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/c1) 2 for early consumers, 1(1/c2) 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.