Assume a manufacturer produces one final good using two different inputs x1 and x2 according to the following technology: f(x1, x2) = x 1 3 1 x 1 3 2 ,

1. Does this production function exhibit increasing, constant, or decreasing returns to scale?

2. Derive the conditional input demand functions.

3. Derive the cost of production as a function of the output level y, where the factor prices w1 and w2 are given.

4. What is the firm's supply in the long run assuming p = $50, w1 = 1 and w2 = 4?