 points). Under what condition on ??M will the Village accept to make the transfer? b. (4 points). Under what condition on ??M will the firm accept the transfer and change technology? 4. Suppose now that there is no mediator: the firm quotes the transfer it demands, ??F ? ?cF. a. (5 points). What is the expected benefit of the new technology to the village, given the firm's quoted transfer ??F? Why is it different from your answer to 2. above? b. (5 points). Will the village accept? Does your answer depend on r? Does it depend on cF? c. (4 points). Can we conclude that if adopting the new technology is efficient, it will be adopted? (For the curious among you, this is an application of the ideas in George Akerlof, "The Market for Lemons", Quarterly Journal of Economics, 1970).

Question 2. (30 points). The recognition that information problems can unravel markets is well-established. Here is another example, applied to a possible Coasian solution of the polluting firm problem.
A polluting firm must decide whether to adopt a new cleaner technology, at some fixed cost cF, or do nothing. The technology has no other effect on the firm's profits, besides the fixed cost of adoption. The cost is higher the cleaner the technology, but only the firm knows the one technology it can really adopt. Thus the firm knows cF, but the rest of the world only knows that cF can take any value between 0 and some ceiling c?F, all with equal probability. In this problem, the counterpart to the firm is the village, represented by a single actor (for example, the mayor). The benefit of the new technology to the village depends on how clean it is, but in any case it is a multiple of its cost to the firm. The village's total benefit is:
bV = rcF
where r is a known parameter larger than 1.
1. (5 points). Is it socially efficient for the Firm to adopt the new technology? Does you answer depend on cF?
2. (3 points). What is the Village's expected benefit from the new technology?
The firm has the legal right to remain with its current technology. However, it can be induced to change technology by receiving a transfer ?? from the Village.
3. Suppose first that a proposed transfer ??M is set by an external mediator. As everyone else, the mediator only knows that cF can take any value between 0 and some ceiling c?F, all with equal probability.
a. (4 points). Under what condition on ??M will the Village accept to make the transfer?
b. (4 points). Under what condition on ??M will the firm accept the transfer and change technology?
4. Suppose now that there is no mediator: the firm quotes the transfer it demands, ??F ? ?cF.
a. (5 points). What is the expected benefit of the new technology to the village, given the firm's quoted transfer ??F? Why is it different from your answer to 2. above?
b. (5 points). Will the village accept? Does your answer depend on r? Does it depend on cF?
c. (4 points). Can we conclude that if adopting the new technology is efficient, it will be adopted?
(For the curious among you, this is an application of the ideas in George Akerlof, "The Market for Lemons", Quarterly Journal of Economics, 1970).

Added by Sergio S.

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