Question 1 [15 points] Consider a Cournot duopoly with two firms 1 and 2. Let qi and q2 be quantity produced by firms 1,2 and let the inverse demand given by p = 12 - q1- q2 where p = price of the good. Both firms have unit cost 2. Assume each firm can produce only one of the following levels of quantity: 2, 4 or 5. Table 1: Profit and best response of firm 1 q2 = 2 92 = 4 q2 = 5 q1 = 2 12 q1 = 4 16* 91 =5 15 Table 1 presents the profit of firm 1 and its best response to specific q2. The profits at q2 = 2 are shown and best response is identified by *. Filling up the missing values, identify best response of firm 1 to other values of q2. Table 2: Profit and best response of firm 2 q2= 2 q2 = 4 92 = 5 q1 = 2 12 16* 15 q1 =4 q1 = 5 Table 2 presents the profit of firm 2 and its best response to specific q1. The profits at q1 = 2 are shown and best response is identified by *. Filling up the missing values, identify best response of firm 2 to other values of qi. Table 3: Profits and best responses of both firms q2 = 2 92 = 4 q2 = 5 q1 = 2 91 = 4 q1 = 5 Using the information from Tables 1,2, present the profits of firms in Table 3 together with best responses. For each cell, write the profit of firm 1 in the left box and profit of firm 2 in the right box. Then identify all Nash Equilibrium (NE) of this Cournot duopoly