Question

Problem 1: Suppose that a car-rental agency offers insurance for a week that costs $100. A minor fender bender will cost $3,500, whereas a major accident might cost $16,000 in repairs. Without the insurance, you would be personally liable for any damages. What should you do? Clearly, there are two decision alternatives: take the insurance, or do not take the insurance. The uncertain consequences, or events that might occur, are that you would not be involved in an accident, that you would be involved in a fender bender, or that you would be involved in a major accident. Develop a payoff table for this situation. What decision should you make using each of the following strategies?
a) aggressive strategy
b) conservative strategy
c) opportunity-loss strategy

Problem 2: The DoorCo Corporation is a leading manufacturer of garage doors. All doors are manufactured in their plant in Carmel, Indiana, and shipped to distribution centers or major customers. DoorCo recently acquired another manufacturer of garage doors, Wisconsin Door, and is considering moving its wood door operations to the Wisconsin plant. Key considerations in this decision are the transportation, labor, and production costs at the two plants. Complicating matters is the fact that marketing is predicting a decline in the demand for wood doors. The company developed the following three scenarios:
Scenario 1 (Probability of happening 0.15): Demand falls slightly, with no noticeable effect on production
Scenario 2 (Probability of happening 0.40): Demand and production decline 20%
Scenario 3 (Probability of happening 0.45): Demand and production decline 40%

Slight Decline 20% Decline 40% Decline Stay in Carmel $1,000,000 $800,000 $840,000 Move to Wisconsin $1,100,000 $950,000 $750,000

The following table shows the total costs under each decision and scenario.

Use this information to answer the following:
a) What is the Expected Value of the decision "Stay in Carmel"
b) What is the Expected Value of the decision "Move to Wisconsin"
c) Should DoorCo Stay in Carmel or Move to Wisconsin? Explain your answer.

Answer 1

The values in columns are cost, and therefore are negative payoffs

Option / state of nature	No accident	Fender bender	Major accident
Buy insurance	-100	-100	-100
Don't buy insurance	0	-3500	-16000

(i) Agressive strategy =Maximax = Max ( max payoff under each alternative) = Max ( -100,0) =0

which corresponds to buying of no insurance.

(ii) Conservative strategy Maximin = Max ( min payoff under each option)

= Max ( -100,-16000) =-100

which indicates towards buying insurance.

(iii) Minimax regret option

Option / state of nature	No accident	Fender bender	Major accident
Buy insurance	100	100	0
Don't buy insurance	0	3400	15900

Min ( max regret) = Min ( 100, 15900) = 100

which indicates towards buying insurance

2

EV of staying in Carmel = 0.15x1000000+0.4*800000+0.45*840000 = 848000

EV of moving in Wisconsin = 0.15x1100000+0.4*950000+0.45*750000 =882500

The cost is less in staying in carmel, so it is the preferred alternative.