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Monetary Economics in a Free Market

I tried to make the title reflect the level of excitement in the post.  I don’t want to mislead anyone after all.  If you’re not into economics just skip this one. What I want to do here is describe how the monetary system would function in a free market economy.  By this I mean an economy with no central bank or other government interference with the money supply and financial markets.  This is nothing like what is taught in economics classes these days.  It is a first step toward overcoming the serious confusion among people who, like me, would like to see such a system put in place.  The reason for the confusion is the same reason that it is not taught in economics classes.  We don’t live in an economy like that.  We have created a system which is at odds with natural economic forces.  So we don’t teach natural macroeconomic forces.  This is also the reason nobody understands the macroeconomics that we teach in economics classes.  As a warning, the casual reader will probably not understand this either, but if you are an undergraduate econ major and you apply yourself somewhat, it should make a lot more sense than intermediate macro.  In order to understand how our current system works (and why it will end in disaster), we must be able to start from here.

So take an economy where the money is some precious metal such as gold.  Notice that multiple commodities can be used simultaneously, they would each still behave in the way described.  In this case, the money supply is exogenous (determined by nature outside of the model).  In a more complicated model, this could be made endogenous but it would still be determined by natural factors like the amount of gold in the ground and the cost of extraction.   Here we will just consider it exogenous.  Similarly, assume that output and the real interest rate are exogenously given.  Output is determined by the efficient allocation of all factors which, frankly, there is no reason not to expect (at least approximately) in this case.  The real interest rate of course, is determined by people’s’ subjective time preferences and results from their choice of consumption today vs. consumption in the future.  This decision is of interest to us but we will put it aside for now.  Call the real rate r,  in keeping with tradition.

Our goal here will be to explain the determination of prices, interest rates and inflation/deflation rates.  The key to doing this is liquidity preference.  This is people’s willingness to sacrifice some other goods in order to hold part of their wealth in money rather than in other assets.  In other words it means people will accept a lower rate of return on their money than on their other assets in return for its greater usefulness in exchange.

This gives us a pair of portfolio balance conditions.

r=i+d                                                     [1]

r=a+d                                                   [2]

where d is the deflation rate and a is the rate of liquidity preference.  I use the deflation rate instead of the inflation rate because in this environment it makes more sense.  If you substitute -pi for d in the first equation you get the Fisher equation.  This essentially makes the benefit from borrowing/lending in nominal terms equal to the cost.  The second equation says  that, on the margin, the benefit to holding money is equal to the cost.  The benefit in this case is the liquidity premium (a) plus the rate of deflation.  The liquidity premium is a direct benefit which acts similarly to a risk premium (though in the opposite direction) while the deflation rate is the actual return on the money due to the prices of other goods in terms of money falling.  The cost is the return on an alternative investment which could be bought with the money, namely the nominal interest rate (i).

If you solve the second equation for i and plug this into the first, you get the following condition.

i=a

In other words, the nominal rate represents the premium paid to hold investment in dollars instead of some other form.  This happens because people choose the amount of money to hold such that the benefit (a) is equal to the cost (i).  But what does this mean “people will choose the amount of money to hold?”  The  quantity of money is exogenous.  But the rate at which it changes hands depends on how willing people are to part with it.  And prices depend on the rate at which this exogenous supply of money changes hands.  To determine these two things we turn to another well-known equation.

MV=PY                                   [3]

Here M is the money supply, V is velocity, P is the price level and Y is output.  Given the definitions of these variables, this equation can’t help but be true.  This allows us to close our model because of the relationship between velocity and liquidity preference.  The higher the velocity, the higher the liquidity preference will be.   If you hold $100 in cash and you spend on average $10/day, the added convenience from having an additional dollar in cash will be relatively small compared to if you hold $100 and spend on average $100/day.  Another way of coming to the same conclusion would be to say that for given cash holding, the liquidity preference will be higher when prices are higher because the same amount of cash represents a smaller amount of real money balances (M/P).  Either formulation amounts to the same thing since V and P are positively related via the equation of exchange.  But we will write it like this.

a=A(V)                                           [4]

A'(V)>0

Finally, for now,  let’s take the depreciation rate as given.  This will be determined by a similar process occurring in the next period but we can add this in later.  This closes the model.  We have four equations and four unknowns (P, i, a, V).  Here is an example.

