A company has a production function: y = x_1^()* x_2^(1 ), where 0 < <1. Factor input 1 costs w1> 0 and factor input 2 costs w2> 0. The company o wants to minimize its production costs when it produces y> 0 units of output 1.1. Derive the company's input demand functions for x1 and x2 as a function of w1, w2 and y. Ie. how much will the company demand of input x1 and x2 when it stands opposite input prices w1 and w2 and o want to produce y units? Call these x 1 (w1, w2, y) and x 2 (w1, w2, y). 1.2. What is the elasticity of (x 2 / x 1) with respect to (w2 / w1), ie what is: (x 2 / x 1) (w2 / w1) (w2 / w1) (x 2 / x 1). 1.3. What does the elasticity of the share of total cost spent on input 1. 1.4. Derive the company's cost function C (w1, w2, y) where y is the production. 1.5. Show that the company's marginal cost is constant in y (ie depends on w1, w2 but not y)