In the lectures, we discussed the Greek philosopher Thales, who used derivatives to generate a profit from Attica's olive orchards. Suppose that the probability of a good harvest is 80%, while the probability of a bad harvest is 20%. In a good harvest, olives sell for 50 drachmas per ton; in a bad harvest, they sell for 5 drachmas per ton. Thales signs his contracts with olive farmers in the wintertime, well before the harvest. Thales is risk-neutral.

2. Thales contracts with all of Attica's olive farmers for all of their olives. He agrees to pay the farmers 10 drachmas per ton of olives upon harvesting. This is a forward contract, with no deposit or other transaction fees. What is Thales's expected profit per ton of olives?

(A) 51 drachmas. (B) 41 drachmas. (C) 31 drachmas. (D) 21 drachmas.

3. Instead, suppose that Thales negotiates a call option with the farmers for a 2 drachma per ton premium. Otherwise, the terms are the same as in question 2 above. If there is a bad harvest, Thales does not execute the option to buy. What is Thales's expected profit per ton of olives?

(A) 41 drachmas. (B) 40 drachmas. (C) 39 drachmas. (D) 38 drachmas.

4. Now suppose that Thales has a forward contract to purchase from farmers at 10 drachmas per ton, along with a put option to sell to suppliers at 30 drachmas per ton. The put option has a premium of 3 drachmas per ton. What is Thales's expected profit per ton?

(A) 35 drachmas. (B) 33 drachmas. (C) 31 drachmas. (D) 28 drachmas.