Adam is considering the possibility of entering the labor force. His preferences are described by the utility function, U = h2/3 c1/3, where h denotes his hours spent in leisure and c denotes his consumption of a composite good. Let w denote the wage per hour, and normalize the price of the composite good to 1 (i.e., Pc = 1) . Assume that Andy has a non-labor income of y per day, and further that his daily time constraint is H = 24 = 1 + h hours, where I indicates hours of labor supplied. Based on this information, answer the following: A. Find (i) an expression for Adam's labor supply choice ( 1 ) as a function of the wage rate (w ) and his non-labor income y and (ii) the condition that ensures he would never accept a job offer requiring he work 8 hours per day. [15 points] B. Now suppose that condition is satisfied, but that Adam finds part-time work (i.e., where he can supply less than 8 hours per day). Suppose further that the government imposes a proportional tax, 7 where 0