Explain how a currency drain affects the size of the money multiplier. In your explanation, suppose that a bank gains $1 million in new deposits and reserves

Further suppose that the desired reserve ratio is 10 percent and the currency drain is 50 percent.

A currency drain decreases the size of the money multiplier. The money multiplier reflects the fact that the banking system has a magnified effect on any change in reserves because the reserves are loaned by many banks. A currency drain decreases the amount of reserves that stay within the banking system.
For example, take the bank that gains $1 million in new deposits and reserves. With the desired reserve ratio equal to 10 percent, start by assuming there is no currency drain. In this case, the desired reserve ratio of 10 percent means that the bank will keep $100,000 as reserves and so it will loan $900,000. The entire $900,000 will be deposited in a second bank. The entire $900,000 deposit adds to the initial $1 million deposit to create $1.9 million of new money. That bank will then keep $90,000 as reserves and loan $810,000. In this stage, the entire $810,000 will be deposited in a third bank and so the total new money (so far) created will become $2.71 million. Now, suppose that there is a currency drain, say of 50 percent. In this case, of the $900,000 first loan, only $600,000 is deposited in the second bank because $300,000 (50 percent of the $600,000 of newly created deposit money) is kept outside the banks as currency. Hence the second bank, which must keep $60,000 as reserves, can loan only $540,000. And of this loan, 50 percent or $180,000 is kept as currency and only $360,000 is deposited in the third bank. Therefore the amount that each bank can loan is reduced and so the ultimate effect on the quantity of money is decreased.