Consider a Cournot duopoly in which firm i has marginal cost ci and firm j has marginal cost cj. The firms face inverse
Posted: Sat Feb 19, 2022 2:41 pm
Consider a Cournot duopoly in which firm i has
marginal cost ci and firm j has marginal
cost cj. The firms face inverse demand function
p = KQ
where K > 0 is a constant
and Q = qi + qj is aggregate output.
Assume that ci, cj ≥ 0. (a) Derive the
Cournot equilibrium outputs qiC and qjC.
(b) Derive the Stackelberg equilibrium
outputs qiS and qjS of the game in which
firm i first sets its quantity qi and then
firm j responds by setting its quantity qj.
(c) Compare the Cournot equilibrium output qiC of
the first mover to its Stackelberg equilibrium output qiS,
distinguishing between the three cases (i) ci = cj,
(ii) ci < cj and (iii) ci > cj. Are
there qualitative differences? If so, explain what these
differences are in terms of strategic substitutes and strategic
complements.
marginal cost ci and firm j has marginal
cost cj. The firms face inverse demand function
p = KQ
where K > 0 is a constant
and Q = qi + qj is aggregate output.
Assume that ci, cj ≥ 0. (a) Derive the
Cournot equilibrium outputs qiC and qjC.
(b) Derive the Stackelberg equilibrium
outputs qiS and qjS of the game in which
firm i first sets its quantity qi and then
firm j responds by setting its quantity qj.
(c) Compare the Cournot equilibrium output qiC of
the first mover to its Stackelberg equilibrium output qiS,
distinguishing between the three cases (i) ci = cj,
(ii) ci < cj and (iii) ci > cj. Are
there qualitative differences? If so, explain what these
differences are in terms of strategic substitutes and strategic
complements.