Challenge Question: Consider the following production function f (L, K) = L^aK^b.

1. Show what returns of scale is exhibited by this production for every value of a and b.

2. Now consider the following production function: f (L, K, H) = K^aH^b(L)^1-a-b where H is human capital, 0 < a < 1 and 0 < b < 1. What is the intuitive interpretation for parameters a and b? What returns to scale does this production function exhibit?

3. Find the cost-minimizing input bundle (L*, K*, H*) for this function.