Archive for April, 2017

Marginal Propensity to Consume and the Velocity of Money

April 1, 2017 2 comments

My last post pointed out my frustration with the treatment of the marginal propensity to consume and the spending multiplier in a traditional principles text.  I just want to briefly point out how this whole business fits nicely into my alternate paradigm where the aggregate demand curve is thought of as PY=MV (as opposed to Y=C+I+G+NX).

Here is how Mateer and Coppock approach the MPC (emphasis added):

When a person’s income rises, he or she might save some of this new income but might be just as likely to spend part of it too.  The marginal propensity to consume (MPC) is the portion of additional income that is spent on consumption.

The problem here is the dichotomy between consumption and saving.  As I have mentioned before, it matters what we mean exactly by “saving.”  Normally (outside of the Keynesian AS/AD model) we assume that saving means investment and investment is also in the CIG equation (it’s the I).  So if “saving” means that you lend part of your income to a firm who buys investment goods, then doesn’t that part of your income become the income of the producer of those investment goods and isn’t that exactly the same as the portion you spent on consumption goods?  (Yes.)  So then is this all just nonsense or is there some grain of truth in here that we are just saying in an idiotic way?

Well, there is one and only one way of saving that is not exactly the same as consuming in the sense that when you do it, the money you devote to it becomes another person’s income.  That way is holding money.  So what happens if we change the way we explain this slightly so that instead of saying that people consume a fraction of their income c and “save” the rest, we say that people spend a fraction of their income c and hold the rest as money and this spending may be on either consumption or investment goods.

Now you can ask yourself “what is the effect on total spending of a given increase in government expenditure.  Let’s assume that the government borrows $100 from the central bank and spends it on something and let’s assume that the marginal propensity to spend (MPS) is 0.9.  Then the person who gets that initial $100 will spend 90 and the person who gets that will spend 81 and so on.  Take that series out to infinity and you will get the total increase in spending of 100/(1-MPS) or the familiar spending multiplier.

But now notice that another way to see this is to notice that people are holding 10% of their income as money and we have increased the money supply by $100.  This means that total incomes (which must equal total spending) must rise by–you guessed it–1/(1-.9) times the change in the money supply.  Or, to put it another way, incomes have to rise enough that people become willing to hold the new money.

But now you are coming strikingly close to another similar concept.  If people are willing to hold 10% of their income as money, that means each dollar in the economy will have to change hands 10 times on average for people to become willing to hold all the money.  Or in other words, the velocity of money will be one over the average propensity to hold money.  (There is, of course, the possibility that the average and marginal propensities may not be the same but that’s not of particular importance to my point.)  And that is just 1-MPS.  So in other words, if you characterize this thing correctly (it’s about spending and not consuming) then the Keynesian spending multiplier just becomes the velocity of money.

Of course, if you look at it this way, you are forced to notice that the real cause of the increase in aggregate demand in this case is an increase in the money supply not something magical about government spending.  If they just dumped the money into the economy from helicopters, the effect would mostly be the same.  And that’s exactly why this way is better, and probably also why it isn’t what we do.

However, there is one magical thing about government spending which is that the government can choose a higher MPS (usually 1) and so can get more spending bang  per dollar of increase in M in the first round.  So the “helicopter multiple” (if you will) would be slightly less ((1/(1-MPS))-1).  And because of this, it becomes theoretically possible that the government could boost aggregate demand without increasing the money supply by borrowing or taxing.

If they increase taxes by $100, they reduce private consumption and/or investment by $100 times the helicopter multiple but then when they spend it they increase private consumption and/or investment by the same amount but with the government spending added on top (assuming that the propensity to spend is unaltered).  This, of course, is a standard fiscal policy implication (see textbook claim 2 in the previous post).  But if you think about it in the context of the equation of exchange, you can actually see what’s going on here.  Essentially, the government is just increasing the velocity of money by taking it away from people and spending it at a higher rate than they would have.

And there you find the special power of government to boost aggregate demand.  Just like the special power of government to do anything else, it boils down to their ability to force people to do a thing more or less.  In this case it’s the ability to force them to spend more money.  The same thing would happen if you put a horde of killer robots on the streets programmed to shoot missiles at anyone they ran across holding any money.  Or, for that matter if–in some crazy, hypothetical, sci-fi universe–all money were somehow electronic and it was possible for the government to charge you interest for holding it and they simply increased the rate of interest so that you would want to hold less money for any given income level.  This would also increase the velocity of money and boost aggregate demand.  I wonder though, would they call it fiscal or monetary policy? (And would they call the increase in interest rates tightening or loosening?)


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