28. Oligopoly
Oligopoly
A. Oligopoly is the study of the interaction of a small number of
firms
1. duopoly is simplest case
2. unlikely to have a general solution; depends on market struc-
ture and specific details of how firms interact
28.1 Choosing a Strategy
B. Classification of theories
1. non-collusive
a) sequential moves
1) quantity setting — Stackelberg
2) price setting — price leader
b) simultaneous moves
1) quantity setting — Cournot
2) price setting — Bertrand
2. collusive
28.2 Quantity Leadership
C. Stackelberg behavior
1. asymmetry — one firm, quantity leader, gets to set quantity
first
2. maximize profits, given the reaction behavior of the other
firm
3. take into response that the other firm will follow my lead
4. analyze in reverse
5. firm 2
a) maxy2 P(y1 + y2)y2 − c(y2)
b) FOC: P(y1 + y2) + P′(y1 + y2)y2 = c′(y2)
c) solution gives reaction function, f2(y1)
6. firm 1
a) maxy1 P(y1 + f2(y1))y1 − c(y1)
b) FOC: P(y1 + f2(y1)) + P′(y1 + f2(y1))y1 = c′(y1)
c) see Figure 26.2.
7. graphical solution in Figure 28.4.
D. Price-setting behavior
1. leader sets price, follower takes it as given
2. given p1, firm 2 supplies S2(p1)
3. if demand is D(p), this leaves D(p1) − S2(p1) for leader
4. hence leader wants to maximize p1y1 − c(y1) such that y1 =
D(p1) − S2(p1)
5. leader faces “residual demand curve”
28.5 Simultaneous Quantity Setting
E. Cournot equilibrium — simultaneous quantity setting
1. each firm makes a choice of output, given its forecast of the
other firm’s output
2. let y1 be the output choice of firm 1 and ye
2 be firm 1’s beliefs
about firm 2’s output choice
3. maximization problem maxy1 p(y1 + ye
2)y1 − c(y1)
4. let Y = y1 + ye
2
5. first-order condition is
p(Y ) + p′(Y )y1 = c′(y1)
6. this gives firm 1’s reaction curve — how it chooses output
given its beliefs about firm 2’s output
8. look for Cournot equilibrium — where each firm finds its
expectations confirmed in equilibrium
9. so y1 = ye
1 and y2 = ye
2
28.6. Example of Cournot
1. assume zero costs
2. linear demand function p(Y ) = a − bY
3. profit function: [a − b(y1 + y2)]y1 = ay1 − by2
1 − by1y2
4. derive reaction curve
a) maximize profits
b) a − 2by1 − by2 = 0
c) calculate to get y1 = (a − by2)/2b
d) do same sort of thing to get reaction curve for other firm
5. look for intersection of reaction curves
28.9 . Bertrand – simultaneous price setting
1. consider case with constant identical marginal cost
2. if firm 1 thinks that other firm will set p2, what should it set?
3. if I think p2 is greater than my MC, set p1 slightly smaller
than p2
4. I get all the customers and make positive profits
5. only consistent (equilibrium) beliefs are p1 = p2 = MC
28.10 . Collusion
1. firms get together to maximize joint profits
2. marginal impact on joint profits from selling output of either
firm must be the same
3. max p(y1 + y2)[y1 + y2] − c(y1) − c(y2)
4. P(y1 + y2) + P′(y1 + y2)[y1 + y2] = c′(y1) = c′(y2)
5. note instability — if firm 1 believes firm 2 will keep its output
fixed, it will always pay it to increase its own output
6. problems with OPEC
7. if it doesn’t believe other firm will keep its output fixed, it
will cheat first!
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