EC260 Chapter Notes - Chapter 14: Risk Premium, Utility, Risk Neutral

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6 Sep 2016

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We define risk as a hazard or chance of experiencing a loss. We define probability as the likelihood or chance that an event will take place. If r is the number of times we repeat an experiment (i. e. , rolling a single dice) and r is the number of times the outcome a occurs, then the probability of a is defined as: In rolling a single die, the probability of obtaining any of the six possible outcomes will be 1/6. This is called the frequency definition of probability. Since it is sometimes impossible or unrealistic to repeat an experiment over and over again, managerial economists use a subjective definition of probability. According to this definition, the probability of a certain outcome is the degree of confidence a manager has that the outcome will occur. The probabilities of all possible outcomes must sum to one.

Related Questions

1- Two friends on a trip, A and B, meet by chance and want to dine together, although both recognize that A prefers to eat at Chili's and B prefers to eat at Steak-n-Shake. Each wonders what to say and accept in negotiating a joint decision. Let O₁ = both eat at Stake-n-Shake, O₂ = A eats at Stake-n-Shake and B eats at Chili's, O₃ = B eats at Stake-n-Shake and A at Chili's, and O₄ = both eat at Chili.

Write an ordinal utility function for each of the friends in respect of the possible outcomes:

Friend A: u_A(O₁) = Friend B: u_B(O₁) =

u_A(O₂) = u_B(O₂) =

u_A(O₃) = u_B(O₃) =

u_A(O₄) = u_B(O₄) =

Construct a 2 x 2 matrix that models this situation, including players, strategies, and the ordinal utilities of each player over the possible outcomes. Make sure you label everything (i.e., strategies, players, etc.).

2- Using the situation described above:

Construct an interval utility function for each player, assuming the following: A is indifferent between (i) its second most preferred outcome and a lottery composed of a .6 chance of its most preferred outcome and a .4 chance of its least preferred outcome, and (ii) A is indifferent between its third-most preferred outcome and a lottery with a .9 chance of its second most preferred outcome and a .1 chance of its least preferred outcome. However, B is indifferent between (i) its second most preferred outcome and a lottery composed of a .7 chance of its most preferred outcome and a .3 chance of its least preferred outcome, and (ii) B is indifferent between its third-most preferred outcome and a lottery with a .8 chance of its second most preferred outcome and a .2 chance of its least preferred outcome.

Construct a 2 x 2 matrix that models the situation, as described above, including players, strategies, and the interval utilities of each player for the possible outcomes.

3- An angry faction, A, is considering whether or not to challenge a status quo power, B, by highjacking B's plane and threatening to kill the passengers if B does not release some terrorists previously imprisoned by B, and whether to carry out its threat or release the passengers if B does not concede to its demands, were the demands made. Let the possible outcomes be: O₁ = A does not highjack the plane, O₂ = The passengers are saved after B releases the imprisoned terrorists in response to the threat made by A, O₃ = the passengers are killed by A after B refuses to submit to A's demand for the release of prisoners, O₄ = the passengers are released by A after B refuses to submit to A's demands. Assume (a) that the best outcome for B, but the worst for A, is for the passengers on the plane to be released after a highjacking, given the reputation for toughness B would gain at A's expense, (b) that the best outcome for A would be for B to release the prisoners after A makes its threat, (c) that A prefers to kill the passengers after a failed attempt to obtain the release of the terrorists over doing nothing at all to obtain the release of the terrorists, and (d), of course, B prefers having to do nothing to have to concede to A's demands, if A decides to challenge B.

Write an ordinal utility function for the angry faction and the status quo power in respect of those outcomes:

Angry A: u_A(O₁) = Power B: u_B(O₁) =

u_A(O₂) = u_B(O₂) =

u_A(O₃) = u_B(O₃) =

u_A(O₄) = u_B(O₄) =

b. Construct a 2 x 2 matrix that models this situation, including players, strategies, and the ordinal utilities of each player over the possible outcomes. Make sure you label everything (i.e., strategies, players, etc.).

