I have a quick question about social insurance down below. The answer is attached for the reference as well.

\"Consider an economy of identical individuals who earn a wage of 200 while working and nothing when they don't. With probability q, the individuals get injured and cannot work. When injured, the individuals get a worker's compensation benefit of b from the government. When working, individuals pay a tax of (200 - 7') to finance this insurance system. Assume that the agents have no other source of consumption in either state. Let u(c) = c1/3 denote the individual's utility from consuming c in a given state." (a) "Write the individual's expected utility as a function of b, q and 7-." Solution: Expected utility is the weighted average of the utility in each state: injured/ not injured. EU = (1 q) - U (utility when not injured) + qU (Utility when injured) = (1 q) - {200(1 7)}1/3 + q - 121/3