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A farmer can either invest in irrigation for their farm or not. There's a 30% chance that they will receive adequate rain such that the irrigation is not necessary, and a 70% chance that the irrigation will be useful if acquired. Assume that the farmer will receive $5,000 if their crops are adequately watered, and $1,000 otherwise. Irrigation costs $3,000. For simplicity, assume this is a one-off game and that nature is not perverse.
a. Draw the extensive form of this game, with the farmer acting first and nature second.
b. What is the expected value of each strategy for the farmer?
c. What is the expected value of perfect information on the weather?
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