Question

1. Suppose Sara is risk averse and wants to insure her​ store, which is worth ​$120,000. There is a 25% probability that her store will burn next year. If a fire​ occurs, the store will be worth only ​$60,000. The local government assesses a property tax of ​$4,000 on​ Sara's store. If the tax is collected whether or not the store​ burns, how much fair insurance does Sara​ buy? If the tax is collected only if the store does not​ burn, how much fair insurance does Sara buy?
2. What type of risk behavior does the person exhibit who is willing to pay $5 for the chance to bet $60 on a game where 20% of the time the bet returns $100, and 80% of the time returns $50? Explain.

Answer 1

Answer :-

given :-

price of store = $120,000.

Probability of burn = 25%.

Price of store after burn = $60,000.

Property tax = $4000.

(1) :-

There is 25% probability that she will have store worth $60,000 and 75% probability that she will have store worth $120,000

Expected worth

= 25% x 60000 + 75% x 120000

= 25/100 x 60000 + 75/100 x 120000

= 25 x 600 + 75 x 1200

= 15000 + 90000

= 105000

[Expected worth = $105,000. ]

Property tax = $4000

So store price( after deducting tax)

= 120000 - 4000

= 116,000

Store price after burn = 60000 - 4000

= 56000

Case-1 :-

Expected worth

= 25% x 56000 + 75% x 116000

= 25/100 x 56000 + 75/100 x 116000

= 25 x 560 + 75 x 1160

= 14000 + 87000

= 101000

Expected worth = $101,000

116000 - 101000 = $15000

So she is willing to have maximum fair

insurance= $15,000.

Case-2 :-

Expected worth

= 25% x 60000 + 75% x 116000

= 25/100 x 60000 + 75/100 x 116000

= 25 x 600 + 75 x 1160

= 15000 + 87000

= 102000.

Expected worth = $102,000

116000 - 102000 = $14000

So, fair insurance = $14,000

(2)​​​​ :-

Expected return = 20% x 100 + 80% x 50

= 20/100 x 100 + 80/100 x 50

= 20 + 40

= 60

Expected return = $60.

So behavior of The person is  risk loving.

The expected return is the same whether the person is making a bet or not, however the person is willing to pay $5 to make the fair bet.