Hi there, I need help solving a problem and am unsure how to go about solving the question. It is a practive question from a textbook and am trying to understand it further. I need a bit more help solving 1 a) and b). I have already obtained the values of the expected return at t = 0 and the expected utilities at t = 0 for both scenarios (direct investing) and (depositing with the bank). Thanks Here is the question: Consider the basic setup of the Diamond-Dybvig (1983) model. Specifically, there are three periods, denoted t = 0, 1, 2, a single consumption good, and an illiquid investment opportunity that pays gross return 1.1 if liquidated at t = 1, or gross return 2.2 if liquidated at t = 2. There are 30 people in the economy, each endowed with 1 unit of the consumption good at t = 0. At t = 1, exactly 11 will randomly realize that they need to consume at t = 1 (the early consumers), the remaining 19 people will need to consume at t = 2 (the late consumers). The utility derived from consumption is 1 − (1/c1)2 for early consumers, 1 − (1/c2)2 for late consumers, where the subscript denotes the time of consumption. Suppose a bank can offer an asset that is more liquid, with gross returns Rd 1 = 1.36 and Rd 2 = 1.74 (depending on the time of liquidation). a) Calculate the bank’s profit after t = 2. In other words, what amount of funds remains at the bank once all depositors have withdrawn? b) Now suppose the late consumers pretend to be impatient and withdraw early. How many people can be paid before the bank runs out of funds?
Hi there, I need help solving a problem and am unsure how to go about solving the question. It is a practive question from a textbook and am trying to understand it further. I need a bit more help solving 1 a) and b). I have already obtained the values of the expected return at t = 0 and the expected utilities at t = 0 for both scenarios (direct investing) and (depositing with the bank). Thanks
Here is the question:
Consider the basic setup of the Diamond-Dybvig (1983) model. Specifically, there
are three periods, denoted t = 0, 1, 2, a single consumption good, and an illiquid
investment opportunity that pays gross return 1.1 if liquidated at t = 1, or gross
return 2.2 if liquidated at t = 2.
There are 30 people in the economy, each endowed with 1 unit of the consumption
good at t = 0. At t = 1, exactly 11 will randomly realize that they need to consume
at t = 1 (the early consumers), the remaining 19 people will need to consume at t = 2
(the late consumers). The utility derived from consumption is 1 − (1/c1)2 for early
consumers, 1 − (1/c2)2 for late consumers, where the subscript denotes the time of
consumption.
Suppose a bank can offer an asset that is more liquid, with gross returns Rd
1 = 1.36 and Rd 2 = 1.74 (depending on the time of liquidation).
a) Calculate the bank’s profit after t = 2. In other words, what amount of funds
remains at the bank once all depositors have withdrawn?
b) Now suppose the late consumers pretend to be impatient and withdraw early.
How many people can be paid before the bank runs out of funds?
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