Suppose households preferences are described by the utility functionU(C, l) = 3l1/2+C,

whereCstands for consumption of market goodslstands for leisure.

The total number of hours available to the representative consumer is 1, and the market real wage isw.

Output is produced using the production functionY= (Nd)^1/2 . For simplicity, let us assume

that there is no government, that isG= 0. The firm distributes a profitto the consumer.

1. Solve the consumer's problem and find the optimal values ofC*,l*, and then deduceNs.
2. Solve the firm's problem and deriveNd.
3. Compute the competitive equilibrium wage rate (w*), and deduce employment (N*), and the aggregate output (Y*) in this economy.