
C 

(c) Final outcome Figure 9.6 Cournot duopoly
(c) Final outcome Figure 9.6 Cournot duopoly
Both firms charge price OP3, and total supply to the market is twothirds the competitive level of sales.
Assuming a market demand curve of P = 100 — Q and a constant marginal cost of 10, the competitive output will be 90 and the monopoly output 45. In a Cournot oligopoly, convergence of the sales of both firms is shown in Table 9.1, for five rounds. Firm 1 initially sets the monopoly price and makes profits of £2,025. The sales of firm 1 reduce from the monopoly output of 45 toward 30, and the sales of firm 2 increase from 22.5 toward 30. Eventually, both firms have a residual demand curve of P = 70 — Q, both selling 30 with a market price of £40.
Cournot equilibrium and reaction functions
An alternative approach to explaining equilibrium in Cournot oligopoly is to construct reaction curves for both firms in a duopoly. A reaction curve, or best response
Table 9.1 Cournot duopoly, collusion and cheating (£)
Period 
Firm 1's sales 
Firm 2's sales 
Market sales 
Market price 
Firm 1 
Profits Firm 2 
Industry 
Cournot duopoly 






1 
45.00 
0.00 
45.0 
55.0 
2,025.0 
0.0 
2,025.00 
2 
45.00 
22.5 
67.5 
32.5 
1,012.5 
506.25 
1,518.00 
3 
33.75 
28.125 
61.875 
38.125 
949.21 
791.02 
1,740.23 
4 
30.94 
29.53 
60.47 
39.53 
913.65 
872.02 
1,785.67 
5 
30.24 
29.88 
60.12 
39.88 
903.57 
892.81 
1,796.38 
Final 
30.00 
30.00 
60.00 
40.00 
900.00 
900.00 
1,800,00 
Collusion 
22.5 
22.5 
45.0 
55.0 
1,012.5 
1,012.5 
2,025,0 
Cheating 







Firm 1 
23.5 
22.5 
46.0 
54.0 
1,034.0 
990.0 
2,024.0 
Firm 2 
22.5 
23.5 
46.0 
54.0 
990.0 
1,034.0 
2,024.0 
Note Assumes market demand is given by P — 100 — Q, marginal revenue by 100 — 2Q and marginal cost is equal to 10.
Source Author function, for firm 1 defines the profitmaximizing output for firm 1, given the output of firm 2. Given that firm 2 sells Q2 units of output, firm 1's output can be expressed as Q1 — R1(Q2). For firm 2 the reaction function is given by Q2 — R2(Q1).
Reaction functions for a duopoly are shown in Figure 9.7, where firm 1's sales are measured on the horizontal axis and firm 2's on the vertical axis. The horizontal intercept of firm 1's reaction curve Qf1 assumes that firm 2 sells nothing and that firm
1 behaves as a profitmaximizing monopolist. The vertical intercept of firm 1's reaction curve QC assumes that firm 1 sells nothing and firm 2 sells the competitive output where price is equal to marginal cost. Using the demand equation P — 100 — Q, the horizontal intercept would be at sales of 45 and the vertical intercept at sales of 90. Firm 2's reaction curve is derived in a similar way, with the vertical intercept QM having a value of 45 and the horizontal intercept QC a value of 90.
If firm 1 initially behaves as a monopolist, then it will sell output OQf on reaction curve R1. Firm 2 will respond by choosing point A on its reaction curve (R2), selling output OQ2. Firm 1 reacts by moving to point B on its reaction curve, producing OQ2. Firm 2 will respond by moving to point C on its reaction curve, producing output OQ2. The process continues until Cournot equilibrium is reached at point E, where firm 1 sells OQ1 and firm 2 sells OQ; this is a position from which neither firm would want to move, given the other firm's output.
Reaction functions can also be derived algebraically. To maximize profits, firm 1 must set marginal revenue equal to marginal cost for any given level of firm 2's output. Therefore, when P — 100 — Q:
Total revenue (IR) — QiP — Qi(100 — Qi — Q2) or R — 100Qi — Qj — QiQ2 Marginal revenue (MR) — STR1/SQ1 — 100 — 2Q1 — Q2
Since marginal cost is equal to 10, marginal revenue equal to marginal cost can be expressed as:
Qi = f (Q2) = [(90  Q2)/2] = 45  2 Q2 Q2 = f (Qi) = [(90  Qi)/2] = 45  2Qi
If firm 2 sells 40 units, then firm i would choose to produce [(90  40)/2], or 25. If firm 2 produces 30, then firm i would produce [(90  30)/2], or 30. The equilibrium output is to be found at point E in Figure 9.6. At this point, both firms make profits of £900, which is derived by deducting marginal cost from price multiplied by output or (40  i0) * 30.

Post a comment