We now turn to the case of Cournot competition in which firms choose quantities rather than prices at stage 2 after committing to quality levels at stage 1. The game played by firms is set out in 4.1 and the respective effects of LDC and developed country policies towards quality are explored in 4.2 and 4.3.
4.1 The two-stage model of firm behavior: Cournot competition.
Examining the second-stage first, we solve for pL = PL/qL and pH = PH/qH from the demand functions (5), so as to obtain the inverse demand functions:
This includes the possibility that both firms set the same qualities (i.e. qL = qH), since, setting r = 1 in (22), we obtain, P = (1- (xL + xH ))q‘ for i = L,H, as in (3). Recalling that productions are zero, for any given qualities, qL and qH , committed at stage 1, firm L sets xL to maximize its revenue, RL = PLxL, taking xH as given and firm H sets xH to maximize its revenue, RH = PHxH , taking xL as given. Thus from (22), xL and xH satisfy the first order conditions:
where the second order and stability conditions are also satisfied. Also, since 0R/0x is decreasing in xj for i,j = L,H and i g j, the outputs are strategic substitutes as is typical for Cournot competition.