Consider a Hotelling line city model, where two firms are located at the two extreme points. The

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Question:

Consider a Hotelling line city model, where two firms are located at the two extreme points. The length of the city is 1, and the consumers are evenly distributed over the line. Transportation cost per unit is $tt$ . The utility of the good for each consumer is 2 and each consumer only consumes one unit of good. Consumer's utility is zero without purchase. Suppose price charged by firm $i(i=1;2)i(i=1;2)$ is $pipi$ .

Derive demand function for both firms (one lives at point $x=0x=0$ and the other lives at point $x=1x=1$ ) and draw a graph to show demand function.