Cournot with N rms (revisited)

Transcription

1 Cournot with N rms (revisited) Cournot model with N symmetric rms, constant unit variable cost c, and inverse demand function P(Q) = a bq where Q = N i=1 q i The results: q = a c b (1 + N) p = a + Nc 1 + N π = (a c)2 () December 1, / 4

2 Cournot with N rms and entry cost Suppose now that there is also an entry cost: > 0. TC i = + cq i () December 1, / 4

3 Cournot with N rms and entry cost Suppose now that there is also an entry cost: > 0. TC i = + cq i Once the rm decided to enter the market, this is a sunk cost () December 1, / 4

4 Cournot with N rms and entry cost Suppose now that there is also an entry cost: > 0. TC i = + cq i Once the rm decided to enter the market, this is a sunk cost So, pro ts are simply: π = (a c)2 () December 1, / 4

5 Cournot with N rms and entry cost Suppose now that there is also an entry cost: > 0. TC i = + cq i Once the rm decided to enter the market, this is a sunk cost So, pro ts are simply: π = (a c)2 So, how many Cournot- rms will this market have in equilibrium? () December 1, / 4

6 Cournot with N rms and entry cost Suppose now that there is also an entry cost: > 0. TC i = + cq i Once the rm decided to enter the market, this is a sunk cost So, pro ts are simply: π = (a c)2 So, how many Cournot- rms will this market have in equilibrium? Zero-pro t condition regulates entry (a c) 2 b(1+n ) 2 = 0 () December 1, / 4

7 Cournot with N rms and entry cost Suppose now that there is also an entry cost: > 0. TC i = + cq i Once the rm decided to enter the market, this is a sunk cost So, pro ts are simply: π = (a c)2 So, how many Cournot- rms will this market have in equilibrium? Zero-pro t condition regulates entry Re-arranging (a c) 2 b(1+n ) 2 = 0 (a c) 2 b = (1 + N ) 2 () December 1, / 4

8 Cournot with N rms and entry cost Suppose now that there is also an entry cost: > 0. TC i = + cq i Once the rm decided to enter the market, this is a sunk cost So, pro ts are simply: π = (a c)2 So, how many Cournot- rms will this market have in equilibrium? Zero-pro t condition regulates entry Re-arranging Yields: N = (a c) 2 b(1+n ) 2 = 0 (a c) 2 b = (1 + N ) 2 (a c) p 1 b () December 1, / 4

9 Cournot with N rms and entry cost extension Suppose now that aggregate market demand is given by: P(Q) = (a bq) S S 1 is some measure of the size of the market. When S grows, demand expands for a given price. () December 1, / 4

10 Cournot with N rms and entry cost extension Suppose now that aggregate market demand is given by: P(Q) = (a bq) S S 1 is some measure of the size of the market. When S grows, demand expands for a given price. Pro ts in the standard N- rm Cournot (i.e., without entry cost) model will now be homework for yourselves to work it out " # π (a c) 2 = S () December 1, / 4

11 Cournot with N rms and entry cost extension Suppose now that aggregate market demand is given by: P(Q) = (a bq) S S 1 is some measure of the size of the market. When S grows, demand expands for a given price. Pro ts in the standard N- rm Cournot (i.e., without entry cost) model will now be homework for yourselves to work it out " # π (a c) 2 = S When including entry cost > 0, we have: π = S h (a c) 2 i b(1+n ) 2 () December 1, / 4

12 Cournot with N rms and entry cost extension Suppose now that aggregate market demand is given by: P(Q) = (a bq) S S 1 is some measure of the size of the market. When S grows, demand expands for a given price. Pro ts in the standard N- rm Cournot (i.e., without entry cost) model will now be homework for yourselves to work it out " # π (a c) 2 = S When including entry cost > 0, we have: π = S Solution: N = (a c) r S b 1 h (a c) 2 b(1+n ) 2 i () December 1, / 4

13 Cournot with N rms and entry cost extension Suppose now that aggregate market demand is given by: P(Q) = (a bq) S S 1 is some measure of the size of the market. When S grows, demand expands for a given price. Pro ts in the standard N- rm Cournot (i.e., without entry cost) model will now be homework for yourselves to work it out " # π (a c) 2 = S When including entry cost > 0, we have: π = S h (a c) 2 i b(1+n ) 2 Solution: r S N = (a c) 1 b So, number of rms N grows with the size of the market, S () December 1, / 4

14 Strategic Behaviour Entry Deterrance Back to Stackelberg Model Two rms in a sequential Cournot model: Leader and ollower Timing: 1 irm 1 chooses q 1. 2 irm 2 observes q 1 and then chooses q 2. How do we nd the solution to model? By backwards induction: start by stage 2, and then move backwards to stage 1 We start by solving the problem of irm 2, given the value of q 1 Next, we solve for q 1, given the response of irm 2 to each possible q 1 In the end, everything is solved as a function of q 1 () December 1, / 4