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When I was studying the Mundell-Fleming Model, I came across the assumptions :
1- Exchange rate expectations are static
2- Capital mobility is less than perfect
I ended up with the following questions :
Q1) Does capital mobility less than perfect implies $r \ne r^{*}$ where $r$ is the domestic interest rate and $r^{*}$ is the foreign interest rate. Or does it mean $r \neq r^{*} + \delta S^{e}$ Which is the UIRP
Q2) What is meant by "exchange rate expectations are static"?
The expression "Static Expectations" unfortunately can be found to be used with two different meanings in the economics literature
1) The one apparently less used but used nevertheless is, for some variable $x$ that needs to be predicted while standing at period $t$ (the superscript $e$ denotes "expectation" in the general meaning of the term, without specifying how it is formed)
$$x^e_{t+1 |t} = b, \;\;\; \forall\, t$$
where $b$ is some constant. This reflects the following attitude: agents are oblivious to any information accrual as time passes, they even ignore possible movements in the realized values of $x$, and if asked, they always think that "tomorrow" the value will be $b$ (perhaps a better way to describe such expectations would be "fixed expectations" rather than "static").
2) The other and most widely used meaning of "Static expectations" is
$$ x^e_{t+k |t} = x_t, k=1,2,...$$
i.e. "what is will continue to be".
In the Mundell-Fleming model, the expression is used with this meaning.
(I note that with this meaning, "Static Expectations" coincide with Rational Expectations when the $x$-variable follows a pure random walk -but again, in Static Expectations we do not specify how we arrive at the value we expect).
Given this, imperfect capital mobility would lead to the domestic interest rate being different in equilibrium from the international interest rate in the sense $i \neq i^*$, since the exchange rate is not expected to change. So the Uncovered Interest Rate Parity (in logarithmic terms) $i = i^*+\Delta s^e$ becomes under Static Expectations $i = i^*$, and stops to hold under imperfect capital mobility.
