We find that the equilibrium of P1 does not change,
regardless of whether Firm 3’s SLR exceeds that of Firm 2.
The intuition is straightforward; the lower price support for Firms 2 and 3 rises above their respective minimum prices.
Therefore, the equilibrium is unaffected by whether the
minimum prices of Firms 2 and 3 switch order, because neither
is part of the equilibrium price ranges for those two
firms. Furthermore, although Firm 2 may have the highest
SLR, it still sets its lower price support partially in response
to Firm 1’s higher support, because Firm 1 forgoes competition
for s123. Firm 1’s main issue is that both Firms 2 and
3 have higher SLRs, regardless of whose is greater.