Question

Please provide explanations and graphs as well. Thank you!

Question 2. Labor supply (3 points) Consider Raymond's preferences for leisure (Z) and other goods (C), U(Z,C)=C+2VZ. The associated marginal utilities are MUC = 1 and MUz = 1. Suppose that Pc = 1 and the wage rate is w. Raymond has no non-labor income and has at most 24 hours to divide between labor and leisure time. 1. Are Raymond's preferences quasi-linear? 2. Show how the number of units of leisure Raymond chooses depends on the wage rate. Detail your work and illustrate graphically. 3. How does Raymond's labor income depend on the wage rate? 4. Does Raymond work more when the wage rate rises? 5. Suppose that Raymond has non-labor income equal to A > 0. How would, if at all, your answers to questions b), c) and d) change?

Please provide explanations and graphs as well. Thank you!

Answer 1

Yes. Raymond's preferences are quar Lincore, since it is lineac in c but noterecer ② Since U (2, c) = C+257, where Z= leisure and c = other goods. Pe=1 and wage -w. Total haures available=24. Since z= leisure hours, 24-2) = labor hours w (24-2) is the labor income Since there is no non-labor encome, total income = w(24-2).. With Pe= 1, total expenditure - Budget constraint becomes le=w(24-2). - 0 Using is utility function, we get u(z) = w(24-2) + 282. Objective is to maximize utility U(z) = w C24-2) +252 Finst arder condition w C24-2) + 2V2] = 0 - W + 2x12 + z =0 t =w = we 2 = 1 - 2 - ③ As shown by equation , the leisure haures (2) depends on wage rate. @ As mentioned in (2) above, labor income = wage & labor hours Labor income = w(24-2) =w (24 - 12) = 24w - tu Equation depicts the relationship between labor income and wage rate. ③ Equation shows that za t ire as w rises a falls and hence. labor hour increases. Hence, Raymond works more when erate reises. In other words, (24-2) Lw since za to. ③ of Raymond has mon-labor income equal to A70, the budget constreaint would be c = A +W (24-2) Using new budget constraint in the utility function, we get U(2) = A+W (24-2) + 2v2. Since A is constant, the maximization of utility yiels the same result as (2) above. i.. aw taxt. 72 = 0 => 2 = 2 Labor income = w (24-2) = 24w-to Hence, the answers in (2), (3) and (4) remain unchanged even if Raymond has some non-laber income of AO.

Quasilinear indifference curves and budget constraint Other Goods (C) 0 2 4 6 8 16 18 20 22 24 10 12 14 Leisure (2)

Leisure as a function of Wage Leisure 0 0.2 0.4 8 0. 1 0.6 Wage

Labor income as a function of Wage Labor Income o 0.2 0.4 0.6 0.8 1 1.2 Wage