GATE 2024 Question 65: Monopolistic competition and oligopoly

Consider a duopoly market where Firm 1 and Firm 2 produce differentiated products such that the demand function of each firm is given by:

$q_1(p_1,p_2) = 18-p_1+p_2$ $q_2(p_1,p_2)=18+p_1-p_2$

Here, $q_1$ and $q_2$ are the outputs produced by Firm 1 and Firm 2, respectively, and $p_1$ and $p_2$ are the corresponding per unit prices.

Cost of production for the $i^{th}$ firm is given by $C_i(q_i)=2q_i \ \forall\ i=1,2$.

The firms compete in prices. The price set by Firm 2 such that the market is in Nash equilibrium will be ______ (in integer).