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# Answer to stimulus formula equals inflation

March 9, 2009
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One of the reasons so many folks don't like economics courses is that we economists use so much math. But, in our present circumstance, one equation is especially helpful, if not joyful. So, just stick with me for a few minutes.

The "equation of exchange" theorizes that MxV=PxY. On the left-hand side of the equation, we have money supply (M) and the velocity of money (V). On the other side is the price level (P) and output (Y), often referred to as gross domestic product, or the total size of the economy.

The U.S. money supply is affected by the Federal Reserve and the Treasury, agencies that can tinker with interest rates or print and distribute money. The velocity of money is how often that money circulates through the economy in a year. The rate is determined by banks and consumers through hundreds of billions of individual decisions each year.

Over the past few months, the money supply has exploded to historic levels. The Federal Reserve has lowered interest rates and invested in banks. The Treasury has in effect printed lots of money to finance the federal stimulus. All of this increases the supply of money.

In contrast, velocity has dropped significantly as consumers do not spend and banks do not lend. The total of MxV has declined, and like all well-behaved equations, this one must balance.

So, if MxV increases, PxY must increase by an identical amount. But, over the past few months, the increase in M has not outpaced the shrinkage of V. So, together, MxV shrinks and, thus, PxY must also decline. This is a recession.

When economists worry about the health of the banking system, it is not because we admire the snappy dress of bankers. We are concerned with a stable velocity of money. If the velocity of money shrinks further, it is likely the recession will deepen.

If the velocity of money increases back to its 2007 levels, MxV will grow and so, too, will PxY. When we are in a recession, Y can grow for the simple reason that we have idle resources (workers and factories). But, there is a natural limit to Y in the short run. If there were not, then simply printing money would yield unending economic growth and prosperity. North Korea would be an economic powerhouse.

If the stimulus works, we will return to full employment, and the economy can grow no further in the short run. This is the point of the stimulus.

However, the equation must stay in balance, and that's when we need to consider that the supply of money has increased to historic levels. The only variable in our equation that can change is P, the price level. In our quest to balance the equation of exchange without suffering a big drop in Y, we risk a big increase in P.

There is another name for the increase in P: inflation.

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Hicks is director of the Center for Business and Economic Research at Ball State University. His column appears weekly. He can be reached at cber@bsu.edu.
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