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Consider the quantity theory of money: $MV=PY$. "Consider an example of a demand shock: the introduction and expanded availability of credit cards. Because credit cards are often a more convenient way to make purchases than using cash, they reduce the quantity of money that people choose to hold. This reduction in money demand is equivalent to an increase in the velocity of money. When each person holds less money, the money demand parameter k falls. This means that each dollar of money moves from hand to hand more quickly, so velocity $V (= \frac{1}{k})$ rises."

This is the argument given in Mankiw's intermediate macroeconomics text. I found this argument not correct in some sense. First of all, Mankiw's says people reduce the demand of money. This is not right. The total amount of money in the economy is a given. I think what Mankiw is trying to argue is people have less cash and less money in the demand deposit account. But then the money go to their saving account, or maybe they invest in some securities. But all these money they invested will become someone else's deposit account and an increase in saving account balance and the decrease in checking account balance does not change the total money supply. The money supply is inherently fixed then.

Mankiw also argues that each person hold less money so velocity goes up. The problem is although ordinary consumers are holding less money, banks are actually holding more cash to pay for people's purchases associated with the credit card. This is because merchants are not going to wait until people's statement balance get due in the next two months to collect their money. They want to settle the payment ASAP, which is why banks have to pay them earlier. And consumers will pay back the money to the bank later.

I believe another problem is what is the difference between real money supply and real money demand. In the problem Mankiw assumed Price Level does not change, and since the money supply is exogenous, $M/V$ does not change, i.e., real money supply does not change. So there is no way people is holding less money. They have to hold it somewhere, maybe in saving, maybe in checking. And like I said before, if they invest in securities, the balance they've invested show up on someone else's deposit account.

I really struggle with this seemingly easy problem. Any comments, corrections, and help is appreciated.

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