In the following duopoly model, the firms operate in a market where their products are not...

 

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In the following duopoly model, the firms operate in a market where their products are not completely identical but can be considered substitutes for each other. If Firms 1 and 2 choose unit sales prices p₁ and p2, respectively, the quantity that consumers demand from Firm 1 is 91(P₁.P2) a P₁+ bp2 and from Firm 2 is 92(P1 P2) = a-p2 + bp₁ where 0 < b < 2 reflects the extent to which Firm i's product is a substitute for Firm j's. The total cost to Firm i for producing q, units is cq, where c<a. The firms announce their prices simultaneously, with 0≤p, <∞ for i=1,2. Each firm seeks to maximize its net profit. (a) Give an example of a market where this type of scenario might occur. (b) Find all pure strategy Nash equilibria. In the following duopoly model, the firms operate in a market where their products are not completely identical but can be considered substitutes for each other. If Firms 1 and 2 choose unit sales prices p₁ and p2, respectively, the quantity that consumers demand from Firm 1 is 91(P₁.P2) a P₁+ bp2 and from Firm 2 is 92(P1 P2) = a-p2 + bp₁ where 0 < b < 2 reflects the extent to which Firm i's product is a substitute for Firm j's. The total cost to Firm i for producing q, units is cq, where c<a. The firms announce their prices simultaneously, with 0≤p, <∞ for i=1,2. Each firm seeks to maximize its net profit. (a) Give an example of a market where this type of scenario might occur. (b) Find all pure strategy Nash equilibria.

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a One example of a market where this type of scenario might occur is the market for gasoline Gasolin... View the full answer