Problem 1: Monopolis'tic Competition. Two companies 1,? are monopolistic competitors: demand for each rm's product is a function of prices of both rms: 91(P11P2}=a5P1 +0519: (1} QEQDL'PZJ = G 5392 + 05191 Where mind are positive coefcients. Both lms have constant marginal cost a. The two rms simultaneously announce their prices pl, 322. a. What should be the price charged by rm 1 if rm 2's price is 112'? Derive the best response inction 331(3):} b. \"That should be the price charged by rm 2 if rm 1's price is 311? e. Solve for the Nash Equilibrium prices of both lms and aggregate output. {1. How does equilibrium price level depend on marginal cost .2? How does it depend on cross elasticity of demand d? Answer as sharply as you can how equilibrium price changes if those move up or down. 13. Imagine there are n competitors indexed 1: 2, ___,n and that each rm\"s demand depends on its own price and on the average of other comp ctitorsI prices: 1 91(1011 -..,pn] = a 15131 + d_ (pg + +33\") with similar demand functions for rms 2,3, ...'rL. \"'hat will be the price level in a spnmetric equilibrium? Does it increase or decrease as a. grows larger? Provide intuition. f. Assume that there are only two competitors as in (a) but the game instead of simultaneous is sequential: rm 1 chooses and announces its price rst. then rm 2 gets to choose its price. Find the subgame perfect Nash Equilibrium. Compare it with the equilibrium in (c)