Question

Problem 5: Product Differentiation in a Bertrand Setting. Firms 1 and 2 face the same AC = MC = 30 but sell differentiated products. The demands for firms 1 and 2 are given by D.(P1, P2) = 70 – P1 + P2 D2(P1, P2) = 70 – P2 +5 P1 The firms choose prices Pı and P2 simultaneously. a) For each firm, represent profits as a function of both prices p and p2. b) Find the best response function for each firm. c) Find the equilibrium price p* = P = P2. d) Suppose instead that demands are: D ( p2) = 70 - P+ P2 D2 (P1, p2) = 70 - P2+ Does this change reflect more or less product differentiation? Will this increase or decrease competition? What will happen to the equilibrium price? (You don't have to do any calculations for part d. Explain your answer to each question.)

Answer 1

P.DI-30 D (P-30) D A-30) (40-t P213) CPg- 30) (40-Pat Pi/3) 1 1 a) BR func b) CA-30) -1) + (0-Pit fal3) =0 We 4o-it 3 tP -30)(-1) -0 40-Pt fa13 t30- O. loo +fa13=aP BR- A00+ fa13 Shmi laaly (00t P13 cSolwing fune two BR 50t

P1 = 50+50/6 + P1/36

35P1/36 = 350/6

P1 = 350*36/(6*35)

P1 = 60

So P1* = 60 & P2* = 60

D) both reaction functions will get steeper, thus it implies more product Differentiation

So this will decrease competition

& So eqm prices will rise