Consider a farmer faced with the option of choosing three different cultivars. Each has an independent probability of 0.10 of succumbing to disease.
(a) Enumerate (a simple table is best) all of the possible event outcomes, using “Win” and “Lose” to denote survival (W) or failure to survive (L) disease. Be sure to include both the probability and resulting payoff associated with each of the events.
(b) Given that the risk-averse farmer has utility function u(p) = p 1/2 (where p is the payoff), add a column to your table that shows expected utility.
(c) Determine whether the farmer prefers having three cultivars over two cultivars.
(d) What is the certainty equivalent of this three-cultivar option, and how does it compare to one- and two-cultivar options?