Unit 4 : Utility Theory
What is the expected monetary value (EMV) if Allen has a 30% chance of winning a contract for $100,000 and 70% chance of winning another contract for $250,000?
$205,000
Which of the following cannot be Allen's certainty equivalent value if Allen has a 30% chance of winning a contract for $100,000 and 70% chance of winning another contract for $250,000?
$250,001 *** $350,000
What is risk premium?
(Expected monetary value (EMV)) − (Certainty equivalent)
What value is assigned to the worst payoff in the utility theory?
0
What is the range of utility function in the utility theory?
0 ≤ utility function ≤ 1
Which one of the following is incorrect regarding utility theory?
A person's utility function is always the same.
An increasing concave utility function implies which of the following? a. Loss avoidance, a loss is felt more strongly than an equal gain b. Increasing return to scale c. Law of diminishing returns d. Pareto principle that 80% of the effects comes from 20% of the causes e. The Peter principle that people rise to their level of incompetence
A, C
A call option on a stock gives the option holder the right but not the obligation to buy the stock at a specified price (called the strike price) for a specified time. Suppose that you buy an option with a strike price of $50 for a price of $4, and the expiration date is 3 months hence. If the stock rises above the strike price, you can get the difference. If the stock does not rise above the strike price, the option will expire worthless. Let your utility be the monetary value. Which of the following graphs represents the option?
D......................______________/
What is the value of risk premium for a risk avoider person? What is the value of risk premium for a risk prone person?
Greater than 0 Less than 0
Who has a risk premium of 0.50?
Risk indifferent person
A CONCAVE function is one that lies below the line connecting points, as shown on the following graph (OgreBot, 2015): In formulas, a function f is concave if, for any X1, X2, and tE[0,1] f(X1t+X2(1-t))=>tf(X1)+(1-t)f(X2) Suppose that a utility function of monetary return is concave. What does that imply about the attitude toward risk?
Risk-averse
Utility theory is one way of dealing with the fact that people often act in ways that defy the cramped vision of economists. Suppose that you prefer to take $20,000 over a bet that offers a 50% chance of winning $50,000 and a 50% chance of getting nothing. Are you risk-seeking, risk-averse, or risk-neutral? What is the risk premium?
Risk-averse, >5,000
A CONVEX function is one that lies below the line connecting points, as shown on the following graph (Osherovich, 2010): In formulas, a function f is convex if, for any X1, X2, and tE[0,1] f(X1t+X2(1-t))=<tf(X1)+(1-t)f(X2)
Risk-seeking
People sometimes act in ways that differ from the way that the imaginary profit-maximizing people of economic theory are expected to act. Utility theory is one way to account for this difference. Suppose that you prefer to take a bet that offered a 50% chance of winning $80,000 and a 50% chance of getting nothing over a sure payment of $45,000. Are you risk-seeking or risk-averse? What is the risk premium?
Risk-seeking, < -5,000
Suppose that you work for Acme Company and are considering a project that has the potential to add $100 to the company's profit. If the project goes badly, the profit is also reduced by $100. Based on the information that you have, there is a slightly less than 50% chance of the project succeeding. A big part of your compensation depends on a profit-sharing plan. The current projected profit is $1,300 (all profit figures are in millions), and if the company achieves this level of profit, you will get your base pay. For every unit above this, you will get a $100 bonus. So for example, if the profit is $1,310 you will get $1,000 as an additional bonus. On the other hand, if the profit falls below $1,300, you will not get any bonus, but your base salary will be unaffected. Using the bonus payment, what is the utility of getting $100 below the $1,300? What is the utility of achieving the $1,300? What about $1,400?
0, 0, 100
What value is assigned to the best payoff in the utility theory?
1
A put option on a stock gives the option holder the right but not the obligation to sell the stock at a specified price (called the strike price) for a specified time. Suppose that you buy a put option with a strike price of $50 for a price of $4, and the expiration date is 3 months hence. Including the cost of the put option, which of the following graphs shows the value of the option based on the stock price?
A .......................\_____
What is the value of certainty equivalent?
Between any two payoff values-
Although there are exceptions, a utility function will be __________ in general.
increasing and concave
