Theoretical Problem

A government employee can exert effort e ? [0,1] to produce a good. Effort has a cost ce²/2 and is unobservable. The probability that the good is produced is e and each citizen gets ?(?) utility for an arbitrary, given ? if the good is produced but 0 otherwise. One citizen is a monitor who can a cost ?m²/2 to observe whether the good was produced or not, and the monitor can successfully determine whether or not the good was produced with the probability ?. If he is successful, he pays a cost s to share the information with everyone else. If the government employee does not produce the good and the monitor informs everyone else, the government employee gets punished and has to pay ?. The timing of this game goes as follows:

• Monitor announces ?
• Government employee chooses ℯ
• Payoffs are realized

1. a) What happens to the equilibrium effort of the government employee if the arbitrary n decreases?
   17. The equilibrium increases because the equilibrium e is increasing in u
   18. The equilibrium increases because the equilibrium e is decreasing in u
   19. The equilibrium decreases because the equilibrium e is increasing in u
   20. The equilibrium decreases because the equilibrium e is decreasing in u
   21. The equilibrium decreases because the equilibrium e is decreasing in p
   22. The equilibrium decreases because the equilibrium e is increasing in p
   23. The equilibrium increases because the equilibrium e is decreasing in p
   24. The equilibrium increases because the equilibrium e is increasing in p

8. Recall that a rival good is a good that, when consumed by one person, cannot be consumed by another. An excludable good is a good that a person can be prevented from using, either through technology or by requiring a payment.

Which type of good is a common-pool resource (a fishing area is an example of a common-pool resource)?

8. 1. Rival and excludable
   2. Non-rival and non-excludable
   3. Rival and non-excludable
   4. Non-rival and excludable
9. Recall that a rival good is a good that, when consumed by one person, cannot be consumed by another. An excludable good is a good that a person can be prevented from using, either through technology or by requiring a payment.

Which type of good is a private good?

1. Rival and excludable
2. Non-rival and non-excludable
3. Rival and non-excludable
4. Non-rival and excludable

10. Recall that a rival good is a good that, cannot be consumed by another. An excludable good is a good that a person can be prevented from using, either through technology or by requiring a payment.

Now suppose that p is a function of n and u(n)=10 and p(n)=n. This set-up provides information to suggest that the good is mostly likely:

1. Rival
2. Non-rival
3. Excludable

11. In equilibrium when u(n)=10 and p(n)=n, how does the equilibrium level of m and e change as ? increases?
    1. ? increases and e decreases
    2. ? increases and e decreases
    3. ? and e both increase
    4. ? and e both decrease

1. Is the Capital Asset Pricing Model a good description of the way financial markets work during a global crisis? Justify your answer and explain why or why not.

2. Barber and Odean, in their 2002 Journal of Finance paper entitled “Trading Is Hazardous to Your Wealth: The Common Stock Investment Performance of Individual Investors” state that:

“Our most dramatic empirical evidence supports the view that overconfidence leads to excessive trading. On one hand, there is very little difference in the gross performance of households that trade frequently (with monthly turnover in excess of 8.8 percent) and those that trade infrequently. In contrast, households that trade frequently earn a net annualized geometric mean return of 11.4 percent, and those that trade infrequently earn 18.5 percent.” Attempt to explain these findings using the behavioural finance theory.

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1256 with a standard deviation of 41 years. The distribution of dates was more or less mound-shaped and symmetrical about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between   and   A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between and  A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between  and  A.D.

Suppose that the national average for the math portion of the College Board's SAT is 548. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places.

1. Suppose that the national average for the math portion of the College Board's SAT is 528. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores.

If required, round your answers to two decimal places. If your answer is negative use “minus sign”.

1. If you have an investment in a mutual fund, how can you determine the dollar value of your investment?

2. Which of the following are empirical asset pricing models? CAPM, FAMA FRENCH 3. BOTH, NEITHER

3. According to the CAPM, which of the following is true for a stock with a beta of 1.5? Its covariance with the market is greater than the variance of the market. Its expected return will be 50% more than the expected return of the market. Adding it to the market portfolio will reduce the risk of the market portfolio. All of these are true.

4. Which of the following are THEORETICAL asset pricing models? CAPM, FAMA FRENCH 3. BOTH, NEITHER

5. If most stocks go down in value when inflation expectations rise, you would expect the risk premium for inflation expectations to be ________ in a multifactor model.

Suppose that the national average for the math portion of the College Board's SAT is 535. The College Board periodically rescales the test scores such that the standard deviation is approximately 75. Answer the following questions using a bell-shaped distribution and the empirical rule for the math test scores. If required, round your answers to two decimal places.

(a) What percentage of students have an SAT math score greater than 610? ______%

(b) What percentage of students have an SAT math score greater than 685?______ %

(c) What percentage of students have an SAT math score between 460 and 535?______ %

(d) What is the z-score for a student with an SAT math score of 630?

(e) What is the z-score for a student with an SAT math score of 395?

Carbon, hydrogen, and oxygen are not the only elements that can be characterized by combustion analysis. If a compound also contains sulfur or nitrogen, then it will form CO_2?2?? (from the carbon), H_2?2??O (from the hydrogen), N_2?2?? (from any nitrogen), and SO_2?2?? (from any sulfur). The amount of oxygen in the original sample is determined from subtracting the masses of the other elements from the total, as in the combustion analysis described earlier. If a 0.500 g sample of a compound yields 0.814 g CO_2?2??, 0.204 g H_2?2??O, 0.0288 g N_2?2??, and 0.132 g SO_2?2?? when burned, then what is its empirical formula? Give your answer in the form C#H#N#O#S#, where the number is the subscript.

At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1252 with a standard deviation of 45 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.

(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between  and  A.D.

(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between  and  A.D.

(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between  and  A.D.

1. The composition of a compound is 34.6% carbon, 3.9% hydrogen, and 61.5% oxygen . What is the empirical formula of the compound?

2. A mixture consisting of 15.0 g of iron(II) sulfate and 15.0 g of sodium phosphate is reacted in the following reaction:

3 F e S O 4 ( a q ) + 2 N a 3 P O 4 ( a q ) ⟶ F e 3 ( P O 4 ) 2 ( s ) + 3 N a 2 S O 4 ( a q )

Formula weight of FeSO₄ = 151.91 g/mol

Formula weight of Na₃PO₄ = 163.94 g/mol

Formula weight of Na₂SO₄ = 119.05 g/mol

Answer the following two questions:

• What is the maximum number of grams of sodium sulfate that can be obtained?

• Calculate the grams remaining of the excess reactant.