2. A prot-maximizing competitive rm uses n inputs 2:1,. ..xn to produce one output 3!. Let n'(p) be the maximum prot attainable at prices p = (py.p1,. . up\"), where py is the price of the output and pi the price of the sci-good. a.) (4) Show that 1:07) is homogeneous of degree 1 in p. b.) (10) Show that 1r(p) convex in p. c.) (4) Suppose that the rm faces randomly fluctuating prices due to an exogenous factor. We imagine that the price vector is p with probability q and p' with probability 1 - q so that average prices are p" = qp + (1 q)p'. Is the price fluctuation better for the firm than a price stabilization at 1.0"? Why