4- Why, as game theorists, do we want to obtain an interval measurement of preferences rather than an ordinal measurement? In particular, what does an interval measurement allow us to do that an ordinal measurement doesn't? Are there any limitations on interval measurements? Be specific.

5- What is the difference between decisions under risk and decisions under certainty? What significance does this have for the relevant decision principles for a given game? If a decision principle used for games under uncertainty is applied to a game under risk and it contradicts the decision principle normally used for games under risk, which decision principle should be used, and why? Give an example.

6- Name the two types of irrational actions and explain what they are. Give an example of each. What relevance do irrationalities have for game theory?

7- Josiah, a young man, is considering whether or not to ask Lydia to go to prom with him. Lydia is either willing to go with him or not. Josiah surmises that there is a .6 chance that Lydia would say yes. If Josiah does not ask Lydia out, he will find out whether or not she would have accepted his offer afterward. Let O₁ = Josiah asks and Lydia accepts, O₂ = Josiah asks and Lydia denies, O₃ = Josiah doesn't ask and Lydia would have accepted, and O₄ = Josiah doesn't ask and Lydia wouldn't have accepted. Josiah prefers O₁ to O₄, O₄ to O₃, and O₃ to O₂. That is, O₁ > O₄ > O₃ > O₂.

a) Assume that Josiah is indifferent between O₄ and a lottery with a .9 chance of O₁ and a .1 chance of O₂, and likewise assume that he is indifferent between O₃ and a lottery with a .4 chance of O₁ and a .6 chance of O₂. Construct an interval utility function for Josiah over the respective outcomes:

Josiah: u(O₁) =

u(O₂) =

u(O₃) =

u(O₄) =

b) Use these utilities to construct a 2 X 2 matrix representing the situation. Use the Bayesian decision principle to determine which strategy Josiah would take, were he rational.

c) We treated this game as a game against nature, or a parametric game, rather than a strategic game. Which of these two types of games would be a more realistic model of the described situation? Why or why not?

8- It's Saturday night and Josiah is trying to decide where to take his new girlfriend, Lydia, out to dinner. He has two options: Taco Bell and Macaroni Grill. Lydia prefers Macaroni Grill to Taco Bell, and Josiah prefers what Lydia prefers. There is a problem, however. Martin works at both Taco Bell and Macaroni Grill, and he is practically Josiah's stalker. If Josiah is anywhere near Martin, Martin will find Josiah and ruin dinner for Lydia, which is all that Josiah cares about. Luckily, Martin is either at Macaroni Grill or Taco Bell, not both. Unluckily, neither Josiah nor Lydia has any idea which restaurant Martin is working at or any way of finding out. Lydia prefers eating at Taco Bell without putting up with Martin to eating at Macaroni Grill while putting up with Martin. If Lydia has to put up with Martin, she would still rather eat at Macaroni Grill than Taco Bell.

a) What are the relevant outcomes?

O₁ =

O₂ =

O₃ =

O₄ =

b) Construct an ordinal utility function for these outcomes. Remember, Josiah only cares about what Lydia prefers.

u(O₁) =

u(O₂) =

u(O₃) =

u(O₄) =

c) Construct a 2 X 2 matrix using the utilities from above. Consider two decision principles: maximin and the Bayesian decision principle + the principle of insufficient reason. Determine if each principle can actually be applied to this game. For any principle which does apply, use it to determine Josiah's rational strategy, if the principle recommends one.

9- Consider the following game between play S and player T.

	T1	T2	T3	T4
S1	1, -1	4, -4	10, -10	1, -1
S2	9, -9	5, -5	7, -7	6, -6
S3	3, -3	1, -1	8, -8	5, -5
S4	10, -10	3, -3	1, -1	2, -2

a) Determine the saddlepoint strategies of both players. Show your work.

b) Remove T4 and S4 from the game and determine the outcome using dominance reasoning. Show your work.

whiteherring176

Q5. Table 5.5

Total Output Total Costs

0 10

1 18

2 21

3 23

4 24

5 26

6 29

7 33

8 38

9 44

10 51

In Table 5.5, the marginal cost of the third unit is

a. 2.

b. 4.

c. 3.

d. 1.

