Suppose households preferences are described by the utility function U(C, l) = 2C 1/2 + 3l, where C stands for consumption of market goods l stands for leisure. The total number of hours available to the representative consumer is 1, and the market real wage is w. Output is produced using the production function Y = (Nd ) 1/2 . For simplicity, let us assume that there is no government, that is G = 0. The firm distributes a profit = 0 to the consumer.

1. Solve the consumer's problem and find the optimal values of C ? , l ? , and then deduce Ns . 2. Can the income effect ever dominate the substitution effect or not? 3. Solve the firm's problem and derive Nd . 4. Compute the competitive equilibrium wage rate (w ), and deduce employment (N ), and the aggregate output (Y ) in this economy. 5. Compute the equilibrium profit . Is it approximately equal to the value = 0 initially assumed? Can we trust the w ? obtained in Question 4)