# Exercise 1 of Microeconomics I

Universitat Pompeu Fabra, 1998/1999

Due October 7, 1998

1. A mother's utility function is increasing in her son's effort e in studying a course, and decreasing in the amount of money that she gives to her son (d). The utility function is Um=5e-d. The son's utility function is decreasing in his effort (e) and increasing in the money the he receives from his mother (d). His utility function is: Uh=d-e2. There are only three levels of effort: 1, 3 and 9.

1. Assume that the payment may be contingent on the effort level. (as the father may verify the effort level). What is the minimum amount of money that the mother has to pay in order to induce each level of effort? Given these amounts, what is the effort level that the mother would like to induce?

2. Assume now That the mother cannot make the payments contingent on the effort level, as it is not observable. The only observable is the final grade that the son receives in the course. It may be of two levels: pass (represented by 1) or fail (represented by 0) The value zero is obtained with probability (1-0.1e) and the value 1 with probability 0.1e. That is, the probability of passing increases in the effort level, but one cannot guarantee a passing grade. The mother pays an amount x in case the son passes and zero if he fails.

1. For each level of x, what is the utility of the son for each level of effort? What is the optimal effort for each level of x?
2. What is the mother's utility level for each level of x, given the optimal choices of her son; what will be the mother's choice of x?
3. Compare the answer to this question to the previous one, where the effort was observable.

3. "In 1990 the company [Iberia Seguros] decided to implement an ambitious expansion plan. In four years it expanded from 4,100 million pesetas in insurance policies, five offices, and 667 insurance agents in 1990, to 8,371 million pesetas in insurance policies, 20 offices, and 2.012 insurance agents in 1994. However, it created a large increase in management costs." El País, November 30, 1997.

1. Do you think the the increase in Iberia Seguros's costs may have related to the issues discussed in this course? Why?

4. Some employers would like to know the marital status of their employees (as they may think that it affects his/hers productivity). However, the society believes that employers should not use this information when hiring an employee. As a result there is a law that states that employers may not ask their employees this information.

1. Do you think that the law achieves its purpose?
2. Do you think that there may be another way to avoid discrimination based on marital status?

5. Some biologists claim that the fact that certain birds have feathers of very noticeable colors during the mating season is a result of a signaling game. Could you explain why?