Based on 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 (impatient consumers), the remaining 300 people will need to consume at t= 2 (the patient consumers). The utility derived from consumption is 1 (1/c₁)²for early consumers, 1(1/c₂)²for late consumers, where the subscript denotes the time of consumption.

1. Calculate the expected return (from a t= 0 perspective) of direct investing.
2. Calculate the expected utility (from a t= 0 perspective) derived from direct investing.