## Sunday, July 24, 2011

### Intro to Economics for Physicists Part 3: GDP, Velocity of Money, and Money Supply

In a previous post, I discussed how printing money can be inflationary, if all other things stayed the same in our society. However, as with everything in macroeconomics, nothing stays the same. So, I'll discuss the relationship between the Gross Domestic Product (GDP), the Velocity of Money, and the Money Supply. In a work- or electricity-backed currency, the units for these terms are:   Power [GW],  Frequency  [1/yr], and Work [GW-yr], respectively. In these units, it's fairly easy to see the relationship between the terms.

There is a rather famous equation used by economists to describe the relationship between Price, Quantity, Velocity of Money, and Money Supply. This is sometimes called Fisher's Equation. In simple terms, the equation is:

GPD = SUM(P x Q) =  M  x  V

where GPD = the gross domestic product   [\$   or  kW-hr  ]
P = the price of a final product                    [\$/unit    or   kW-hr/unit ]
Q = the quantity of a final product               [unit]
M = money supply                                    [\$       or  GW-hr ]
V = velocity of money                                [1/yr]

There are two main variables used to describe the money supply, depending on the ease at which the money could hypothetically be accessed if there were a run on the banks. (Let's hope that there isn't a run on the banks any time soon.) Remember: since money is the capability to do work, the amount of money has to be limited by the ability to do generate mechanical and electrical work. There is more money in checking deposits than there is hard currency and even more money if you include money market accounts. See below
M0 ~ currency            [Readily Available at Hand]
M1 ~  small money supply   (hard currency, checking deposits)         [Easy to Get]
M2 ~  large money supply   (M1+ money markets, etc...)          [M1 + More Difficult to Get]

The velocity of money is measured with respect to the particular money supply. It is defined to be the GDP divided by the particular money supply. So...
V0 =  GDP / M0
V1 =  GDP / M1
V2 =  GDP / M2

We can ask ourselves, what are the units of velocity? In order for the units to balance in the equations above, the only option is 'per time', such as [1/yr]. Clearly the units of velocity in economics are different than in physics, but that's okay. Let's just call it a frequency, and see if the economists eventually decide to yield to physicists    :-)

So, from here on out, I'll try to use frequency in place of velocity. V1 and V2 are the frequency at which money is exchanged within the economy. It is the amount of times per year that currency is used to purchase goods. Typical values of V1 are around 20 times per year, and typical values of V2 are around 2 times per year. This is because the M2 money supply is roughly an order of magnitude larger than M1 money supply. So, the equations above are nothing more than a definition for the frequency of exchange and a definition for the GDP.

In an electricity-backed currency, we see that the GDP is a measure of the amount of electricity produced in a year. It has units of power, such as [GW]. Strictly speaking, the GDP is the power produced in the country, averaged over the year. In the US, this value is on the order of one half of a TeraWatt (~480 GW). But electricity is not the only source of power in the US; there's also vehicle power, animal power and human power. In the US, electricity is roughly 60% of the power produced and vehicles are roughly 40% of the power produced in the US. Human and animal power are negligible compared to the amount of electrical and mechanical power (i.e. we can't jump on treadmills and solve our electricity problems.) So, we can infer that the GDP of the US is roughly 810 GW. Let me state this again for emphasis. The GDP of the US is roughly 800 GW. Here I've defined GDP in the correct units.
Simply put, the wealth of a nation is its ability to generate and use mechanical and electrical power, and the wealth of a nation should be measured in such units as average yearly power [GW].

But let's step back from the real world in which society generates both mechanical and electrical power and look at the easier to analyze case of a hypothetical society in which the only source of power is electricity (i.e. all of our cars and trucks run on electricity generated at power plants) and in which there is a Federal Reserve that maintains the ~3-month average electricity price at a constant value:  X  \$'s per MW-hr.
In this case, how does Fischer's equation look?

Price of electricity (in \$/GW-yr) * Avg Power (in GW) = GDP (in \$/yr) =  M (\$)  * V  (1/yr)

You can verify that the units balance on each side of the equation. Both sides are in units of [\$/yr]. If we require the monthly average price of electricity to be a constant, then we can measure the GDP in units of GW's. This appears to be an easier way of calculating the GDP than what we do right now.

