Problem 1. Probability Distribution, Profit Maximization, Utility Maximization and Risk Assessment: A manager must determine which of two products to market. From market studies, the manager constructed the following payoff matrix of the present value of all future net profits under all the different possible states of the economy:

State of the economy	Product 1	Product 2
Probability	Profit ($)	Probability	Profit ($)
Boom	0.2	50	0.2	30
Normal	0.5	20	0.4	20
Recession	0.3	0	0.4	10

The manager's utility function for money is

U = 100M - M²

where U is the total utility of money (in utils) and M refers to the dollars of profit.

1. Determine if this manager a risk seeker, risk neutral, or a risk averter. Explain your answer.

1. If the manager's objective was profit maximization regardless of risk ( ), which product should the manager introduces? Explain your answer.

1. Evaluate the risk associated per dollar of profit with each product, i.e. find the coefficient of variation for each project.

1. If the manager's objectives were utility maximization, which product should the manager introduce? (Hint: in this section, you can assume the same probability distribution indicated in the table above.)

Problem 2.Certainty Equivalents. During the subprime mortgage crisis in the USA, the housing market suffered the worst slump in nearly two decades. Hot housing markets like Boston, Ft. Lauderdale-Florida, and Washington DC cooled as rising interest rates and tightened lending standards eliminated lots of potential buyers. With job losses in the auto industry, the housing downturn was especially serious in Detroit and surrounding areas. Suppose a real estate speculator ( ) seeking to profit from the downturn bought a pool of home mortgages for $1 million on the expectation of quickly selling them to out-of-town investors for $1.5 million. If the deal falls through , the speculator would be able to just as quickly dump the pool of home mortgages in the secondary market for $800,000.

1. Calculate the speculator's expected payoff if there is a 50/50 chance of successfully selling the pool of home mortgages to out-of-town investors.

1. Calculate the certainty equivalent adjustment factor for this investment. Is the speculator's decision to buy the pool of home mortgages consistent with risk-averse behavior?

Problem 3. Standard Normal Concept and Standardized Variables:Speedy Business Cards, Inc., supplies customized business cards to commercial and individual customers. The company is preparing a bid to supply cards to the Nationwide Realty Company, a large association of independent real estate agents. Because paper, ink, and other costs cannot be determined precisely. Speedy anticipates that costs will be normally distributed around a mean of $20 per unit (each 500-card order 500 ) with a standard deviation of $2 per unit.

1. What is the probability that Speedy will make a profit at a price of $20 per unit?

1. Calculate the unit price necessary to give Speedy a 95 per cent chance of making a profit on the order.

1. If Speedy submits a successful bid ( ) of $23 per unit, what is the probability that it will make a profit?