You have been hired as an agent representing Johnny Baseball. Johnny doesn't care about risk, but he discounts the future at a rate of 10% per year.

Johnny has an offer of $20 million a year for the four years 0 through 3 from the Red Sox.

1. The Guardians are going to make Johnny an offer where he plays in the minor league for year zero at $1 million and then plays for 3 years at a constant salary. How large does that salary need to be for Johnny to take it over the Red Sox offer?

Johnny's prospects are uncertain. If Johnny were to strike a new 2-year contract after two years of play on the open market, there is a 50% it would be for $20m a year, a 25% change it would be for $30 million a year, and a 25% change it would be for $10m. These are the values to the Guardians and the values he could get on the open market.

1. The Guardians want to offer Johnny a contract that pays a fixed amount per year for years 0 and 1, and then gives the team the option (but not obligation) to sign him for $20m a year for year 2 and 3. How large does that fixed amount in year 0 and 1 need to be for Johnny to take it over the Red Sox offer?

1. The Guardians want to offer Johnny a contract that pays a fixed amount per year for years 0 and 1, and then gives Johnny the option (but not obligation) to sign up for $20m a year in year 2 and 3. How small can the fixed amount in year 0 and 1 be for Johnny to take it over the Red Sox offer?