In the loanable funds market, the main reason we believe that the supply of loanable funds slopes upward, i.e. more funds are offered for borrowing if the real interest rate is higher, is that
This is the right answer. Remember, our model is always ceteris
paribus, i.e. everything else unchanged. So, in the supply and demand
diagram for US loanable funds, we measure the US real interest rate on
the vertical axis, the US quantity of loanable funds on the horizontal
axis, for the US market. When we move up on the vertical axis, increase
the US real interest rate, the real interest rate in London, Frankfurt,
Tokyo, etc is assumed unchanged. Short term capital is highly mobile, so
the increased real interest rate in the US will cause loanable funds to
switch from those foreign markets to the US market, increasing the quantity
of loanable funds offered in the US market -- so the supply of loanable
funds slopes upward.
Much as many people would like to believe this, we cannot be sure
of it. There is both a substitution effect -- the higher real interest
rate means the opportunity cost (interest foregone) of consuming now is
higher, so we would expect households to save more, consume less -- and
an income/wealth effect -- the higher interest rate means real lifetime
income is higher, we should tend to consume more, save less [suppose you
were trying to save enough to buy a car or get enough to produce an income
to retire on; with the higher interest rate you now need to save less
to achieve the same target]. The two effects go in opposite directions
and we have no way of knowing which will be bigger overall, so this is
not a convincing reason why the supply curve should slope up.
This has to do with the demand for loanable funds, not the
supply; it is a reason the demand curve for loanable funds slopes down.