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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. Illustrate what happened to his wage and substitution effects
Illustrate what is the relation between marginal benefit and marginal cost at this level of the control variable.
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