Given the reserve-holding ratio e and the fraction of deposits held as cash c,the money multiplier becomes

Question

Quizplus · Accepted Answer

The money multiplier is given by 1/rr, where rr is the reserve ratio. The reserve ratio is the fraction of deposits that banks are required to hold as reserves, so e = 1/rr. Therefore, we have:

1/rr = 1/e     ⇒     rr = e

The amount of money that banks can lend is the difference between deposits and reserves, or (1 - rr)*D, where D is the amount of deposits. Of this amount, the fraction held as cash is c, so the amount that is lent out is (1 - rr)*D*c. Therefore, the money supply is:

M = (1 - rr)*D*c/rr

Substituting rr = e and simplifying, we get:

M = (1 - e)*D*c/e

Dividing both sides by D, we get:

M/D = (1 - e)*c/e

This is the formula for the money multiplier, which shows how much the money supply expands for every dollar of deposits. The correct answer is therefore (1 + c)/(e + c).

Given the Reserve-Holding Ratio E and the Fraction of Deposits