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2. Consider a linear city where consumers with unit demand are uniformly distributed along a line with length 1 . Two firms sell the same good produce with $MC=c$. Firm 1 locates at $a?0$, firm 2 locates at $1?b$, where $b?0$. Assume $a?1?b$. Assume there is transportation cost for consumers traveling to the firm to purchase: $f(d)$, where $d$ is the distance to the frm. Assume the two firms first, set their locations and then compete in prices. (20 points) (a) Show that there will be maximum differentiation if $f(d)=td_{2}$. (b) Show that there will be minimum differentiavion if $f(d)=td$.

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