Currently, we calculate GDP in terms of final products. But there is no such thing as a final product. It's one of the biggest lies that economists tell themselves (and they tell themselves a lot of lies...such as "the economy is naturally stable and balances about an equilibrium point.")  What is a final product? Every product is used in order to make some other product. The difference between a final product and an intermediate product is completely artificial.
This is why GDP is so hard to calculate. This is why we need to throw away the current definition of GDP. As I've pointed out before, our current definition is completely underestimating the size of China's and India's economies. This by itself should be enough reason for us to stop using the current definition and to instead move to the real definition: the average power generation in a year. This is not only the correct definition, but it's also easier to calculate. And you don't have to adjust the value of GW's for inflation, and you don't have to make any conversion between currency. A GigaWatt is a GigaWatt, regardless of when you calculated it and in which country you calculated it in.
So, instead of measuring the final products in an economy, we should measure that which is required to produce all products: mechanical and electrical work. So, instead of arbitrarily determining what is a final product versus an intermediate product, we should measure the total amount of work generated to make all of these products. Stated differently, mechanical and electrical work are both the initial and final products, i.e. Work Self-Propagates. Life is the self-propagation of mechanical and electro-chemical work.
GDP is the total amount of mechanical and electrical work generated in a country per year. And this is why it should have units of power  [GW-yr / yr].

So, let's go back to the equation above.

Price of electricity (in \$/GW-yr) * Avg Power (in GW) =  M (\$)  * V  (1/yr)

In an electricity (work) backed currency, the average price of electricity is maintained as a constant. This doesn't mean that the price won't change from minute-to-minute, hour-to-hour, day-to-day, or state-by-state. What this means is that the average price of electricity in the US as measured every, let's say, 3 months would be held constant.

How would we maintain a constant price of electricity in such a society while new power plants are being built and the price of fuels might be changing?

The job of maintaining a constant price of electricity would be left to the US Federal Reserve. Luckily, it's really easy to do, and it doesn't require a PhD in economics. In fact, it might be better if the person in charge of the Federal Reserve didn't have a PhD in traditional economics because it should be obvious to everybody what the Federal Reserve is going to do before they actually act to maintain price stability. (This will cut back on the amount of corruption between Wall Street and the Federal Reserve. An example of corruption is that the Federal Reserve buys US Treasuries bonds through Goldman Sacks at prices higher than the US Treasury sold the bonds to Goldman Sachs. This is silly!)
Instead, the goal of the Federal Reserve would essentially be to just maintain price stability. We will take out of their hands the job of trying to keep unemployment low. Why?  Because the Federal Reserve isn't any good at keeping unemployment low, and because the Federal Reserve appears only capable of keeping unemployment low on Wall Street (Goldman Sachs, for example.) So, how would this new, streamlined Federal Reserve act? There's only a few possible cases:

Case#1:  Electricity Prices are increasing
In this hypothetical case, the average price of electricity across the society has been increasing over last three month, i.e. the dollar has been losing value over the last three months, and it's the job of the Fed to fix this problem. What variables does the US Federal Reserve have to maintain the price of electricity? (i.e. to maintain the purchasing power of your dollar)
First, let's assume that the amount of electricity being generated has stayed constant during last the three months. And also let's assume that the money supply is the same as three months ago. So, since the Federal Reserve has no direct control over the amount of power produced. They either have to lower M or V  (i.e. lower the money supply or lower the frequency that the money is exchanged.)

