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Suppose there are 125 risk averse individuals, each with a $1 to invest in a project at t = 0.The project will yield $1 if liquidated at t = 1 and $2.20 if liquidated at t = 2.At t = 0, no individual knows what his type will be at t = 1.If he turns out to be type D, his utility taction for consumption will be while if he turns out to be type L, his utility for consumption will be .It is known at t = 0 that 40% of the individuals will type D and 60% type L at t = 1.
-Suppose you are a type L depositor.You assume that all other depositor will withdraw at t = 2.Should you withdraw at t = 1 or t = 2?

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Suppose there are 125 risk averse individuals, each with a $1 to invest in a project at t = 0.The project will yield $1 if liquidated at t = 1 and $2.20 if liquidated at t = 2.At t = 0, no individual knows what his type will be at t = 1.If he turns out to be type D, his utility taction for consumption will be while if he turns out to be type L, his utility for consumption will be .It is known at t = 0 that 40% of the individuals will type D and 60% type L at t = 1.
-Suppose you are a type L depositor.You assume that all other depositor will withdraw at t = 2.Should you withdraw at t = 1 or t = 2?

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The payoff from withdrawing at t = 2 is $2.20, while the payoff from withdrawing at t = 1 is $1.00. The difference between these two payoffs is $1.20. However, the depositor is risk averse, so he values the certainty of a lower payoff at t = 1 more than the possibility of a higher payoff at t = 2. The expected payoff from withdrawing at t = 1 is $0.60 * $1.00 + $0.40 * $0.00 = $0.60, while the expected payoff from withdrawing at t = 2 is $0.60 * $2.20 + $0.40 * $0.00 = $1.32. The difference between these two expected payoffs is $0.72. Therefore, the depositor should withdraw at t = 1.

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