4. Note: the objective of this problem is to take you through an example of how one might think about consequences and trade-offs involved in social insurance. Think about it as an extension of lectures rather than a problem to be solved. What needs to be done in the problem is mathematically relatively simple, the hard part is interpreting the solution. Suppose that a person has the utility function given by x/aD where C is consumption and D is the dis-utility of work or other effort. A person that is employed has the dis-utility of work given by D. A person that is unemployed and exerts effort of s to nd a job experiences disutility of search given by 32. A person that works earns w. She has therefore the utility of VIED (we assume that all income is consumed). A person that loses a job searches for a new one and nds it with the probability of .5. The utility of a jobless person is given by s