how to find (1-x)=(Pa-Pb)/2 + 3/4? There are many consumers who live in a street, represented by

 

how to find (1-x)=(Pa-Pb)/2 + 3/4?

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There are many consumers who live in a street, represented by the interval [0, 1] Consumers are distributed uniformly on this interval. There are 2 stores, A and B. located at points 0 and 1/2 (as shown in the following figure), who sell the same good. For simplicity, suppose that the marginal cost to produce the good is 0. A B x 0 1/2 1 Each consumner chooses one store to shop and buys at most one unit of the good. However, to purchase the good, everyone needs to pay a transportation cost tx where x is the distance from where he lives to the store he shops, and t is the unit cost. Stores A and B first simultaneously decide their prices, P, and P, and then consumers decide which store to shop. Suppose that every consumer's willingness to pay for the good is 0, which is large enough to cover the price he pays. Let (pp.) denote the Nash equilibrium prices. (ACost=B) PA++x= Po+t (-) PB-PA x= zt (1-x)=- PA-PB zt +44 (A 87 demand) 3 +4 (B ) There are many consumers who live in a street, represented by the interval [0, 1] Consumers are distributed uniformly on this interval. There are 2 stores, A and B. located at points 0 and 1/2 (as shown in the following figure), who sell the same good. For simplicity, suppose that the marginal cost to produce the good is 0. A B x 0 1/2 1 Each consumner chooses one store to shop and buys at most one unit of the good. However, to purchase the good, everyone needs to pay a transportation cost tx where x is the distance from where he lives to the store he shops, and t is the unit cost. Stores A and B first simultaneously decide their prices, P, and P, and then consumers decide which store to shop. Suppose that every consumer's willingness to pay for the good is 0, which is large enough to cover the price he pays. Let (pp.) denote the Nash equilibrium prices. (ACost=B) PA++x= Po+t (-) PB-PA x= zt (1-x)=- PA-PB zt +44 (A 87 demand) 3 +4 (B )