Suppose Jim's utility for consumption and leisure is U(C, L) = C^0.5 L^0.5. His wage rate is w dollars per hour and he has $V in his bank account (non-labor income). The price of the consumption good is $1, and he has T hours in the week.
(a) Derive Jim's optimal labor supply (that is, hours worked as a function of the wage, w, and his non-labor market income V).
(b) Find Jim's reservation wage, wR.
(c) Suppose V=$5, what is Jim's labor supply function? Draw his labor supply curve. What can you say about his income and substitution effects?
(d) Suppose V=$0, what is Jim's labor supply function now? Draw his labor supply curve. What happened to his income and substitution effects