ASSIGNMENT 11
Labor Supply

An individual's utility function is given by W(C,R) = u(C) + v(R), where C is consumption and R is hours of leisure. The derivatives of the utility function are as follows: u' > 0, u'' < 0, v' > 0, v'' < 0. The price of the consumption good is unity (i.e. 1) and the wage rate is w. The individual spends all of her income on consumption.

Denote hours worked by L, so that R + L = 24.

1. Obtain the budget constraint.
2. Set up the formal utility maximization problem.
3. Obtain the FOCs. Show that they yield
       wu'(C) - v'(R) = 0     (1)
       C + wR = 24w.     (2)
4. Differentiate the equations totally. (Note that w is a parameter.)
5. Use Cramer's Rule to obtain dC/dw and dR/dw.
6. Will an increase in the wage rate cause hours worked to rise--or fall? (Use the derivatives in Q. 5 to obtain your result.) Sketch the labor supply curve.
7. What is the effect of higher wages on consumption?