Question

The owner of a chicken processing plant makes $1,000,000 per year from his chicken processing plant, and $1,000,000 per year from other sources. He notices that a total of $30,000 worth of chickens per year are being taken home by his 100 employees to supplement their minimum wage living standards (this works out to less than $6 per week per employee). These chickens are being taken out through the fire safety doors, so the owner is considering blocking the doors permanently. This is against the law because any reasonable person knows that sealing fire doors kills people in the event of a fire. The probability of a fire is 0.01 per year (one percent per year). If a fire breaks out it will be discovered that the owner sealed the safety doors, and the owner will have to pay $F = 700, 000 worth of fines and legal fees. The owner's von NeumannMorgenstern utility function is u(x) = √x where x is the owner's income in a given year. The owner cares only about x.

Answer 1

1. 1,403.567

2. 1,411.473

3. Algebraic expression 0.99*2,000,000^0.5+0.01*(2,000,000-F)^0.05

4. 1,877,600

5. 1411.761

Step-by-step explanation:

1. Computation for the owner’s expected utility if he leaves the fire doors unsealed.

First step is to calculate the Owner's income if he leaves the doors unsealed

Owner's income if he leaves the doors unsealed=1,000,000 +1,000,000-30,000

Owner's income if he leaves the doors unsealed=1,970,000

Now let determine the expected utility if he leaves the doors unsealed

Expected utility=1,970,000^0.5

Expected utility=1,403.567

Therefore the expected utility if he leaves the doors unsealed will be 1,403.567

2. Calculation to determine the owner’s expected utility if he permanently seals the doors

First step is to calculate the The Owner's expected income if he seals the door

Owner's expected income if he seals the door=1,000,000 +1,000,000-700,000*0.01

Owner's expected income if he seals the door= 1,993,000

Now let calculate the Expected utility if he leaves the doors sealed

Expected utility if he leaves the doors sealed= 0.99*2,000,000^0.5+0.01*1,300,000^0.05

Expected utility if he leaves the doors sealed=1,411.473

Therefore The Expected utility if he leaves the doors sealed is 1,411.473

3. Calculation to determine the algebraic expression for the owner’s expected utility as a function

First step is to calculate the The owner's expected income with a fine F

Owner's expected income with a fine F= 1,000,000 +1,000,000-F*0.01

Owner's expected income with a fine F = 2,000,000-0.01F

Now let determine The algebraic expression for the owner's expected utility if he seals the door with a fine F

Algebraic expression= 0.99*2,000,000^0.5+0.01*(2,000,000-F)^0.05

Therefore The Algebraic expression is 0.99*2,000,000^0.5+0.01*(2,000,000-F)^0.05

4. Calculation to solve for the minimal fines and legal fees that will make the owner decide not to seal the doors using the expression from the previous problem and the owner’s expected utility if he leaves the fire doors unsealed

Based on the information given the owner may decide that he won't seal the door In a situation where the expected utility from sealing is as well equal to the expected utility from not sealing the door which was Calculated as:

0.99*2,000,000^0.5+0.01*(2,000,000-F)^0.05=1403.567

Now let calculate Fines and legal fees

Fines and legal fees=(2,000,000-F)^0.05=100(3.49857)= 349.857

Fines and legal fees=2,000,000-349.857^2=1,877,600

Therefore based on the above calculation in a situation were the Fines as well as the legal fees are equal to or higher than F=1,877,600 which means that the owner may decide not to seal the doors.

5. Calculation to Find the C that gives the plant owner complete coverage

First step is to calculate the owner expected utility will in a situation were the owner contributes $C to state politicians

Expected utility= 0.99*(2,000,000-C)^0.5+0.01*(1,300,000+100C)^0.05

Second step is to calculate the The plant owner complete coverage when 100C=700,000

Plant owner complete coverage=700,000/100

C=7000

Third step is to calculate what the owner will likely make this contribution if the expected utility is:

0.99*(2,000,000-C)^0.5+0.01*(1,300,000+100C)^0.05 is greater than 0.99*2,000,000^0.5+0.01*1,300,000^0.05

=1411.473

Hence,

0.99*(1,993,000)^0.5+0.01*(2,000,000)^0.05= 1411.761

Therefore the owner expected utility in a situation were the owner contributes $C to state politicians is 1411.761