Question

Market demand curve for a good produced only by two firms is given by P= 70- 20. Both firms produce with constant and identical marginal cost of 3. 10, that is MC, = MC, = 10. (P,Q.4-42,) in Cournot equilibrium. a) Find b) Find (P,Q,q1,92,,, 2) in Stackelberg equilibrium with Firm 1 acting as the leader. c) Compare your findings with monopoly and competitive equilibria.

R​​​​​​1=(70-2(q1+q2))*q1-10q1

dR1/dq1=70-4q1-2q2-10=0 which gives (60-2q2)/4=q1 similarly,(60-2q1)/4=q2 by differentiating R2 putting value of q1 in second equation (60-30+q2)=4q2 hence q2=10 which gives q1=10, π1=π2=(70-2(10+10))*10-10*10=200

b)for stackelberg with firm1 as leader firm 2 Maximizing output is given by differentiating as earlier q2=(60-2q1)/4 which firm 1 knows is the Maximizing output for firm 2 and hence it will already take this into its account for maximizing profit

π1=(70-2(q1+q2))*q1-10q1=(70-2(q1+(15-q1/2)))*q1-10q1, 30q1-q1^2=π1 differentiating 30-2q1=0 hence,q1=15 which gives q2==30/4

π1=(70-2(15+7.5))*15-15*10=225 and π2=(25)*7.5-75=112.5

c) when compared with competitive equilibrium MR=MC=P is where profit maximise which gives 70-2Q=10 and hence Q=30 which will be the total quantity produces hence out put in both the earlier cases were lowerr than perfect equilibria and total profit will be 0 which is lowe than the earlier cases, In monopoly maximum profit (70q-2q^2-10q differentiating 70-4q-10=0 hence q=15 and π=450 hence output is lower whereas profit is higher

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