Let us consider the Brander and Krugman (1983) model with imperfect competition. In country H, in a given sector with homogeneous final output, there are two firms: one is domestic and the other is foreign. The marginal cost for production in country H of the domestic firm is c, while the marginal cost for production of the foreign firm is c/τ, where the parameter τ < 1 represents freeness of trade, which is inversely related to the level of trade barriers (transport costs, tariffs, etc.). Let us also recall that, when the domestic firm has market power, the profit maximizing price is p, being equal top = σc/(σ - s)where σ is the market demand elasticity, and s is the market share of the domestic firm in country H.i) When there is autarchy there are no competitors for the domestic firm in market H. What is the autarchy price, pA, that she charges in this case?
Question
Let us consider the Brander and Krugman (1983) model with imperfect competition. In country H, in a given sector with homogeneous final output, there are two firms: one is domestic and the other is foreign. The marginal cost for production in country H of the domestic firm is c, while the marginal cost for production of the foreign firm is c/τ, where the parameter τ < 1 represents freeness of trade, which is inversely related to the level of trade barriers (transport costs, tariffs, etc.). Let us also recall that, when the domestic firm has market power, the profit maximizing price is p, being equal top = σc/(σ - s)where σ is the market demand elasticity, and s is the market share of the domestic firm in country H.i) When there is autarchy there are no competitors for the domestic firm in market H. What is the autarchy price, pA, that she charges in this case?
Solution
In the case of autarchy, the domestic firm is the only player in the market, meaning it has a market share of 1 (s=1). We can substitute this into the given formula for the profit maximizing price:
p = σc/(σ - s)
Substituting s=1, we get:
pA = σc/(σ - 1)
This is the autarchy price, pA, that the domestic firm charges when there are no competitors in market H.
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