If the central bank raises intereat rates, isn't the money supply now less and the exchange rate is greater? I have run into opposite statements and dont know how to approach this problem. Thanks in advance for everyone's help
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$\begingroup$ What do you mean when you say, "the exchange rate is greater"? $\endgroup$ – Art Jan 8 '20 at 6:13
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$\begingroup$ @Art that a unit of, say, dollars is now worth more pounds $\endgroup$ – segozcan Jan 8 '20 at 11:24
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If by “greater”, you mean higher number It depends on how you quote exchange rate. Under American system the exchange rate between USD and euro would be given by $S=EUR/USD$ under European system the exchange rate would be quoted other way around as $S=USD/EUR$. So under American system if the USD appreciates due to higher interest rates the $S$ would actually get lower while under the European system appreciation would actually lead to greater/higher exchange rate $S$.
Otherwise, ceteris paribus, higher interest rate has to lead to appreciation under the standard exchange rate model since the exchange rate is given in standard monetary model of exchange rates:
$$S=ln(p)-ln(p_f)= ln(m)-ln(m_f) -(ln(y)-ln(y_f))+\lambda(i-i_f) $$ (where $p$ is price level, $m$ money supply, $y$, real GDP i interest rate and $f$ denotes foreign sector - also I assume that $ ln(L(i)) \approx \lambda i$so the exchange rate should appreciate when interest rates $i$ increases and nothing else change.
