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.

The 25-year flood occurs on average once every 25 years and has a probability of 1 over 25, or 4 percent

therefore ,

probability of the “25-year” flood taking place in any given year = 4% = 0.04

b.

if he choose to store in flood plains :

P(high damage) = P(high damage | flood)*P(flood) = 0.50*0.02 = 0.01

loss(high damage) = 600000 $

P(low damage) = P(low damage | flood)*P(flood) = 0.50*0.02 = 0.01

loss(low damage) = 400000 $

E(loss) = sum of loss * P(loss) = P(high damage)*loss(high damage) + P(low damage)*loss(low damage)

= 0.01*600000 + 0.01*400000

E(loss) = $ 10000

if he stores in protected area

rent of protected area = 35000$ per year = 35000/12 $ per month

rent of plain area = 10000$ per year = 10000/12 $ per month

cost = no. of months * (rent of protected area - rent of flood plain are(as it is unused))

= 3 * ( 35000/12 - 10000/12 )

cost (protected area) = $ 6250

cost (protected area) < E(loss in flood plain area)

therefore ,

the contractor should choose to store in protected area

c.

indifference probability : assign probability by just seeing number of options and not any other reason or logic

P(flood) = 1/2 {two options flood or no flood}

P(high damage flood) = P(high damage)*P(flood) = 0.5 * 1/2 = 0.25

P(low damage flood) = P(low damage)*P(flood) = 0.5 * 1/2 = 0.25

{this may seem illogical but this is t=the principle of indifference}

P.S. (please upvote if you find the answer satisfactory)

for further reference :

P.S. (please upvote if you find the answer satisfactory)