Problem 4 (10 points) A price-taking firm producing a single product according to the production function y = f(x1, X2) faces price p for its output and prices w1, w2 for its inputs.Assume that f(0, 0) = 0 and that f is strictly increasing, strictly concave, twice differentiable, and such that 82 f 6$16$2 for all 3:1, 332 > 0. Let 31(p,w1, 1112) and 352(1), w1, w2) be the rm's unconditional demand functions for inputs 1 and 2. Prove that the demand for input 1 is increasing in the price of input 2, that ($1,532) 0 61122\"), 1: 2) for all $1, 332 > 0. You may use without proof the fact Ihat the demand for input 2 is decreasing in its own price, that is, 6562 am W1,U)2)