Question 2
a) Find the profit functions
π1 = TR1 - TC1 π2 = TR2 - TC2
= (160 - q1 - q2)q1 - 10q1 = (160 - q1 - q2)q1 - 10q1
Find the derivative of profit (marginal profit) to maximize it
π'1 = 0 π'2 = 0
150 - 2q1 - q2 = 0 150 - 2q2 - q1 = 0
Best response functions are
q1 = 75 - 0.5q2 and q2 = 75 - 0.5q1
b) NE occurs when
q1 = 75 - 0.5*(75 - 0.5q1)
0.75q1 = 37.5
q1 = q2 = 50
This is the required NE. Market price = 160 - 50 - 50 = $60
c) Profits are
π1 = (160 - q1 - q2)q1 - 10q1 = (160 - 50 - 50)*50 - 10*50 = 2500
π2 = (160 - q1 - q2)q1 - 10q1 = (160 - 50 - 50)*50 - 10*50 = 2500
d) CS = 0.5*(Max price - current price)*current qty = 0.5*(160 - 60)*100 = 5000.
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's...
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