Question

You are offered a job with a new startup or Accenture Global Health Consulting.   Accenture would pay you $40,000 for sure. The start-up will pay you one of two salaries based on firm performance. You determine that if you take the job at the start-up there is 50% chance you would earn $90,000 but also a 50% chance you earn only $6,400.

1. (5 points) If you made your job choice based on the expected income which job would you choose?
2. (5 points) If you made your job choice based on the expected utility of your income and your utility function is given by U = √I (utility is equal to the square root of income) what job would you choose?
3. (9 points) Under the expected utility model what is the lowest amount of no-risk income Accenture could offer you and still have you choose them over the start-up?
4. (10 points) Now assume (with the same utility function as in (b)) that you can hire an investment analyst who has inside information on how well the start-up will perform. You know that 50% of the time they will tell you that you will earn the $90,000 and 50% of the time they will tell you that you will earn $6,400. Once you pay for the information – you can then eliminate the uncertainty and they will tell you whether the startup will be successful. What is the maximum amount of money you would pay for this information.

Answer 1

a) expected income from startup

• (1/2)*90,000 + (1/2)*6,400

=45,000 + 3200 = 48200

Accenture expected income

• Since the probability of getting 40,000 is 1, thus expected income = 40,000 *1 = 40,000
• And, 48200 > 40,000 --->we will choose startup

b)

• Here utility from startup (190)<utility from Accenture(200)
• Thus, we will choose Accenture

c) we will choose Accenture until it gives us more utility than startup ( that is more than 190). By maximum, Accenture can reduce our income till our expected utility become equal to 191 atleast. In this scenario we will still choose accenture.

• Thus Accenture can decrease income by 3,519 (40,000 - 36,481) and still we will prefer to work at Accenture as it's expected utility (=191) is greater than startup expected utility (=190)