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As far as i understand in the Krugman target zone model the following equation describes the behaviour of the exchange rate within and outside a target zone $s_t = f_t + \alpha E_t(ds_t/dt)$. But if the fundamental $f_t$ follows a random walk why is $s_t = f_t$ (the 45 degree line on the S-curve) a solution to the equation in the free float case?

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