Consider and economy with the following production technology: Y = 9K^1/3 L^2/3, where the aggregate capital stock is K=100, and the aggregate labor is L=100. The price of output is 1.
1. Calculate the equilibrium wage and the capital return.
2. Calculate the total payments to labor and the capital.
3. Demonstrate the Euler's Theorem holds, i.e. show that total payments to labor and capital equal the value of output.
4. Explain what share of output goes to capital and labor?
5. Assume there is an increase in L, what would be impact on the capital returns and wages?