You own a family farm, worth $500,000, and need to decide what to do with this years earnings of $400,000.

(i) You could put the money in the bank and earn a safe 5% return.

(ii) Or you could pay $200,000 to plant a new crop, which will yield a harvest in six months; if there is rain, the harvest will bring in $1.000,000 in revenues, but if there is a drought it will yield just $100,000 in revenues.

(iii) A third alternative is to plant Santo drought-resistant seed corn, which will cost $500,000, but yield revenues of $1,000,000 if there is rain or $700,000 if there is no rain.

You are risk averse, and your reference for family wealth (W) is given by U(W) = W [Square root of W]. The probability of a summer drought is 0.33.

Which of the three options should you choose? Explain.