Before we answer this, we need to take a moment and discuss why a definition of money matters. Imagine you live in a country where the only good produced is pizza. That’s it. Every year the country makes 100,000 pizzas that sell for $10 each. GDP for this country is therefore $1,000,000.
Now, how much money (whatever that means) has to be in circulation to support this $1,000,000 in spending? First, let’s assume that each Dollar exchanges hands exactly twice each year. (This is an important assumption we’ll relax later. But for now, go with it.) Then the answer is $500,000. Here’s why. If each of $500,000 is spent exactly twice, the total amount spent is $1,000,000. And GDP is by definition the amount spent on final goods and services – pizzas in our example.
If there were only $250,000 in money available (and each Dollar is still spent twice), then it wouldn’t be possible to spend $1,000,000. Either a lot of pizzas would go unsold, or the price of pizzas would have to come down, or some combination of these two. But GDP couldn’t be more than $500,000 (i.e. $250,000 X 2).
Reasonable. But what if there were $1,000,000 in money circulating? Certainly all 100,000 pizzas could be purchased. But would people do with the rest of the money. There’s absolutely nothing else to buy. Perhaps save it until next year? But then what will they do with all the extra money next year? One of two things will happen. With the extra money, buyers want more pizza. And so, either the pizza places see the opportunity to raise price. Or, the extra demand will motivate the pizza places to make more pizzas. Or maybe some combination of both these. But if there’s $1,000,000 and each Dollar is spent exactly twice, then GDP (i.e. the number of pizzas X the price of pizza) must equal $2,000,000.
The following equation (less the reference to pizza) is referred to as the Equation of Exchange:
Money X Velocity = RGDP X Price Level
Money refers to the amount of money in circulation. Velocity is the number of times the average Dollar is spent in a given year. RGDP is Real GDP and refers here to the actual quantity of items sold and finally the Price Level measures what happens to product prices in general.
This Equation of Exchange is an identity. It has to be true. If we assume velocity (i.e. the average number of times a Dollar is spent in a year) = 2, then the amount of money spent (i.e. the left-hand side of the equation) must equal the amount of money received (GDP).
This finally brings us back to the importance of correctly defining money. If the monetary authority doesn’t put enough money into circulation, GDP will fall. If there’s too much money, GDP will go up. But this might be due to price inflation rather than an increase in RGDP. And so, the goal is to keep the amount of money consistent with the target level of GDP. But to do this, we have to be able to define what we mean by “money” to begin with.