Quiz 3: Distributive Justice and Autonomy

You wish to estimate the utility to you of earning the annual salaries in the left column of Table 3.1. You fix the utility of $10,000 arbitrarily at 15, and the utility of $40,000 arbitrarily at 25. You decide that you are indifferent between (a) receiving a sure salary of Q between $10,000 and $40,000 and (b) taking a chance of receiving $40,000 with probability p and $10,000 with probability 1 ? p , where Q and p are shown in the table. Calculate the utility of salaries $15,000, $20,000, and $30,000.

Now suppose you wish to estimate the utility of $5,000. You are indifferent between (a) receiving $10,000 for sure and (b) receiving $40,000 with probability p and $5,000 with probability 1 ? p , where p = 1/3. Use this to calculate the utility of $5,000. Hint. Suppose, in general, that you fix utilities for salaries Q 1 and Q 2 (here, $10,000 and $40,000, respectively) and wish to calculate the utility of some salary Q that is less than $10,000. If you are indifferent between (a) receiving Q 1 and (b) a lottery in which you receive Q 2 with probability p and Q with probability 1 ? p , then This allows you to solve for u ( Q )in terms of u ( Q 1 )and u ( Q 2 ).

Suppose you are indifferent between (a) receiving a salary of $40,000 for sure and (b) a lottery in which you receive $50,000 with probability p and $10,000 with probability 1 ? p , where p = 0.9. Use this fact to calculate the utility of $50,000.

Plot your utility curve using the results of the previous three exercises.

A drug is discovered that cures all mild cases of diabetes but has no effect on severe cases. It is therefore prescribed only for patients who have mild cases. Does this policy satisfy the Difference Principle?

Suppose the drug in the previous exercise cures all mild cases but has only a small positive effect on severe cases. The drug is in short supply, and to make the best use of it, it is prescribed only for patients with mild cases. Does this policy satisfy the Difference Principle?

Some provincial governments conduct daily lotteries. Studies have found that those who buy the lottery tickets are the poorest people in the province. Does this type of lottery satisfy the Difference Principle?

An economics game. A popular economics game teaches an important lesson in rationality. You are granted $100 along with the option of donating any portion of the grant (from $0 to $100) to an anonymous person. That person, to whom the donor is anonymous, is given the option of accepting or rejecting the donation. If the gift is rejected, both parties forfeit the money. No collusion is allowed. Clearly, rational self-interest requires that you donate a very small positive amount (say, one cent) and that the recipient accept it. If you donated zero, the recipient could reject it without penalty, but it is irrational to turn down even one cent. Actual behavior is quite different. The average donation tends to be in the range of $30-40, and close to half give away $50. This behavior is normally cited as a demonstration that people are irrational. Yet this follows only if rationality is interpreted in the narrow sense of rational self-interest. How can the observed behavior, particular the behavior of those who donate half the money, be seen as entirely rational from a Rawlsian perspective?