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Unformatted text preview: nvests Incumbent monopolist decides on how much to invest in process
R&D - knowing that entry could happen
Suppose a technology is already available, and incumbent has
to decide whether to adopt.
to Let x(i) (with i = „innocent“) the optimal investment when
incumbent assumes that competitor will enter in next period.
incumbent Incumbent may also act strategically try to discourage
entry Invest more (e.g. more costly but better technology) so that the
entrant would not be profitable if incumbent adopts it credible
commitment to be a fierce competitor in case of entry.
Let x(p) be the predatory investment level [x(p) > x(i)].
If entrant observes that incumbent invests x(p), it will withdraw.
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
technology (R&D investment)
technology Assume quadratic cost for investment
F(x1) = x2 Assume that F2 cannot invest properly in R&D before
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
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 Game Start
Start with last stage suppose here firm enters
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 q1 = (1 – q2 – c1)/2 q2 = (1 – q1 – c2)/2
34 Game Plugging q2 into R1 and q1 into R2, we get the
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 Game final phase without entry taking place: If F2 would not enter, F1 would be
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 Game Two cases. first: „Innocent behavior“ F1 takes F2‘s entry as given, and it maximizes
profits with regard to investment
profits Use profits from second stage, but now PR1 = (1+2x-c)2 / 9 – x2 Take FOC 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
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
not even need to behave strategically in its
choice of x. F2 would never choose to enter.
38 Game Strategic behavior In
In F2‘s profits, one can see that they decrease
with F1‘s investment
Recall: PR2 = (1-2c2+c1)2 / 9
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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.
- Spring '13