Aggregate Model

Consider the aggregate income of a given economy and call it Y.

The aggregate real output is the number of goods (and services) produced per year and is represented by Q.

The aggregate price is Y/Q = p and is called the price level so that pQ = Y.

Y can also be expressed as the product of the money stock m and money velocity V so that Y = mV

The equation of exchange is the statement that (1)  pQ = mV

Income Growth

Income growth is measured in percentages. From the equation of exchange, it follows, then, that

(pQ)’/(pQ) = (mV)’/(mV), where f’ = df/dt

This leads to (2)  p’/p +Q’/Q = m’/m + V’/V

A corollary to (2) is the equation (3)  p’/p – V’/V = m’/m – Q’/Q

where the demand terms are grouped on the LHS of (3) and the supply terms are the RHS.

, the aggregate price, is the demand for Q ,  the aggregate goods flow.  , the money velocity, is the demand for m , the money stock. Y is always the product of a demand term and an appropriate supply term.

If  m’/m – Q’/Q = c , then it must be true that  p’/p – V’/V = c as well.  In other words, if supply terms grow at different rates then demand terms will change at the same differing rate.

A frequent error made in discussions of the Quantity Theory of Money is the statement that an increase in money supply leads to inflation, leaving out consideration of the other 2 terms, ie., Q’/Q and V’/V.  This causes many to conclude, erroneously, that the Quantity Theory of Money is “not true”.

Real Product Growth

Real product Q is the product Q = aL where a is productivity which is defined as product per worker.  L  is the work force. L , in turn. is the product of population n ,  and employment level E , so that  Q = anE ,  and Q’/Q = a’/a+n’/n+E’/E .  Both a and n vary slowly over time so that it is possible to write

a’/a = α  and n’/n = β with α,β  constant  so that  Q’/Q = α+β+ E’/E.  From this, it can be seen that Q’/Q depends directly on employment growth,  E’/E.

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