Exam 12: Decision Making Under Uncertainty

An individual is uncertain whether to bet on a football game. He believes that the probability of his team winning is 40%. If his team wins, he will receive $180. If his team loses, he'll pay $120. If the decision is based on the expected value criterion, then the individual will:

The probability of an outcome:

A financial analyst considers three funds. The funds' estimated returns depend on future economic conditions - summarized by outcomes A, B, C, or D. The table lists the probabilities of these outcomes and each fund's expected return for each outcome. (a) Which fund has the greatest expected monetary return? (b) Comment on the appropriateness of the expected-value criterion.

It is uncertain (odds are 50-50) whether Firm X will enter a new market in the next three months. Firm Y is thinking of entering the same market but won't be ready to do so for six months. Firm Y expects to earn $4 million if it is the sole market supplier but will lose $6 million if it must share the market with Firm X. If Firm X employs an optimal entry strategy, its overall expected profit (before Firm X has made its move is:

A manager who chooses among options by applying the expected value criterion is:

A firm supplies aircraft engines to the government and to private firms. It must decide between two mutually exclusive contracts. If it contracts with a private firm, its profit will be $2 million, $1 million, or -$1 million with probabilities .25, .4, and .35, respectively. If it contracts with the government, its profit will be $4 million or -$2.5 million with respective probabilities .4 and .6. Which contract offers the greater expected profit or loss?

A firm might be liable for $10 million if a lawsuit is brought against it. The firm judges that the probability the suit will be brought is .6. In addition, it believes that its chance of winning such a suit (in which case it owes $0) is .7. The firm's overall expected liability is:

A manufacturer of air-conditioning systems expects to sell 10,000 units next year if the economy recovers from the present recession. If the economy remains at its present state, the firm expects to sell 7,000 units, and if the recession worsens, sales will fall to 3,000 units. A survey of 40 economists reveals that 30 of them are forecasting recovery, 5 of them are expecting no change, and the rest expect a worse recession. Estimate the expected sales of air-conditioning systems for next year.

Which of the following is true of a decision tree?

The expected profit determined from a decision tree is the weighted average of all possible outcomes. The weights represent the:

Which of the following is a feature of the expected-value standard?

Define uncertainty with an example.

The following is the distribution of outcomes from two alternative advertising strategies: $\quad$ $\quad$ $\quad$ $\quad$$\text { STRATEGY X }$ PROBABDTTY REVENUE 0.2 \ 100,000 0.4 \ 200,000 0.4 \ 300,000 0.2 \ 400,000 $\quad$ $\quad$ $\quad$ $\quad$ $\text { STRATEGY Y }$ PROBABMTTY REVENUE 0.1 \ 50,000 0.2 \ 60,000 0.4 \ 300,000 0.2 \ 600,000 0.1 \ 800,000 Which strategy is the riskier strategy? Explain.

Based on the following utility schedule determine the decision maker's attitude toward risk. $\quad$ $\quad$ $\quad$ $\quad$$\text { UTILITY SCHEDULE }$ MONEY(000's) UTILITY INDEX 10 5 20 10 30 15 40 20 50 25

A firm must decide whether to launch a new product before knowing whether sales demand will be strong or weak. In addition, depending on how demand unfolds, the firm has the flexibility to set either a high price or a low price. The best order in which to draw the firm's decision tree is:

You are the chief appraiser for a large art dealer in a major American city. You are offered a chance to examine, and buy, a work of art. You have reason to believe that it is a piece from a famous artist of the 15th century that has been lost to the art world for hundreds of years. Such a painting would have an estimated market value of $1 million. However, you face two risks. First, the painting may be a forgery, a chance that you estimate to be .4. Second, even if the painting is authentic it may be stolen. Once you buy the painting, you bear all risk. If it is a fake, its value is $0. If it proves to be stolen (a .2 risk in your estimation), you must return the painting to its rightful owner and you cannot recover the purchase price. (a) You have the chance to buy the painting for $500,000. As a risk-neutral decision maker, should you make the purchase? (b) Suppose you can buy insurance against the risk of theft. You pay a premium of $20,000, and the insurance company compensates you according to your purchase price if the work proves to be stolen. Should you buy the painting for $500,000?

Consider a situation where an insurance contract has a negative expected value for the purchaser. Under this insurance policy, the premium paid exceeds the expected payout. Is it rational to buy this insurance? Give explanation with reason.

An individual is risk neutral if her utility curve for wealth is:

An individual has a utility of money function U = 20 +.5M and considers two options: Option 1: Invest $100,000 in a building plot, which will be sold for $150,000 if interest rates decrease or for $80,000 the interest rates do not change. Option 2: Invest the same $100,000 in bonds, which will be worth $135,000 if interest rates decrease, and $100,000 if the interest rates remain the same. The consensus among economic forecasters is that interest rates have an 80% chance of decreasing and 20% chance of remaining constant. Which investment option will this individual select?

A manager's utility of money schedule is (monetary amounts are in $,000s): MONEY UTILITY 100 10 200 18 300 25 400 30 500 32 Two investment opportunities have the following net present values (again in $000s): (a) Select the optimal investment based on the expected-value criterion. (b) Make your selection using the expected-utility criterion. (c) Comment on the difference in your answers in part (a) and (b).