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1. 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 if liquidated at t = 1, or gross return 2.2 if liquidated at t = 2. There are 500 people in the economy, each endowed with 1 unit of the consumption good at t = 0. At t = 1, exactly 200 will randomly realize that they need to consume at t = 1 (the early consumers), the remaining 300 people will need to consume at t = 2 (the late consumers). The utility derived from consumption is 1 (1/41)2 for early consumers, 1-(1/02)2 for late consumers, where the subscript denotes the time of consumption. (i) Calculate the expected return (from a t = 0 perspective) of direct investing. (ii) Calculate the expected utility (from a t = 0 perspective) derived from direct investing Suppose a bank can offer an asset that is more liquid, with gross returns RI = 1.33 and R = 1.71 (depending on the time of liquidation). = (iii) Calculate the expected return (from a t = 0 perspective) of depositing with this bank. How does it compare to the expected return from direct investing? (iv) Calculate the expected utility (from a t = 0 perspective) derived from depositing with the bank. Do you conclude that people would prefer banking to direct investing at t = 0? (v) Calculate the bank's profit after t = 2. In other words, what amount of funds remains at the bank once all depositors have withdrawn? 1. 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 if liquidated at t = 1, or gross return 2.2 if liquidated at t = 2. There are 500 people in the economy, each endowed with 1 unit of the consumption good at t = 0. At t = 1, exactly 200 will randomly realize that they need to consume at t = 1 (the early consumers), the remaining 300 people will need to consume at t = 2 (the late consumers). The utility derived from consumption is 1 (1/41)2 for early consumers, 1-(1/02)2 for late consumers, where the subscript denotes the time of consumption. (i) Calculate the expected return (from a t = 0 perspective) of direct investing. (ii) Calculate the expected utility (from a t = 0 perspective) derived from direct investing Suppose a bank can offer an asset that is more liquid, with gross returns RI = 1.33 and R = 1.71 (depending on the time of liquidation). = (iii) Calculate the expected return (from a t = 0 perspective) of depositing with this bank. How does it compare to the expected return from direct investing? (iv) Calculate the expected utility (from a t = 0 perspective) derived from depositing with the bank. Do you conclude that people would prefer banking to direct investing at t = 0? (v) Calculate the bank's profit after t = 2. In other words, what amount of funds remains at the bank once all depositors have withdrawn