AIO_price_differentiation_etc

# Accused 30 30 strategic investments consider rd

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Unformatted text preview: nvests Incumbent monopolist decides on how much to invest in process Incumbent R&D - knowing that entry could happen R&D Suppose a technology is already available, and incumbent has Suppose to decide whether to adopt. to Let x(i) (with i = „innocent“) the optimal investment when Let incumbent assumes that competitor will enter in next period. incumbent Incumbent may also act strategically try to discourage Incumbent entry entry Invest more (e.g. more costly but better technology) so that the Invest entrant would not be profitable if incumbent adopts it credible commitment to be a fierce competitor in case of entry. commitment Let x(p) be the predatory investment level [x(p) > x(i)]. If entrant observes that incumbent invests x(p), it will withdraw. 31 31 Let‘s consider a simple model Suppose Suppose firm 1 (F1) is active in a market with homogenous goods with Demand: p = 1 – q F1 faces potential entry of F2. 32 32 Game First: F1 decides on investment in cost-reducing First: technology (R&D investment) technology Assume quadratic cost for investment F(x1) = x2 Assume that F2 cannot invest properly in R&D before Assume entering. Thus it will produce at marginal cost c. After F2 observes investment of F1 in decides whether to enter or not. enter without investment, marginal cost = c without by investing x it becomes more efficient by total cost: C(x,q1) = (c-x)q1 C(x,q If it enters, it has to pay the fixed cost FC. In last stage, active firms set output (Cournot game). 33 33 Game Start Start with last stage suppose here firm enters the market! the In duopoly, firms choose output qi to maximize profits PR1 = (1-q1-q2-c1)q1 PR2 = (1-q1-q2-c2)q2 with c1 = c - x, and c2 = c. Taking Taking FOC and re-arraning, we get the reaction functions functions q1 = (1 – q2 – c1)/2 q2 = (1 – q1 – c2)/2 34 34 Game Plugging q2 into R1 and q1 into R2, we get the we equilibrium quantities equilibrium q1 = (1-2c1+c2)/3 analogous for F2 Then Then we can compute the equilibrium price plug q1 and q2 into demand function p = (1+c1+c2)/3 and then we can calculate profits PR1 = (1-2c1+c2)2 / 9 PR2 = (1-2c2+c1)2 / 9 35 35 Game final phase without entry taking place: If F2 would not enter, F1 would be If monopolist and we would get monopolist q1m pm = (1-c1)/2 = (1+c1)/2 PR1m Now = (1-c1)2 / 4 we go „backwards“ to the first step... 36 36 Game Two cases. first: „Innocent behavior“ F1 takes F2‘s entry as given, and it maximizes F1 profits with regard to investment profits Use profits from second stage, but now PR1 = (1+2x-c)2 / 9 – x2 Take FOC dPR1 dPR1 = (1 – 2c + 4x + c2 – 4cx + 4x2) / 9 –x2 (1 dPR1/dx = (4 – 4c + 8x)/9 – 2x = 0 Optimal investment x = 2/5 – 2/5 c Optimal 37 37 Game Once we have x, we can calculate q1, q2 and p: q1 = (3 – 3c)/5 q2 = (1-c) / 5 p = (1 + 4c)/5 Then we get following profits: PR1 = (1 – c)2 / 5 PR2 = (1 – c)2 / 25 - FC Obviously, F2 would only enter as long as FC <= (1-c)2 / 25 If fix cost FC exceed expected profits, F1 would If not even need to behave strategically in its choice of x. F2 would never choose to enter. 38 38 Game Strategic behavior In In F2‘s profits, one can see that they decrease with F1‘s investment with Recall: PR2 = (1-2c2+c1)2 / 9 and c...
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## This note was uploaded on 01/22/2014 for the course ECON D0T32A taught by Professor Czarnitzkidirk during the Spring '13 term at Katholieke Universiteit Leuven.

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