Consider the following setting: there are three independent markets in 3 countries (1, 2 and 3) and two firms (1 and 2) that belong to countries 1 and 2 respectively. Firm 1 is a monopolist in country 1, firm 2 is a monopolist in country 2 and the two firms compete in country 3. Assume that both firms have zero marginal and fixed costs, there are no trade costs and firms are free to trade. The markets in country 1 and 2 are identical and the respective monopolists face the following inverse demands: p1 = 24 – q1 , p2 = 24 – q2 where pi and qi are the price and quantity the monopolist charges/sells in its home country market. Consumers in country 3 consider the two products to be differentiated and the demand functions are: q13 = 24 – 2 p13 + p23 q23 = 24– 2 p23 + p13 where qi3 and pi3 are the quantity sold and price charged by firm i (i=1, 2) in country 3. 1) Assume that Firm 1 commits to use a Uniform price at home and in country 3 and that Firm 2 commits to use Local prices at home and in country 3. Calculate the Nash equilibrium in prices. 2) Assume that both firms commit to use a Uniform Price at home and in country 3. Calculate the Nash equilibrium in prices.
Consider the following setting: there are three independent markets in 3 countries (1, 2 and 3) and two
firms (1 and 2) that belong to countries 1 and 2 respectively. Firm 1 is a monopolist in country 1, firm 2 is
a monopolist in country 2 and the two firms compete in country 3.
Assume that both firms have zero marginal and fixed costs, there are no trade costs and firms are free to
trade.
The markets in country 1 and 2 are identical and the respective monopolists face the following inverse
demands:
p1 = 24 – q1 , p2 = 24 – q2
where pi and qi are the price and quantity the monopolist charges/sells in its home country market.
Consumers in country 3 consider the two products to be differentiated and the demand functions are:
q13 = 24 – 2 p13 + p23
q23 = 24– 2 p23 + p13
where qi3 and pi3 are the quantity sold and price charged by firm i (i=1, 2) in country 3.
1) Assume that Firm 1 commits to use a Uniform price at home and in country 3 and that Firm 2
commits to use Local prices at home and in country 3. Calculate the Nash equilibrium in prices.
2) Assume that both firms commit to use a Uniform Price at home and in country 3. Calculate the Nash
equilibrium in prices.
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