Consider an economy with the following Cobb-Douglas production function:

Y=K^1/3L^2/3.

The economy has 1,000 units of capital and a labour force of 1,000 workers.

1. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock.
2. If the real wage can adjust to equilibrate labour supply and labour demand, what is the real wage? In this equilibrium, what are employment, output, and the total amount earned by workers?