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.

**p **, the aggregate price, is the demand for **Q , **the aggregate goods flow. **V **, 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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