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Suppose that inverse demand is given by D(Q) = 56 2Q, Q = q1 + q2 and the cost function is TC(qi ) = 20qi + f Find the Stackelberg equilibrium and compare it to the Cournot equilibrium.
ans- Firstly we will find the cournot equilibium in which both the firms chose their quantities simultaneously. For the cournot equilibrium, the firms chose their quantities simultaneously, therefore we differentiate profit functions for both firms with respect to their output levels and then slob=ve them simultaneously for q1 and q2. profit function of firm1= (56-2(q1+q2))q1-20q1-f where f is the fixed cost. differentiating with respect to q1, we get q1(q2)=9-q2/2 profit function of firm1= (56-2(q1+q2))q2-20q2-f differentiating with respect to q2, we get q2(q1)=9-q1/2 solving them simultaneously we get q1=q2=6 price=56-2*12=32 Now we will find the stackelberg equilibrium,assuming the firm 2 to be the follower and the firm1 to be the leader. now there is sequential selection of quantities. Now the…

m 2 will do its simple profit maximization and firm1 will then substitute the value of that q2 into its profit function to get its best response.After substituting the best response of firm2, we get the profit function of firm1 as- profit of firm1=(56-2(q1+q2(q1)))q1-20q1-f differentiating with respect to q1, we get q1=9and q2=9/2 price=56-2(9+4.5)=29 we can clearly see that the output of the leader is more than the output of the follower in the stackelberg equilibrium, whereas in the cournot competiton, it was same for both the firms.

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