Assume that Hap's utility function is [J(C, L) = cos LO-5 where C is consumption measured by total income and L is leisure and is a normal good. Total income is labour income and non-labour income. He has y $200 non-labour income and a total of 40 hours to allocate between work (consumption) and leisure at the market wage rate of w = $10 per hour. (Hint: marginal utility of leisure and consumption are -0-5 cos and MUC = 0.5 LOS C-0-5, respectively.) MUL = 0.5 a) Calculate the reservation wage and briefly explain if he is willing to work at the ongoing market wage. (2 marks) b) Write down the budget constraint and the slope of the budget constraint. (2 marks) c) Assuming that Hap works, solve the optimal consumption (C) and work hours (2 marks) d) Draw the budget constraint in an income-leisure diagram. Carefully label all the axes. Show Hap's optimal point on this diagram. (l mark) Suppose the government introduces an income support program where individuals receive $500 if their earnings from work are a maximum of S250; otherwise, they won't receive the benefits. Also, in this program, the government charges S 100 lump-sum fee from the program participants who work to fund some other job search and training programs. e) Write down the equation(s) for the program and Hap's new budget constraint with all the necessary parts, (5 marks) f) Draw the new budget constraint in the graph in part d. Carefully label all the axes and corresponding hours and income at all the kinked points on your graph. (4 marks) g) What would be Hap's labour supply response to this program? Does he choose the point that maximises his consumption within the program? Using economic theory, briefly explain. (2 marks) h) Tootie, Hap's coworker, works 20 hours more than Hap's optimal hours in part c. What would be Tootie's labour supply response to this prorgam? Brieflv explain. (Assume the same budget constraint for both of them.) (2 marks)