Question

With regard to the simple deposit multitplier model, if borrowers keep higher portions of their loans as cash instead of deposits, then this will

Group of answer choices

increase the multiplier effect

decrease the multiplier effect

not change the multiplier effect

none of the above

Answer 1

Answer

The correct answer is (b) decrease the multiplier effect.

Money multiplier(m) = M/H

where M = Money supply = C + D , H = monetary base = C + R, C = cash , D = Deposit, R = Total reserves

Thus m = M/H = (C + D) / (C + R) = (C/D + 1)/(C/D + R/D)

Now Cr = C/D = Cash to deposit ratio, Tr = R/D = Total Reserve to Deposit ratio.Note that Tr = Total Reserve to Deposit ratio is lesser than 1 and greater than 0 because they have to keep some deposited amount as a required reserve and is lesser than 1 because they put some on loan and hence Reserves must be lesser than deposit => 0 < Tr < 1

So, Multiplier(m) = (Cr + 1)/(Cr + Tr) -----------------------(1)

Now if Cr increases and we have to check whether

$\frac{\partial m}{\partial Cr}<0$$or$$\frac{\partial m}{\partial Cr} > 0$

Using (1) :

$\frac{\partial m}{\partial Cr} = [(Cr &plus; Tr) - (Cr &plus; 1)]/(Cr &plus; Tr)^2 = (Tr - 1)/(Cr &plus; Tr)^2$

As discussed above Tr < 1

$=> \frac{\partial m}{\partial Cr} < 0$

Thus, As Cr(Cash to deposit ratio) increases money multiplier(m) will decrease. So,  if borrowers keep higher portions of their loans as cash instead of deposits then Cr will increase and hence multiplier will decrease and hence multiplier effect will decrease.

Hence, the correct answer is (b) decrease the multiplier effect.