Problem 4 (10 points) A price-taking firm producing a single product according to the production function y = f(21, 22) faces price p for its output and prices w, w2 for its inputs. Assume that f(0, 0) = 0 and that f is strictly increasing, strictly concave, twice differentiable, and such that of (r1, 12) 0. Let xi(p, un, w2) and x2(p, wi, w2) be the firm'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 is . 021 (p. "1, "2)>0 for all r1, r2 > 0. You may use without proof the fact that the demand for input 2 is decreasing in its own price, that is, 012 (p, w1, "2)