Question

ії. Imagine a worker who s preferences for non work tme (h) and resources to spend on all other good (r2) can be represented using a Cobb-Douglas utility function as described above. In this case, the parameter a captures this worker's taste for time spent not working compared to having some income. Using this setup, answer the folowing questions. (a) The worker is trying to divide 10 hrs of his day between work and non-work time, and has no other income than what he gets paid based on how much he works. If a how many hous w he choose to work if he is offered S5 per hour? (b) If the worker's wage increased to S6 per hour, how many more (or fewer) hours would c) Describe the shape of this individual worker's labor supply curve based on your answer (d) If the worker received state assistance of $12 per day regardless of whether he worked he choose to work? to parts (a) and (b). or not, would this worker change the number of hours he chose to work? Assume the wage is S6 per hour and solve for the number of hours he will choose to work.

Answer 1

Labor Leisure choice, X_1 rightarrow leisure, X_2 = consn u(X_1, X_2) = (X_1)^alpha (X_2)^-alpha (a) alpha = 1/4, B.C Total consn = Total Labor Income X_2 = w(T - X_1) X_2 + wX_1 = wT, w = 5, T = 10. Now Max u st B.C L = (X_1)^1/4 (X_2)^3/4 + lambda[50 - 5X_1 - X_2] Foc: partial differential L/partial differential X_1 implies 1/4 (X_2/X_1)^3/4 - 5 lambda = 0, partial differential L/partial differential X_2 = 3/4(X_1/X_2)^1/4 - lambda = 0 thus 1/4 (X_2/X_1)^3/4 middot 1/5 = 3/4(X_2/X_1)^1/4 X_2 = 15X_1, Now from B.C rightarrow 50 = 5X_1 + 15X_1 thus 20X_1 = 50 X_1 = 2.5 thus work hours = 10 - X_1* = 7.5 hours (b) Now w = 6, so L = (X_1)^1/4 (X_2)^3/4 + lambda[60 - 6X_1 - X_2] so at Eq^m X_2 = 18X_1 from B.C 60 = 6X_1 + 18X_1 so 24X_1 = 60, X_1* = 2.5, so work hours = 10 - X_1* = 7.5 (c) Labor ss curve is vertical, at work hours = 7.5