Farmer owns a farming business, which will make $150,000 per year if the weather is normal, but make $50,000 if there is a drought. There is an 80% chance that the weather is normal, and there is a 20% chance of a drought.

Suppose that the farmer can make a bet that there will be a drought at 3-1 odds, which means the following: If there is no drought, the farmer will lose what they bet. If there is a drought, they will get back whatever they bet, plus 3-times what they bet (thus if they bet $10,000 and there is no drought, they lose $10,000. If there is a drought, the farmer keeps the $10,000 bet, and is also paid an additional $30,000).

If the farmer chooses not to make a bet on the weather, what is the expected profit of the farming operation?

To hedge perfectly such that the farmer is indifferent to whether there is a drought, how much should the farmer bet that there will be a drought?

If the farmer bets $25,000 on the drought, what is the expected value of the operation?