M=100

Y=500

d=.05

r=.1

A(V)=V/100

We know that money will circulate at a velocity such that the liquidity preference will be equal to the nominal interest rate and the nominal rate can be found using the Fisher equation.

a=i=r-d=.05

V=100a=5

Note that the liquidity preference equation [2] also holds for these rates.  Then the equation of exchange gives us the price level.

P=(100)(5)/500=1

Note that money is neutral in this model by assumption, so if we double the money supply, the price level doubles and everything else stays the same.  An increase in the real rate will cause the nominal rate, liquidity premium, velocity and the price level to increase.  An increase in the deflation rate will cause a decrease in all of the endogenous variables.  Notice what I just said.  An increase in deflation (decrease in inflation) causes a decrease in nominal interest rates!  This is the point where you should be jumping out of your seat shouting “eureka” and running naked through the streets of Syracuse.  It is the exact opposite implication from the conventional wisdom that low interest rates cause inflation.  The reason for this is that in this model, it is exogenous money creation driving inflation/deflation rates and nominal interest rates.  In our economy, it is nominal interest rates which drive borrowing, borrowing drives money creation, and money creation drives inflation.  It is this attempt to invert the causal relationships that underly a natural economy which is leading us down the road to disaster.  But you can’t fight it until you see the difference.

Now we can deal with deflation in more depth.  To do this we need to state growth rates for output and money supply.  Let’s first imagine that they are both constant at the levels given above.  In this case, velocity and price level will have to be the same in each period or in other words, the deflation rate will be 0.  If the deflation rate is 0, then i and a will both be equal to the real rate (.1).  In this case, the velocity of money will be 10 and the price level will be 2.  The same thing will be the result if money supply and output grow at the same rate, so I will not bother going through this case.

Next imagine that the money supply grows more slowly than output.  This is likely to be the case in a natural economy since one of the main attributes that causes a particular commodity to become money is its ability to hold its value and this is related to the growth in supply of that commodity relative to other goods.  For simplicity’s sake assume that the money supply remains constant at 100 and output grows at 10% per period.  I won’t go through all the algebra here but if we confine ourselves to solutions where the depreciation rate is constant over time we find that the liquidity premium must also be constant and therefore also the velocity.  This means that the 10% increase in output relative to the money supply must cause a corresponding 9% decrease in the price level.  In other words d will be .09.

Using this we can find that the liquidity premium, along with the nominal interest rate, would be .01.  This would make velocity only 1 and would make the price level 1/5 in the first period and 2/11 in the second.  The price level falls dramatically.  This is because the expectation of a high value of money in the future when output is higher (and money supply is not) make people less willing to part with their money.  Because of this the velocity slows way down and prices fall.  The same amount of goods are exchanged using the same amount of money but at much lower prices.

Conversely, if the money supply grows by 10%/period while output stays the same, the deflation rate will become -.1 (10% inflation).  The liquidity premium will be .2, velocity will be 20 and the price level will be 4  in the first period and 4.4 in the second period.  Because of the expected loss in value, people are less willing to hold money and velocity and prices rise until the amount of their holdings is sufficiently small relative to the amount of transacting being done and the nominal value of other assets in their portfolios that the marginal benefit of holding it is sufficient ly high to make them willing to pay the higher premium for holding it.

A more complicated (significantly) model could start from utility functions and production functions and make output, consumption, investment and real interest rates endogenous but it would look a lot like this and I will not go that far here.  The main take away is that in a free market, it would be the exogenous supply of money and other goods which would determine interest and inflation/deflation rates and price levels rather than interest rates (and to some extent inflation expectations) being determined exogenously by a centralized authority and these determining the money supply and the price level.  And in this environment less deflation (higher inflation) would mean higher nominal interest rates in contrast to our system of central banking where inflation and higher price levels are the result of low interest rates.  It is the inability to properly separate these two systems that confounds the thinking of so many on our side.  This is the key to everything.  I wish I could make it more exciting and accessible but I don’t know how.  Nonetheless it is worth the effort to understand it.

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  1. July 24, 2012 at 6:31 pm

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