Question

A highway contractor owns heavy equipment which is used during the warm weather. During the winter months the equipment is to be stored. Two options are available for the coming year. One is to store the equipment in an area owned by the company and located on the flood plain of a small stream. If not used, this area can be rented to another company for $10,000 per year. The other option is to rent a protected area for $35,000 per year. If the contractor stores the equipment at its own area and a severe flood occurs the equipment will be destroyed at a loss of $600,000 with probability 0.50 (high damage) and $400,000 with probability 0.50 (low damage). Of course, if there is no flood there is no damage. If the contractor rents a space there is no damage during a flood.

a. What is the probability of the "25-year" flood taking place in any given year?

b. Which alternative should the contractor choose, assuming that the probability of a damaging flood occurring during the winter is 0.02?

c. What is the indifference probability p of a damaging flooding (assume that the probabilities of high or low damage remain the same at 0.50)

Answer 1

a) 0.04

b) The choice of renting a protected area should be made

c) Indifference probability, P = 0.25

Explanation:

a) Probability that the 25-year flood takes place in a given year.

This means that the flood is taking place once in 25 years, and the probability that it takes place in this given year is 1/25 = 0.04

b) The contractor is left with two alternatives, either to stay in protected area or flood plain area.

We will calculate the cost of staying in protected area and the loss incurred if he stays in the flood plain area. The one with the lesser value will be the more preferred decision.

Probability of a damaging flood, pr (flood) = 0.02

Probability of high damage if he chooses the flood plain = 0.5

Pr(high damage) = 0.02 * 0.5 = 0.01

Probability of low damage if he chooses the flood plain = 0.5

Pr(low damage) = 0.02 * 0.5 = 0.01

Loss(low damage) = $400,000

Loss(High damage) = %600,000

Average loss = [Pr(low damage)*Loss(low damage)] + [Pr(high damage) *Loss(High damage) ]

Average loss = (400000*0.01) + (600000*0.1)

Average loss = 4000 + 6000

Average loss = $10,000

Winter lasts for three months, i.e number of months = 3

Therefore the costs of renting the areas should be charged per month

Cost of renting flood plain = $10000 per year = 10000/12 = $833.22/month

Cost of renting protected area = $35000 per month = 35000/12 = $2916.67/month

The protected area is not used

Cost of rent for 1 month = $2916.67 - $833.22

Cost of rent for 1 month = $2083.45

Cost of renting protected area in 3 months = 3 * 2083.45 = $6250.34

Since the cost of renting protected area is less than the loss incurred in flood plain area, the contractor should rent a protected area

c)The principle of indifference states that in the absence of any relevant evidence, agents should distribute their credence equally among all the possible outcomes under consideration.

The probability of high or low damage = 0.50

Since there are just two options, and indifference does not assign probabilities based on prior information

Probability(flood) = 0.5

Probability that a flood with high damage will occur = Probability (flood) * Pr(high damage) = 0.5 * 0.5 = 0.25

Probability that a flood with low damage will occur = Probability (flood) * Pr(low damage) = 0.5 * 0.5 = 0.25