"Demand for money" - definition What is the definition of "demand for money". The definition given by Wikipedia appears gibberish to me. And just to double check - what are the units of demand for money? Is it measured in "dollars"? or perhaps "dollars per unit time"? Or a ratio between two things?

If I understand it correctly, the level of demand for any produce (other than money) is the rate of flow of money that is currently being used to purchase that produce. So for example, if there is 1 million dollars per day being spent on VW cars, then you can say, "the demand for VW cars is $1m per day". Clearly the meaning of the word "demand" in the expression "demand for money" can't be the same thing - can it?

EDIT: Some definitions sound an awful lot as though a person's demand for money is exactly equal to the amount of money they currently have (and its units would therefore simply be "dollars"). Please include in your answer, an indication of whether or not your definition is identical to a person's current holding of money.

EDIT: Looking at the suggested answers and doing some more reading, I get the feeling that the word "demand" in economics is actually not a single number, but a set of numbers, or a curve. In the case of normal goods (call them Widgets), then the x axis will be price and on the y axis will be "Widgets sold per unit time" (the unit of time could be days, years etc). Please advise if you think I have this bit wrong.
In Economics, to define/describe "demand for $X$", whatever $X$ represents, we need


a definition for $X$ 
a measurement unit for the quantity of $X$
a measurement unit for the price of $X$


Given these, the "demand schedule" for $X$ (terminology dating back to A. Marshall), is the geometric locus of pairs (quantity, price) that reflect the quantity demanded for the corresponding price in the pair.

And that's that: why is the quantity demanded what it is for a given price, is (at least) one level deeper in the economic structure and analysis.

As regards "money", I just record here the usual approach taken:


We have in mind something that is perfectly liquid (and in practice we may include in the definition "essentially liquid" assets), where "liquid" means "immediately acceptable by anyone in any exchange"
The quantity of money is measured in some currency unit (like USD, Euros etc),  
We use the interest rate as "the price of money"


To go this one step deeper, the reason why "demand for money" is not fixed at infinity, has to do with the question that we pose so as to avoid a useless answer. And the question is essentially a question of allocating a given level of assets between different forms/different degrees of liquidity, money included: Given that my wealth is $W$ (measured in a currency unit), and given that the interest rate I will enjoy if I save it all in an interest-bearing form is $i$ (unitless), how much of this wealth do I want to keep in "money form"?

Enter arguments as to why we want to keep money, functional forms that formalize these arguments, etc.

In dynamic models, it is understood that this question is posed and answered by the demand schedule for money for each time-period of the model. In static models, there is a single time period.

Another usual aspect is that we examine "real  money balances", i.e. the deflated value of the nominal money balances.

"Current holdings of money" is not the demand schedule but equilibrium quantity demanded, given whatever constraints we postulate that they exist.

This gives rise to the concept of a possibly "liquidity constrained" economic agent: given his wealth, the interest rate and his preferences, the agent would want to allocate $W_m^*$ of his wealth to money holdings. But we may observe that it allocates something less, for example because the existing markets where the agent can transform non-liquid assets to liquid ones are "incomplete" (as they say), and so the agent finds himself with non-liquid wealth that he would want to transform into money but he cannot (perhaps due to asymmetric information, risks that cannot be priced, etc). While this is a constrained equilibrium also, it is important for economic analysis and economic outcomes to realize that here we may have an additional "binding constraint" on the agent's behavior, and as this constraint changes, the behavior of the agent will also change.

Detecting the existence of such exogenous liquidity constraints is difficult, because it is difficult to separate their effects on money holdings from the effects of other constraints (like the level of existing wealth of the agent).

So "current money holdings" is tautologically equal to "current equilibrium money demanded", but the challenge of economic analysis is to determine which constraints are binding and so characterize the observed equilibrium.