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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 type L depositor will withdraw at t = 1.How long will the queue of depositors have to be before you get nothing i.e., find a constant such that you get nothing if your number in the queue is greater than that constant)?

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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 type L depositor will withdraw at t = 1.How long will the queue of depositors have to be before you get nothing i.e., find a constant such that you get nothing if your number in the queue is greater than that constant)?

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At t = 1, 40% of the 125 individuals will be type D, which means 50 individuals (0.4 * 125 = 50) will be type D. Since type L depositors assume all other type L depositors will withdraw at t = 1, and you are a type L depositor, the project will be liquidated for these withdrawals. The total amount available for withdrawal at t = 1 is $125 (since each of the 125 individuals initially invested $1). The first 50 type D depositors will withdraw their $1, leaving $75 (125 - 50 = 75) for the type L depositors. Since each depositor withdraws $1, the 75th type L depositor will be the last to withdraw their $1 before the funds are depleted. Therefore, you get nothing if your number in the queue is greater than 75. However, the question seems to have a mistake in its formulation or in the provided choices, as none of the choices correctly matches this calculation. Given the choices, the closest (but incorrect based on the provided calculation) would be 78 (C), but based on the logic provided, none of the options accurately reflect the correct answer. The correct approach, however, involves calculating the number of depositors who can withdraw before the funds run out, which would be 75 based on the given scenario. This discrepancy suggests there might be a misunderstanding in the interpretation of the question or a mistake in the question or answer choices themselves.

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