3. Prove the following proposition, that an increase in w, the price of input 1', all else constant, weakly decreases xi, the unconditional input demand for input 1'. Proposition. Suppose w' and w differ only in the i-th component, where wi' > w. The market price of output is fixed at p. Suppose x solves the profit maximization problem at (p, w), and x' solves the profit maximization problem at (19, W'). Then x; 5 xi