Suppose the production function Q = A(K^a)*(L^b) , where K is the amount of capital, L is the amount of labor it uses as inputs, A is a constant and represents the technology. The cost per unit of capital is a rental fee r and the cost per unit of labor is a wage w. The price of the output is P.

1. In the short run, the capital remains unchanged, calculate the labor demand function and the short-run output level in terms of w, r , K and P;

2. In the long run, both K and L are the variable cost, A=1, a=b=0.25, calculate the labor demand and capital demand function in terms of w, r and P.

3. In the long run, both K and L are the variable cost, A=1, a=b=0.5, try to calculate the labor demand and capital demand function in terms of w, r and P, explain why you cannot get these two demand functions(hint: returns-to-scale).