T/F = If the excess to reserve deposit ratio goes up along with the currency to deposit ratio, all else constant, then we are unsure what happens to the money multiplier since the money multiplier is negatively related to the excess reserve to deposit ratio but positively related to the currency to deposit ratio.
The money multiplier m is related to the currency-deposit ratio [C/D], the excess-reserves ratio [ER/D)] and to the required reserve ratio [RRR] by the formula: m = (1 + [C/D])/([RRR] + [C/D]+[ER/D]).
If the excess-reserves ratio and the currency-deposit ratio go up with all other variables remaining the same, there is a decrease in the money multiplier. This is a result of the fact that the currency-deposit ratio is present both in the numerator as well the denominator but the excess-reserves ratio is present only in the denominator. As two terms of the denominator are going up with the third remaining same and only one term goes up in the numerator, the denominator becomes larger at a rate greater than that at which the numerator increases.
The given statement is therefore false. For the conditions that are given, the money multiplier becomes smaller.