I am confused that if investment is a type of saving or a expenditure .if investment is a type of expenditure then is saving is what is left after subtracting consumption and investment from income
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In simplistic national accounts terms $$Y=C+I+X-M$$ is an expenditure identity while $$Y=C+S$$ is a use of income identity.
Implicitly this gives $$S-I=X-M$$ suggesting an excess of saving over investment in an open economy corresponds to a trade surplus in the current account, which in turn corresponds to an outflow in the financial account: the excess of savings over investment leads to an increase in overseas assets.
In a closed economy with no exports, imports or international financial flows, this forces $S=I$ and so no excess of saving over investment. Any production not used for consumption or normal investment has the effects either of increasing stocks (another form of investment) or of being valueless (so not counting towards income or saving).
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$\begingroup$ Would be good to define variables also. I assume $X =$ exports and $M =$ imports but could be clearer. $\endgroup$– snoramCommented Nov 4, 2016 at 19:20
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$\begingroup$ They are fairly standard macroeconomics variables, but yes: $X$ is exports while $M$ is imports, $Y$ is GDP, $C$ is consumption (and here I have either implicitly included $G$ which would be government consumption or ignored it), while $S$ is saving and $I$ is investment $\endgroup$– HenryCommented Nov 4, 2016 at 23:09