A company has a production function:

y = x₁ x₂^1-

where 0 < < 1. Factor input 1 costs w1 > 0 and factor input 2 costs w2 > 0. The company wants to minimize its production costs when it produces y > 0 units of output.

1) Derive the firm's input demand functions for x1 and x2 as a function of w1, w2 and y. That is how much will the company demand of inputs x1 and x2 when faced with input prices w1 and w2 and wants to produce y units? Call these x 1 (w1, w2, y) and x 2 (w1, w2, y).