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In the Dornbush model, when we separate short and long run equilibrium. This is what I apparently have understood:

  • SR1: an increase in Money Supply ($M_s$) leads to a fall in domestic interest rates ($i$) since price are considered sticky in the short-run. Indeed, an excess in money supply will result in a rise in domestic bond demand, hence in bond prices i.e. an fall in interest rates. This is the same reasoning used in ISLM model, where money and bonds are perfect substitutes.
  • SR2: the fall in domestic interest rates means international investors (e.g. from U.S.) would require an appreciation of the domestic currency, so that they would exchange a reduced amount of £ received in interests for more \$ than before, so that at the very ending the still receive the same amount of \$ they received before. Therefore they expect the exchange rate $S_{£/\$}=\frac{£}{\$}$ to fall ($S_{\$/£}=\frac{\$}{£}$ to rise) in the near future.

However my textbook says:

As the domestic interest rates would be lower than the world interest rate, this means that speculators would require an expected appreciation of the domestic currency to compensate. For this reasons the domestic currency jump depreciates at time $t_1$ from $S_1$ to $S_2$ overshooting its long run equilibrium $\bar{S}$.

Where am I wrong? Why $S_{£/\$}=\frac{£}{\$}$ is rising?
Why also in the long run $\bar{S}_{£/\$}$ is rising?

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