You are in charge of development for your housing nonprofit and two new grant opportunities have come to your attention. Unfortunately, both grant applications are due tomorrow and you will only have the time to write an application for one of them.
The first grant is sponsored by the county government. Assuming you choose to apply for this grant, your nonprofit will have a 40% chance of winning $450,000 in grant money, a 50% chance of winning $200,000 in grant money, and a 10% of receiving no grant money.
The second grant is sponsored by the federal government. While the monetary amounts associated with this grant are larger, the odds of a successful application are also lower. Assuming you choose to apply for this grant, your nonprofit will have a 20% chance of winning $1,000,000 in grant money, a 20% chance of winning $500,000 in grant money, and a 60% chance of receiving no grant money.
a. Assuming that your non-profit is risk-neutral, which grant should you apply for?
b. Assuming that your non-profit is risk-averse, with U(X)=sqrt(X) where X is the amount of grant money received, which grant should you apply for?