Q6. When marginal physical product begins to decline, marginal cost begins to increase.

a. true

b. false

Q7. It is possible for a firm to have positive fixed cost and zero total cost.

a. true

b. false

Q8. Which one of the following is TRUE?

a. Marginal cost increases as marginal physical product decreases.

b. Marginal cost decreases as marginal product decreases.

c. Total cost is the difference between marginal cost and total variable cost.

d. Total cost is the sum of marginal cost plus total variable cost.

Q9. The slope of the production function becomes negative when diminishing returns set in.

a. true

b. false

Q10. Table 5.7

Q Total Variable Cost Average Variable Cost Total Cost Average Total Cost

1 10 50

2 50 90

3 40

Refer to Table 5.7. What is the firm's total fixed cost?

a. 20

b. 40

c. 10

d. 30

Q11. When there are economic profits in a perfectly competitive industry

a. firms have no incentive to exit or enter the industry.

b. firms exit the industry.

c. firms enter the industry.

d. the high barriers to entry prevent further competition.

Q12. The market structure of perfect competition is defined by hundreds of firms producing an essential product, with barriers to the entry of new firms.

a. true

b. false

Q13. A single supplier of a good or service for which there is no close substitute is referred to as a(n)

a. monopolistic competitor.

b. strategic competitor.

c. monopoly.

d. oligopoly.

Q14. For the perfectly competitive firm the selling price of its product is determined by

a. the length of time it has been in business.

b. the amount it chooses to spend on marketing.

c. the interaction of market supply and demand.

d. the number of competing firms.

Q15. A company finds that at the MR = MC output level, its total cost is $500, total variable cost is $400, and total revenue is $450. Your advice to the firm is to

a. reduce output to reduce the cost of production.

b. continue to produce, as total revenue covers total variable cost.

c. increase output to reduce the per unit cost of production.

d. shut down immediately.

Q16. For a monopolist

a. P > MR.

b. P = MC.

c. P = ATC.

d. P = MR.

Q17. The perfect competitor

a. chooses the profit-maximizing quantity.

b. chooses the profit-maximizing price.

c. chooses a quantity that will make the most efficient use of his labor and capital resources.

d. produces what he thinks can be sold, regardless of cost.

Q18. In perfect competition, the larger firms will be able to charge a higher price than the smaller firms.

a. true

b. false

Q19. For the perfectly competitive firm, price equals marginal revenue.

a. true

b. false

Q20. For a monopolist, selling more units requires

a. allowing more firms to enter the industry.

b. hiring a more productive labor force.

c. forming a cartel.

d. lowering the selling price.

Q21. Monopolistic competition means

a. monopolies from several countries compete in the global market.

b. a large number of firms producing differentiated products.

c. a large number of firms producing homogeneous products.

d. few firms producing differentiated products.

Q22. Opportunistic behavior is discouraged by the desire to have repeat transactions.

a. true

b. false

Q23. By saying that firms in an oligopoly are interdependent, we mean that

a. actions by one will prompt reactions by others.

b. if one increases its profits, all others will increase profits as well.

c. all firms sell identical products.

d. if one increases its profits, all others will lose profits.

Q24. Price leadership is a form of

a. barrier to entry.

b. tacit collusion.

c. opportunistic behavior.

d. noncooperative behavior.

Q25. A monopolistically competitive firm in the long run

a. earns positive economic profits.

b. earns negative economic profits.

c. earns zero economic profits.

d. suffers economic losses.

Q26. Monopolistically competitive firms produce a product that is homogeneous.

a. true

b. false

Q27. Which of the following is a characteristic of both perfect competition and monopolistic competition?

a. In the long run, the firm will produce the output which minimizes average total cost.

b. Firms sell a homogeneous product.

c. In the long run, the firm will earn zero economic profit.

d. The firm seeks to differentiate its product from those of its competitors.

Q28. A monopolistically competitive firm uses advertising to

a. lower its costs.

b. differentiate its product.

c. signal its competitors that it is serious about staying in business.

d. motivate its work force.

