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Coca Cola and Polar soda companies are engaged in Stackelberg competition
Coca Cola and Polar soda companies are engaged in Stackelberg competition. They face the market inverse demand curve P= 200 - 49, where Q is the total market output consisting of Coca Cola's output, qi, and Polar's output, q2. Each firm produces at a constant marginal cost of $10. In a Stackleberg equilibrium, how many cans of soda will Coca Cola will produce? How many cans of soda will Polar produce?
Expert Solution
Let's start with Polar Soda ( Follower)
Max π??????2 = TR?????2 - TC 2
Therefore,
π??????2 = P*Q???2 - 10Q?????2
= (200-4Q)* Q2 - 10Q2. (Q = Q1 + Q2)
= 200Q2 - 4Q1Q2 - 4Q2² - 10Q2.
dπ2/ dQ2 = 200- 4Q1- 8Q2 - 10 = 0.
Q2 = (90+ 4Q1)/8
Now, firm 1 ( Coca Cola ) will try to maximize it's profits holding followers output constant.
Therefore,
π1 = TR1 - TC1
= (200-4Q)*Q1 - 10Q1
= (200- 4Q1- 4Q2)*Q1 - 10Q1
Replacing the value of Q2 from above
= (200 -4Q1 - 4* ( 90- 4Q1)/8)*Q1 - 10Q1
=(( 400-8Q1-90+4Q1)/2 )* Q1 -10Q1
= ((310Q1- 4Q1²)/2 ) - 10Q1
dπ1/dQ1 = ((310 - 8Q1)/2 ) - 10 = 0
Solving for Q1 = 36 units ( approx) ( Ans)
Therefore Q2 = 29 units ( approx) (Ans)
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