He has more money than meets his monetary demand at the existing prices.

As he seeks to reduce his stock of money to due proportions by buying more goods, he thereby distributes a part of the excess of money to others.

This bids up the prices of goods further until the total value of goods exchanged again bears the same ratio as before to the average monetary demand of each individual.
Take an extreme case: if twice as many dollars get into circulation in a community, either some few men may have far more dollars than before, while others have nearly the same number; or every man may have his due proportion of the new supplies, just twice as many as before in proportion to his income.

The latter result, "other things being equal," is the logical one after equilibrium has been restored.
If prices of goods remained the same as before, there would be twice as many pieces of money available to effect the same number of trades at the same prices.

There is no reason why each person should tie up twice as large a proportion of his income in the form of money.