Q29. For the monopolistic competitor, which is INCORRECT?

a. The profit maximizing rate of output is where the marginal cost curve intersects the marginal revenue curve.

b. The marginal revenue curve is downward sloping and lies below the demand curve.

c. Because the firm has some control over price, its demand curve slopes downward.

d. If the firm in a monopolistically competitive industry were making economic losses, firms would enter the industry.

Q30. Which of the following is TRUE?

a. In the model of price leadership, the dominant firm consistently charges the lowest price.

b. Opportunistic behavior is discouraged by the desire to have repeat transactions.

c. The strategic dependence that characterizes oligopoly means that no firms can earn positive accounting profits.

d. Price wars are most common in perfect competition.

Q31. Antitrust legislation seeks to correct market failure by ensuring that all firms in the industry earn an economic profit.

a. true

b. false

Q32. Market failures arise when

a. people look out for their own best interests.

b. there is a gap between the social and private costs of producing or consuming a good.

c. firms look out for their own best interests.

d. society seeks to operate at a point on the production possibilities curve.

Q33. Cases prosecuted under the Sherman Antitrust Act are intended to correct market failure arising from negative externalities.

a. true

b. false

Q34.

Figure 8.2

Refer to Figure 8.2. The market equilibrium is Q1. Point Q2 represents the optimal point of production. To reach Q2,

a. consumption of the good could be taxed.

b. a subsidy could be given to consumers.

c. production of the good could be taxed.

d. the industry producing the good should operate as a cartel.

Q35. What would happen in a free market system when production of a good generates negative externalities?

a. There would be a shortage of the good.

b. The equilibrium quantity of the good would be more than the efficient amount.

c. The equilibrium quantity of the good would be less than the efficient amount.

d. There would be a surplus of the good.

Q36. If providing a service results in negative external costs, then

a. the market price is below the true opportunity cost of resources used to provide the service.

b. the market price is above the true opportunity cost of resources used to provide the service.

c. the market quantity is too low.

d. market forces will always correct the problem.

Q37. The problem of positive externalities can be addressed by having some firms exit the industry.

a. true

b. false

Q38. The first case prosecuted under the Sherman Act was the antitrust case against Microsoft.

a. true

b. false

Q39. If your marginal tax rate is always higher than your average tax rate, then the tax system is a

a. proportional tax system.

b. regressive tax system.

c. fair tax system.

d. progressive tax system.

Q40. Private goods are characterized by the principle of rival consumption.

a. true

b. false

Q41. Collective bargaining is the process by which unions and employers negotiate the conditions of employment and wages.

a. true

b. false

Q42. The marginal physical product of labor is the addition to total revenue a firm experiences when it hires one additional worker.

a. true

b. false

Q43. A firm's marginal revenue product of labor curve is also

a. its labor demand curve.

b. its total revenue line.

c. its long-run input cost function.

d. its marginal cost curve.

Q44. An increase in the selling price of a product

a. increases the supply of labor to the industry.

b. increases the productivity of labor.

c. raises the firm's demand for labor.

d. decreases the supply of labor to the industry.

Q45. If unions succeed at restricting the supply of labor in any one area of the economy, wages in that sector will increase.

a. true

b. false

Q46. The fact that the labor supply curve slopes upward indicates that

a. workers seek to work more hours when the wage rises.

b. the income effect of a wage increases outweighs the substitution effect.

c. workers seek to work more hours when the wage decreases.

d. firms want to hire more workers when the wage rises.

Q47. The upward slope of the labor supply curve suggests that the income effect of a wage increase outweighs the substitution effect.

a. true

b. false

Q48. The number of strikes occurring in U. S. firms has steadily increased over the past 25 years.

a. true

b. false

Q49. Suppose a perfectly competitive firm faces a labor market in which the going wage rate is $480 per week. If the last worker hired has a marginal physical product of 12 units of output per week, what is the selling price of the firm's output?

a. $40 per unit

b. $480 per unit

c. $240 per unit

d. $12 per unit

Q50. If workers in an industry become less productive due to low employee morale, we would expect the

a. demand for workers to decrease.

b. wages in the industry to increase.

c. supply of workers to increase.

d. demand for workers to increase.

EC260 Chapter Notes - Chapter 14: Risk Premium, Utility, Risk Neutral

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