Intermediate Macroeconomics Homework Question

Answer the following questions given the following Cobb-Douglas production function Y = AK^0.4L^0.6.

1. Show whether the Cobb-Douglas production function has increasing, constant, or decreasing returns to scale. 
2. Derive expressions for marginal product of labor (MPL) and marginal product of capital (MPK). 
3. Show that the real wage and the real rental rate are proportional to average product of labor and average product of capital, respectively. 
4. Show that the share of capital income to total income is 0.4 and that the share of labor income to total income is 0.6.