Exam 6: Decision Making Under Uncertainty

Suppose that an actual (not perfectly reliable) credit report has the following characteristics based on historical data; in cases where the customer did not default on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 80%, while in cases where the customer defaulted on the approved loan, the probability of receiving a favorable recommendation on the basis of the credit investigation was 25%. Given this information, what are the posterior probabilities that an earthquake will and will not occur, given the geologists predictions?

Bayes' is useful in determining the value of perfect information (EVPI).

In decision trees, EMVs are calculated through a ____ process.

The expected value of perfect information (EVPI) is the difference between the EMV with perfect information and the EMV with no additional information.

Tyson Manufacturing (a maker of industrial products) is interested in marketing a new product. The company must decide whether to manufacture this product essentially on its own or employ a subcontractor to manufacture it. Below are two tables that represent the information related to the estimated probability distribution of the cost of one unit of this product under each alternative. Cost under "Make" alternative. Cost under "Buy" alternative. Assuming that Tyson seeks to minimize the expected unit cost of manufacturing of buying the new product, should the company make the new product or buy it from a subcontractor? Show your work.

In general, the expected monetary values (EMV) represent possible payoffs.

Which sensitivity analysis chart is most useful for seeing how the optimal decision changes as selected inputs vary?

Ms. Rich has just bought a new $30,000 car. As a reasonably safe driver, she believes that there is only a 5% chance of being in an accident in the forthcoming year. If she is involved in an accident, the damage to her new car depends on the severity of the accident. The probability distribution for the range of possible accidents and the corresponding damage amounts (in dollars) are shown in the table below. Ms. Rich is trying to decide whether she is willing to pay $170 each year for collision insurance with a $300 deductible. Note that with this type of insurance, she pays the first $300 in damages if she causes an accident, and the insurance company pays the remainder. Distribution of Accident Types and Corresponding Damage Amounts -Construct a decision tree to help Ms. Rich decide whether or not to purchase insurance. Note that the tree should minimize Ms. Rich's annual expected total cost, including the possible insurance premium, deductible payment, and damage payment. In your tree, make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.

If there is a 10% chance that one of the decision maker's family heirlooms, valued at $5,000, will be stolen during the next year, what is the most that she would be willing to pay each year for an insurance policy that completely covers the potential loss of her cherished items?

Decision trees are composed of nodes (circles, squares, and triangles) and branches (lines).

(A) Construct a decision tree to help the investor make his decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. (B) What is the best choice for the investor? Why? (C) Suppose that investor has an exponential utility function for final assets with a risk tolerance parameter equal to $60,000. Which investment opportunity will he prefer in this case? What is his certainty equivalent?

A buyer for a large sporting goods store chain must place orders for professional footballs with the football manufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decide in November how many footballs to order for sale during the upcoming late summer and fall months. Assume that each football costs the chain $45. Furthermore, assume that each pair can be sold for a retail price of $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for $35 each. The probability distribution of consumer demand for these footballs (in hundreds) during the upcoming season has been assessed by the market research specialists and is presented below. Finally, assume that the sporting goods store chain must purchase the footballs in lots of 100 units. -(A) What is the payoff if the store orders 400 footballs and quantity demanded is 400 footballs? (B) What is the payoff if the store orders 400 footballs and quantity demanded is 500 footballs? (C) What is the payoff if the store orders 400 footballs and quantity demanded is 600 footballs? ​(D) What is the payoff if the store orders 500 footballs and quantity demanded is 400 footballs? ​(E) What is the payoff if the store orders 500 footballs and quantity demanded is 500 footballs? ​(F) What is the payoff if the store orders 500 footballs and quantity demanded is 600 footballs? ​(G) What is the payoff if the store orders 600 footballs and quantity demanded is 400 footballs? ​(H) What is the payoff if the store orders 600 footballs and quantity demanded is 500 footballs? ​(I) What is the payoff if the store orders 600 footballs and quantity demanded is 600 footballs?

Which of the following statements are true?

In decision trees, a decision node (a square) is a time when the result of an uncertain event becomes known.

For a risk averse decision maker, the certainty equivalent is less than the expected monetary value (EMV).

Using a strategy region graph, determine what impact, if any, the probability of being in an accident has on her decision. Briefly explain your answer

The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altogether.

Suppose that an actual (not perfectly reliable) market research report has the following characteristics based on historical data: if the program is actually going to be a hit, there is a 90% chance that the market researchers will predict the program to be a hit, and if the program is actually going to be a flop, there is a 20% chance that the market researchers will predict the program to be a hit. Given this information, what are the posterior probabilities that a show will be a hit or a flop, given the market research report?

A risk profile is a chart that represents the probability distribution of monetary outcomes for any decisions.

The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars. Audience -Construct a decision tree to help the station identify its optimal format. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.