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Assume that Hap's utility function is U (C, L) = C \"'5 * L\

Assume that Hap's utility function is U(C, L) = cu5 * LU5, where C is consumption measured by total income and L is hours of leisure and a normal good. Total income is labour income and non-labour income (y) with a total of T hours to allocate between work (consumption) and leisure at the market wage rate of w per hour. Hours worked is denoted as h. (Hint: the marginal utility of leisure and consumption are MUL = 0.5 * L-05 * cos and MUC = 0.5 * * C-05 , respectively.) a) Write down the budget constraint and state the slope of the budget constraint. (4 marks) b) Calculate the reservation wage. How does the total available time, T, affect the reservation wage? (4 marks) c) Derive the labour supply equation as a function of the wage and y (ie, calculate h where h = f (w, y)). Use your answer from part (b) and define the wage range on the labour supply curve that Hap is willing to work. (4 marks)