# Why can't price level be negatively correlated with money demand?

Source: p 585, Economics, 3 Ed, 2014, by NG Mankiw, MP Taylor

Although many variables affect the demand for money, one variable stands out in importance: the average level of prices in the economy. People hold money because it is the medium of exchange. Unlike other assets, such as bonds or stocks, people can use money to buy the goods and services on their shopping lists. How much money they choose to hold for this purpose depends on the prices of those goods and services. The higher prices are,
the more money the typical transaction requires,
[1.] and the more money people will choose to hold in their pockets and bank accounts.
[2.] That is, a higher price level (a lower value of money) increases the quantity of money demanded.

I doubt 1 and 2 that feels too absolutely certain. (They're also restated, but rephrased, on pp 683 and 705.) Why must 1 and 2 be true?

Abbreviate Prior Money as PM, i.e. consumers' money held 'in their pockets and bank accounts' before the price rise.

Suppose that higher prices $\implies$ more money needed for each typical transaction. But even facing a higher price level, consumers may already possess enough PM to transact, and so needn't more money.

Moreover, even with enough PM for their regular purchases, the price rise may cause consumers to spend less. Then money demand would DEcrease.