14 – DISCOUNT RATE

Consider the A and B projects, which net benefits in time are given by the following table:

For a discount rate in discrete time of 5% per year, which project shall be chosen.

15 – DISCOUNT RATE

Consider a young man with 18 years old who is going to decide to make a high graduation. Assume that if he doesn’t make the graduation, he starts working at the 18’s with a annual revenue of $ 10.000, from the age of 18 to 65. Alternatively, he can make the graduation, with a $1.500 cost per year during 5 years, working from the 23 to the 65, with a annual revenue of $ 15.000.

For a discount rate in discrete time of 3% per year, which alternative shall be chosen by the young man. Discuss the result.

8 – DISCOUNT RATE

Suppose that the expected costs of a pollution control program are of 8 million dollars per year, and the benefits are of 50 million dollars per year in the first 50 years and 150 million dollars in the following years.

For a discount rate of 4% per year, which are the net benefits of this program? And for a rate of 2%? Comment the results.

Note: Consider a succession \[{{u}_{1}},...,{{u}_{n}},\ with\ {{u}_{i}}/{{u}_{i-1}}=r.\ So,\ \sum\limits_{i=1}^{n}{{{u}_{i}}}={{u}_{1}}\frac{1-{{r}^{n}}}{1-r}.\]

4 – DISCOUNT RATE

Usually, when the medium rate of consumption grow:

1. The discount rate grow;
2. The discount rate remains constant;
3. The discount rate drop;
4. It is not possible to establish a relation between the changes in the medium rate of consumption and the changes in the discount rate.

Justify.

A consequence of Slutsky’s Equation.

5 – DISCOUNT RATE

If we accept that the effect in the utility of an income variation doesn’t depend on people income, if a raise in the growth of the consumption rate occurs:

1. The discount rate grow;
2. The discount rate remains constant;
3. The discount rate drop;
4. It is not possible to establish a relation between the changes in the medium rate of consumption and the changes in the discount rate.

Justify.

6 – DISCOUNT RATE

If in the future we expect to be poor than we are today:

1. The discount rate of consumption will be surely positive;
2. The discount rate of consumption can be positive or negative;
3. The discount rate of consumption will be surely negative;
4. The consumption discount rate only depends on our impatience related to the future, being independent of our level of richness in the future.

Justify.

REVIEW QUESTIONS – Intermediate Microeconomics – Varian – Chapter 12 – Uncertainty

1. How can one reach the consumption points to the left of the endowment in figure 12.1?
   
2. Which of the following utility functions have the expected utility property?
   1. \[u\left( {{c}_{1}},{{c}_{2}},{{\pi }_{1}},{{\pi }_{2}} \right)=a\left( {{\pi }_{1}}{{c}_{1}}+{{\pi }_{2}}{{c}_{2}} \right)\]
   2. \[u\left( {{c}_{1}},{{c}_{2}},{{\pi }_{1}},{{\pi }_{2}} \right)={{\pi }_{1}}{{c}_{1}}+{{\pi }_{2}}c_{2}^{2}\]
   3. \[u\left( {{c}_{1}},{{c}_{2}},{{\pi }_{1}},{{\pi }_{2}} \right)={{\pi }_{1}}\ln {{c}_{1}}+{{\pi }_{2}}\ln {{c}_{2}}+17\]
3. A risk-averse individual is offered a choice between a gamble that pays $1000 with a probability of 25% and $100 with a probability of 75%, or a payment of $325. Which would he choose?
4. What if the payment was $320?
5. Draw a utility function that exhibits risk-loving behavior for small gambles and risk-averse behavior for larger gambles.
6. Why might a neighborhood group have a harder time self-insuring for flood damage versus fire damage?

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