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ull I C. [60 points, equally divided between the parts) The operations of two firms, unimaginatively named firm 1 and firm 2, produce the same good using the same input, but they interfere with each other in a negative way. Specifically, for a parameter a satisfying 0 0 f121, 12) = axi if (22 - 2x1) > 0 f2(21,22) = if (x1 - axe) 0 71(x1, x2). Without doing the work to explicitly solve for xi(p, w, a, 12), give the signs for the following partial derivatives, and explain why your answer should hold. (a) Oxi/ap. (b) Oxi/ow. () :/. (d) 8x1/202. 3 C.4. Find, as a function of p, w, and a the pair (21,5;) with the property that x solves maxr,20 71(21,2%) and olan mav D.3. Show that the sum of the profits in the previous problem are lower than the profits under joint ownership. (There is a difficult way to do this that involves a lot of algebra. And there is a simple way to do this that involves no algebra. 7 ull I C. [60 points, equally divided between the parts) The operations of two firms, unimaginatively named firm 1 and firm 2, produce the same good using the same input, but they interfere with each other in a negative way. Specifically, for a parameter a satisfying 0 0 f121, 12) = axi if (22 - 2x1) > 0 f2(21,22) = if (x1 - axe) 0 71(x1, x2). Without doing the work to explicitly solve for xi(p, w, a, 12), give the signs for the following partial derivatives, and explain why your answer should hold. (a) Oxi/ap. (b) Oxi/ow. () :/. (d) 8x1/202. 3 C.4. Find, as a function of p, w, and a the pair (21,5;) with the property that x solves maxr,20 71(21,2%) and olan mav D.3. Show that the sum of the profits in the previous problem are lower than the profits under joint ownership. (There is a difficult way to do this that involves a lot of algebra. And there is a simple way to do this that involves no algebra. 7