Consider a static (one period) economy with identical individuals who earn a wage w = 100 while working and nothing when they don't. with probability 1-p, the workers get injured and cannot work. when injured, the individuals get a worker’s compensation benefit of b = 10 from the government. when working, individuals pay the premium x to the government, which is equal to x = 0.1 * w. assume that the premium is only paid if agents work, and the agents have no other source of consumption in either state. now, let’s consider that workers can control the probability p by making efforts to prevent from getting injuries. specially, they pay the effort cost (p) = p2 or p^2 to determine the injury probability p: i. e., higher p implies lower injury (1- p) but requires larger effort costs. to make calculation easy, assume that individuals utility from consumption c is u(c) = c /100 . moreover, the utility from consumption and the disutility from effort cost are separable, i. e., the effort cost (p) does not enter into u(c).1. formulate worker’s optimal decision problem.2. find the optimal p. what is the expected government expenditure (for worker compensation benefit) and revenue (from the premiums)?