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.

1. Calculate the technical rate of substitution(TRS, assume K is on the horizontal axis);

2. In the short run, the capital remains unchanged, calculate the conditional labor demand and total cost function in terms of w, r , K and Q;

3. In the long run, both K and L are the variable cost, A=1, a=b=0.5, calculate the conditional labor demand, conditional capital demand and total cost function in terms of w, r and Q.

4. In the long run, both K and L are the variable cost, A=1, a=b=0.5, calculate the average total cost and show that how will the average total cost be impacted if the total output is doubled.