whereQ=Q1+Qz. a.Find the Cournot-Nash equilibrium.Calculate the profit of each firm at this equilibrium. Todetermine the Courot-Nash,we first calulate the reaction function reach firm,price.quantity,and Firm 1,TR-TCi,is equal to 元=300g-g-222-60g=240g-g-Q22 Therefore, =240-20-Q2 g Setting thisequal to zero and solving for Q in terms of Q1=120-0.5Q. This is Firm I's reaction function.Because Firm 2 has the same cost structure,Firm 2's reaction function is 02=120-0.591 Substituting for in the reaction function for Firm 1,and solving for we find Q1=120-0.5120.0.5Qù.0rQ1=80. By symmetry.Q2=80.Substituting Q and Q2 into the demand equation to determine the price at profit maximization P=300-80-80=$140 Substituting the values forprice and quantity into the proft function 元1=(14080)·(60)(80)=$6,400and 2=(14080)(60(80)=6,400, Therefore,profit is6.400 for both firms in Cournot-Nash equilibrium. b.Suppose the two firms form a cartel to maximize joint profits.How many widgets will be produced?Calculate each firm's profit. Given the demand curve is P=300-Q,the marginal revenue curve is MR=300-2Q Profit will be maximized by finding the levelofoutput such that marginal revenue is equal to marginal cost: 300-2Q-60 Q=120. When output is equal to 120.price will be equal to 180.based on the demand curve.Since both firms have the same marginal cost they will plit the tota output evenly between themselves so they each produce 60 units.Profit for each firm is: where Q = Q1 + Q2 . a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium. To determine the Cournot-Nash equilibrium, we first calculate the reaction function for each firm, then solve for price, quantity, and profit. Profit for Firm 1, TR1 - TC1 , is equal to  1 = 300Q1 − Q1 2 − Q1Q2 − 60Q1 = 240Q1 − Q1 2 − Q1Q2 . Therefore,  1 Q1 = 240 − 2Q1− Q2 . Setting this equal to zero and solving for Q1 in terms of Q2 : Q1 = 120 - 0.5Q2 . This is Firm 1’s reaction function. Because Firm 2 has the same cost structure, Firm 2’s reaction function is Q2 = 120 - 0.5Q1 . Substituting for Q2 in the reaction function for Firm 1, and solving for Q1 , we find Q1 = 120 - (0.5)(120 - 0.5Q1 ), or Q1 = 80. By symmetry, Q2 = 80. Substituting Q1 and Q2 into the demand equation to determine the price at profit maximization: P = 300 - 80 - 80 = $140. Substituting the values for price and quantity into the profit function, 1 = (140)(80) - (60)(80) = $6,400 and 2 = (140)(80) - (60)(80) = $6,400. Therefore, profit is $6,400 for both firms in Cournot-Nash equilibrium. b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit. Given the demand curve is P=300-Q, the marginal revenue curve is MR=300-2Q. Profit will be maximized by finding the level of output such that marginal revenue is equal to marginal cost: 300-2Q=60 Q=120. When output is equal to 120, price will be equal to 180, based on the demand curve. Since both firms have the same marginal cost, they will split the total output evenly between themselves so they each produce 60 units. Profit for each firm is: