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First I am not sure what classical economists say but doesn't increase in Money supply decreases interest rate and cause investment to expand and thus GDP rises. Therefore the aggregate demand increase, causing price level to rise. But what does proportional mean in this case?

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    $\begingroup$ So to sum up, your question is: What does the word 'proportional' mean? $\endgroup$
    – Giskard
    Commented Apr 9, 2016 at 19:27

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It's a bit hard to answer without a precise model structure, but normally an increase in money will propagate into an increase in nominal demand. For the sake of simplicity, suppose money is equivalent to nominal gdp $M$, whereas real gdp by definition is given by $Y=M/P$. In classical economics, real gdp is pinned down completely by fundamentals of the economy, so that accordingly $P\propto M$ (namely by a factor $1/Y$).

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I find the easiest way to think about this problem is with an (absurd) example:

Suppose a government could magically put three zeros at the end of every major currency unit (e.g. dollar) denomination in the entire economy.

Suddenly:

  • if someone previously earned \$1000/week, they now earn \$1,000,000 per week,
  • if something previously cost \$1, it now costs \$1,000

That's an extreme but simple example of how a 1000 times increase in the money supply causes a 1000 times increase in prices.

But the same simple math holds for any increase big (as above) or small (like inflation in most developed countries ~ 2-3% per year)

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