The international cola industry is a Cournot oligopoly in which three firms, A, B and C, produce quantities 9A, 9в and qc, respectively. The aggregate inverse demand function is:
p(Q) = (100+ 60X) where you should substitute X for the last number of your student ID number and Q = 9A + 9B+9c. The three firms have asymmetric costs: in particular, their total cost functions are given by = (40 - α) 9A TCA (9A) TCB (9B) 40qB TCc (qc) (40+ a) qc where 0 < a < 20 is an exogenous parameter capturing asymmetry of costs across firms.
a- Find the best response functions for the three firms (as a function of α if needed), and the quantities produced by the other firms.
b- Find the Cournot equilibrium individual quantities, aggregate quantity and price. Discuss how these variables change with α.
c- Find the consumer’s surplus in the Cournot equilibrium, and discuss how the social welfare depends on α.
d- Find the Lerner index for each firm and the Herfindhal-Hirshman index as a function of α. Discuss how these vary with α.
