{'40 points] Question 1. {The impact of worker compensation} Consider a static {one period} economy with identical individuaLs who earn a wage to 2 l while working and nothing when they don't. 1With probability 1 p. the workers get injured and cannot work. When injured. the individuals get a worker's compensation benet of ii = if! from the govermnent. 1|Iii-"hen working. individuals pay the premium .1: to the government. which is equal to :r = {1.1 x w. Assume that the premium is only paid it agents work, and the agents have no other source of mnsurnption in either state. NowH letis consider that workers can control the probability p by making e'orts to prevent from getting injuries. Specically. they pay the effort cost ilk-[p] : p2 to determine the injury prohahility p: i.e.. higher p implim lower injury {1 p} hut requires larger eifort costs. To make calculation easy. assume that individuals utility from consumption :3 is C sic} = ' Moreover. the utility [rem consumption and the disutility from effort cost are separahle1 i.e.. the effort cost clip] does not enter into etc}. 1. Formulate worker's optimal decision problem. 2. Please nd the optimal 1:}. 'What is the expected government expenditure {for worker compensation benet} and revenue {from the premiums}? 3. Consider the impact of increasing h from it] to 2t]. How will it aiiect p? What is the expected government expendittu'e and revenue? 4. Nova consider that the premium I is set to he hreak even for worker compensation system. Specically. insurance companies set the premium being equal to .'l': = {1 p] x b. Thus1 the premium fully reects the effort individuals exert. i.eH if individuals choose the low eort p. then the premilnn increases. Then. please calculate the optimal p for both E} = ill and t- : 2t]. Moreover, derive the implied premium :1.\" for both It] and El]. 5. Let's x i: = 2d. Moreover. the premium is now xed as if = .153\". which is the implied premilnn derived in question {it}. Consider that individuals take this premium E as given, i.e., they know that the premium is unchanged, like questions (1)-(3), regardless of the effort p they make. With this assumption, derive the optimal p. Is this higher or lower than the one you derived in question (4)? If so, why