Consider a worker whose preferences are given by: U (C,R) = log C + (1 ) log R, where C denotes consumption and R denotes leisure. The worker has T units of time that he can either allocate to leisure, R, or to labor, L. Let p denote the nominal price of one unit of consumption and w denote the nominal wage. We will assume that the worker has V dollars of non-labor income.

Suppose that the rm wants to induce the \"lazy" worker to stop skipping working hours. The rm considers the following policies: I Policy A: The rm subsidizes every worker's wage at a rate of 1: dollars per hour. a Policy B: The rm pays a lump sum horlus1| B, to any worker who works at least H hours. This bonus is independent of actual hours worked. I Policy C: The rm Fine imposes a ne on any worker who does not complete H hours of work. The1 ne, f, is paid for every hour of worked missed. The total ne1 F, is given by F = (H L'} f, where L' represents the actual hours worked. The worker is not compensated for any hours worked in excess of the the requisite H hours. f. If the rm implements Policy A. what is the minimum subsidy it must offer the \"lazy" worker to induce him to work exactly 15' hours? If the rm has to pay both workers the same wage, what is the cost of this policy? Provide a diagram with your answer. g. If the rm implements Policy B, what is the minimum bonus that the rm must pay the \"lazy\" worker to induce him to work H hours? What is the cost of this policy? Provide a diagram with your answer. h. If the firm implements Policy (3', what hourly ne, I, will induce the \"lazy" worker to supply exactly H hours of labor time? What is the cost of this policy? Provide a diagram with your answer. i. Discuss the three policies? Which is the most effective? Which policy would you recom- mend? Why? If you do not recommend any of the three suggested policies, please suggest a dierent policy and provide a mathematical and graphical analysis