Warren Buffy is an enormously wealthy investor who has built his fortune through his legendary investing acumen. He currently has been offered three major investments and he would like to choose one. The first one is a conservative investment that would perform very well in an improving economy and only suffer a small loss in a worsening economy. The second is a speculative investment that would perform extremely well in an improving economy but would do very badly in a worsening economy. The third is a countercyclical investment that would lose some money in an improving economy but would perform well in a worsening economy.
Warren believes that there are three possible scenarios over the lives of these potential investments: (1) an improving economy, (2) a stable economy, and (3) a worsening economy. He is pessimistic about where the economy is headed, and so has assigned prior probabilities of 0.1, 0.5, and 0.4, respectively, to these three scenarios. He also estimates that his profits under these respective scenarios are those given by the following table:

Which investment should Warren make under each of the following criteria?
(a) Maximin payoff criterion.
(b) Maximum likelihood criterion.
(c) Bayes€™ decision rule.

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Improving Economy Stable Economy Worsening Ecomomy Conservative investment Speculative investment Countercyclical investment $30 million 5 million $10 million $40 million S10 million $30 million $15 milliorn -$10 million 0 Prior probability 0.1 0.5 0.4