### Quantity theory of money and fundamental equation of traffic

I have argued that economics is a subset of transport economics, since transport economics includes time and space, and deals with the movement of many goods, while economics tends to be aspatial (and to a lesser extent atemporal) and focus on one good, money. The objective of this post is to suggest the equivalent of two fundamental relationships in two similar but largely unconnected fields, traffic engineering and macro-economics. These are the equation of exchange and the fundamental relationship of traffic.

The fundamental relationship of traffic says: Q=KV.

where:

Q =flow (veh/hr) = Motorcars/Time (motorcars/time)

K= density (veh/km) = Motorcars/Distance

V_{t} = transportation velocity (km/hr) = Distance/Time

or in other words, dimensionally:

(M/D)(D/T) = M/T

The equation of exchange says: MV_{e}=PY

where (quoting and rephrasing wikipedia):

M = the total amount of money in circulation on average in an economy during the period, say a year

V_{e} = economic velocity, or the velocity of money in final expenditures. (number of times a unit of money is spent in a given time period, e.g. a year). This differs from V_{t}.

P = the price level associated with transactions for the economy during the period

Y = total output per unit time.

We achieve equivalence if MV=PY can be mapped to KV = Q

First, let us assume that PY is the output, or GDP, this can be mapped directly to Q or motorcars per time

MV_{e}=PY -> KV_{t} = Q

where PY -> Q

So does MV_{e} map to KV_{t} ?

money supply * number of times money turns over per year =?= (number of motorcars / distance) * (distance / time)

So assuming money supply is a stock like the number of motorcars, and economic velocity V_{e} is in units of time^{-1}, then it maps.

This equation is important in economics to understand inflation. If the money supply increases without any change in real output Y, than the price level must increase (if economic velocity V_{e}is fixed), or the price level can remain constant if the velocity slows down (as in a recession when people spend less).

The equivalent in transportation suggests that if the number of cars in a system increases, and output flow remains constant, then a queue forms and velocity slows.

Other interpretations?

References:

Wikipedia: Quantity theory of money

The New Palgrave Dictionary of Economics - money, classical theory of

## Comments

I've always thought of the Quantity Theory of Money as being akin to Boyles' Law: PV=NRT. The macroeconomy is an aggregate summary of interactions among moles of individual molecules, any of which could be doing practically anything at any given time but which can be accurately characterized in the aggregate.

The thing to remember is that "velocity" is not a natural constant; it's the result of lots of decisions being made. The accounting identity MV=PY is really the way of calculating the current velocity, since M is fixed in the short run (a decision variable chosen previously) and P and Y are observable. In your traffic analogy, this might map to "maximum achievable velocity" in your traffic example, not your "actual velocity" calculation which is more like temperature (average kinetic energy of the molecules).

Posted by: AGMycroft | July 3, 2009 3:56 AM