(a) Do Propositions 8.2, 8.3, and 8.4 remain true when the domain of f is not the set

of all possible preference profiles, but some subset of this set, and when the range

of f is not necessarily A?

(b) Explain where and how we used in the proof of Proposition 8.5 the assumption

that A has three elements.

(c) Prove that if f is monotone and the range of f is A, then there cannot be a

preference profile R and an alternative a ? A such that aPi f (R) for all i ? I.

(d) Give an example of a dominant strategy incentive-compatible direct mechanism

on the set of all single-peaked preferences that is not dictatorial and different from

the direct mechanism described in the proof of Proposition 8.6.

(e) In the setting of Section 8.4 prove that a decision rule that picks the compromise

whenever that is efficient, and otherwise picks A and C with equal probability, is

not Bayesian incentive-compatible

a.Social Web Model: views business as a citizen of the society in which it operates and like all members of a society business must conform to the normal ethical duties and obligations that we all face.

i. Philosopher Norman Bowie has defended one version of CSR that would fall within this social web model.

1. Bowie argues that beyond the economic view's duty to obey the law business has an equally important ethical duty to respect human rights. Respecting human rights is the "moral minimum" that we expect of every person whether they are acting as individuals or within corporate institutions.

2. Bowie identifies his approach as a "Kantian" theory of business ethics. In simple terms he begins with the distinction between the ethical imperatives to cause no harm, to prevent harm, and to do good.

3. According to Bowie as long as managers comply with the moral minimum and cause no harm they have a responsibility to maximize profits.

4. Thus Bowie would argue that business has a social responsibility to respect the rights of its employees even when not specified or required by law. Such rights might include the right to safe and healthy workplaces rights to privacy and rights to due process.

5. But the contractual duty that managers have to stockholder-owners over-rides the responsibility to prevent harm or to do (philanthropic) good.

ii. Stakeholder Theory is perhaps the most influential version of CSR that would fall within the social web model.

1. Stakeholder theory begins with the recognition that every business decision affects a wide variety of people benefiting some and imposing costs on others; in other words that every business decision imposes costs on someone and that those costs must be acknowledged.

2. Any theory of corporate social responsibility must then explain and defend answers to the questions: for whose benefit and at whose costs should the business be managed?

3. The stakeholder theory argues on factual legal economic and ethical grounds that the economic model is an inadequate understanding of business.

a. As a descriptive account of business the classical model ignores over a century of legal precedent arising from both case law and legislative enactments.

b. As a matter of law it is simply false to claim that management can ignore duties to everyone but stockholders.

c. The wide variety of markets failures well-established in economics show that even when managers pursue profits there are no guarantees that they will serve the interests of either stockholders or the public.

d. But perhaps the most important argument in favor of the stakeholder theory rests in ethical considerations. The economic model appeals to two fundamental ethical norms for its justification: utilitarian considerations of social well-being and individual rights. On each of these normative accounts however due consideration must be given to all affected parties. Sometimes as the classical model would hold that balancing will require management to maximize stockholder interests. But sometimes not.

Suppose the function u(x) = In(x) where x is consumption represents your preference over gambles using an expected utility function. You have a probability 8 of getting consumption XB (bad state) and a probability 1-5 of getting XG state). (a) Find the certainty equivalent XCE of the gamble. a Hint: use the fact that aln(x) + Bln (x) = In(x) for any positive numbers X (b) Find the risk premium of the gamble. and X- (good