What options are available?  1) Decrease the money supply directly by removing money from the economy, 2) Increase interest rates on Federal Reserve loans, or 3) Increase the required bank reserves. Let's remove option three from the table because we want to make this as simple as possible.  Option 1) will decrease the money supply, M, and option 2) will decrease the frequency of exchange, V. Either by taking money out of the economy or by raising interest rates, the Federal Reserve will be forcing the economy to focus on high rate of return investment projects, and forcing us to abandon marginal to low rate of return on investment projects. [Note that the Fed will not be picking winner's or loser's] Eventually, as M*V decreases, the price of electricity will begin to decrease. During this time, the amount of electricity generated might decrease as well (i.e. the most expensive power plants will go temporarily off-line), and this will also force electricity prices down. The Federal Reserve will use an equation to estimate how much money to print (or remove) and/or high much to lower (or raise) interest rates based off of the increase in electricity prices during the last three months. The equation will also include data on M, Q, and V over the last few years.
Clearly, the more often the Federal Reserve meets, the smaller the changes would have to be to the money supply or interest rates, but I don't think that it would be helpful for them to meet any more than once a month. (We haven't mentioned so far how the Federal Reserve would remove money from the economy.   Essentially, it would have to sell some of its assets, and then destroy the money that it received from the people who bought Fed assets. Not a pretty thought, but it's exactly the opposite of what it would do when the average price  of electricity is decreasing. In that case, we'll soon see, it can fabricate money out of nothing.)

Case#2: The price of electricity has stayed constant
In this case, the price of electricity has remained constant. So, the Federal Reserve does not need to do anything, even though the amount of electricity generated might have increased. This increase in quantity in power has not increased the price of electricity because the frequency of exchange has gone up. Perhaps, some banks have decided to decrease their bank reserves (while maintaining the required bank reserves as by law.) This is one way to increase the frequency of exchange. My point for this case is that the Federal Reserve does not have to do anything because the price of electricity is still the same.

Case#3:  Electricity Prices are decreasing
In that last three month, the price of electricity has decreased in this hypothetical society. Your hypothetical dollar has been gaining purchasing power over the last three months. This is a good thing, in general, but the goal is to maintain a constant purchasing power for the dollar, so it's the job of the Fed to raise the price of electricity. What variables does the US Federal Reserve have to maintain the price of electricity? (i.e. to maintain the purchasing power of your dollar)
In this case, the Federal Reserve can either increase the supply of money or it can lower interest rates. If it lowers interest rates, then projects that were marginal at the higher interest rates will now be profitable at the lower interest rate. More projects will go ahead, and eventually this will cause the price of electricity to increase back to the goal value that the Fed is trying to maintain. The other option is for the Federal Reserve to fabricate money out of nowhere and buy US Treasuries. This would allow the US government to either: increase spending, decrease taxes, or decrease its debt.
Here, you can see why low electricity prices are a good thing. If the price of electricity is decreasing due to innovation, then the Federal Reserve can print money, and this money can be used to either increase spending, decrease taxes or pay off the debt. It's a win-win!

And here you can start to get a glimpse of the future I see for the US.
I foresee a future in which there is no federal income tax.
I foresee a future in which the federal government pays for itself through the following:
Taxes on pollution   &   Printing Money (as allowed in order to maintain a constant price of electricity)
It might take a long time to get there, but I think that this is entirely possible in the future.
If we could get Federal spending to ~ 15% of GDP, and if we could get a growth rate of 10%/yr (because of no income tax), then we could pay for two thirds of government by printing money (while having no inflation in the price of mechanical or electrical work.)
The other 1/3 of Federal Spending would come from taxes on pollution, such as a tax on greenhouse gas emissions, a tax on acid gas emission, a tax on municipal solid waste, a tax on dumping chemical wastes, etc...
To be clear, I'm not talking about taxing for the sake of taxing. I'm talking about eliminating income tax (i.e. a tax on productivity) and substituting it for a tax on pollution (as well as some printing of money when the economy is growing, such that there is no deflation.)

So, now you can see a glimpse of what I imagine our society could be. No more taxes on productivity. The transition to such a society might be gradual. We could slowly decrease income taxes as we increase pollution taxes and as we slowly decrease federal spending. All along the way, we could sell government property that is sitting idle or barely being used. (such as selling our gold and silver reserves...because in the society described above, there is no reason to hold onto gold reserves.)

This is the prescription for a growing society that doesn't destroy its environment. Clearly, this will be a difficult feat pull off and will require the actions of millions of people in order to to achieve it, but the rewards will be worth the effort. Eliminating income taxes will make it significantly easier to hire new workers, and taxing waste should decrease the amount of waste we generate as society. It's a win-win for everybody.