Question, if you can solve any amount of this that would be great.

In this question, we extend the model with search friction discussed in class by adding non-pecuniary preferences over jobs. There are two periods and workers search for a job every period. Workers have linear utility and no saving. If unemployed, workers draw a job offer from a job offer distribution. Each job offer has two components - a wage w and a disutility 1). Assume that w and v are independently distributed. The distribution of wages is gm and the distribution of disutilities is g\". If the agent accepts the job offer, her utility at that period is given by: u(w,v)=wv If the worker accepts a job at period 1, she remains employed for the next period on the same job. If the worker rejects the job offer from period 1, she receives unemployment insurance I) at that period and searches for a new job in the next period. The worker has to accept the job offer received in the second period. Utility in the second period is discounted by rate 3. 1. Suppose the worker receive job offer (10,11) on the rst period. Write down the value of accepting this job offer in period 1, Vaccept(w, v). . Calculate the expected utility of being unemployed on the next period as function of E(w) and ECU). Hint: Use that the utility is linear, u(w, v) = wv, and that w and v are independently distributed. . Calculate the disutility of rejecting job offer (11),?!) on the rst period, Vrejew, v). . Calculate the utility of receiving job offer (111,11) on the rst period, V(w, 1)), using your answer to questions 1 to 3. . Conditional on a disutility of working 1), plot the utility of rejecting a job and the utility of accepting a job on a graph with wages on the xaxis and the utility value on the yaxis. Mark the reservation wage 16(1)) on this gure. . Calculate the reservation wage as a function of the disutility, 23(1)). Is the worker willing to accept a lower wage if she nds the job more meaningful? . Conditional on a wage w, plot the utility of rejecting a job and the utility of accepting a job on a graph with disutility on the xaxis and the utility value on the yaxis. Mark the reservation disutility '13 (w) on this gure