# Graph that Explains Money

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I have recently been reading Principles of Economics, which I highly recommend. This got me thinking about how our monetary system works, which I will summarize here. If you don't have time to read this, just look at this graph of money in circulation in Canada. Just this one graph will help you understand why housing and the stock market keep going up. That black line was made with the equation
` e^(unixTime * 2.5*10^-9 + 9.98)`
That has an R-Squared of 0.9942, so it fits very closely to the actual money in circulation.

## The Basics

I will reproduce my notes summarizing what I have learned.

### Broad Definitions

The wants of man are infinite, therefore we have scarcity, because we have infinite wants, but finite time and resources.
Scarcity: Human wants for goods & services exceeds what is available.
Microeconomics: Focuses on the actions of individuals within the economy.
Macroeconomics: Looks at the economy as a whole, focusses on broad issues, such as GDP.
There are 3 types of economies:
1. Traditional: Occupations stay in the family, children do what the parents did. This put’s a damper on productivity increases, due to lack of improvements. ie. Certain occupations may cease to exist due to advances in technology (for example grain farming can no longer profitably be completed by hand).
2. Command: A central authority dicatates what is produced. ie. Eygpt building pyramids, Cuba/North Korea.
3. Market: Price signals control supply and demand. Private Enterprises fulfill needs and wants. A persons income is based upon their ability to convert resources into something that society values.

### Decision Making

Opportunity Cost: What a person must give up to obtain something they desire. Due to scarcity, every decision is a compromise. You place values on all of the options, and choose the option with the greatest net present value, if you are a rational economic person.
Law of Diminishing Marginal Utility: As a person receives more of something, the additional utility from each additional unit declines. ie. If you are hungry, then 1 pizza might be great, then second not as great, and the third you might not even want.
Sunk Costs: Costs that were incurred in the past & cannot be recovered. These should not affect your current decisions.
Production Possibility Frontier: Shows the benefit of varying spending between two options, including the effect of diminishing returns, basically a graph of a square root function.
Positive Statements: Describe conditions as they are. Matters of fact.
Normative Statements: Describe the world as it should be. Matters of opinion.
Price Elasticity: The ratio between price of a good, and the number of units demanded or supplied. Used to create the demand curve/line. If this ratio is less than 1, the good is inelastic in price, for example food or housing. If this ratio is greater than 1, it is elastic, for example eating out at restaraunts, or going to movie theatres. Studies have been done, and you can lookup the elasticity of many common goods and services. You could use this information to gain insight on the state of the economy, for example if dining out is at all time highs, the economy is in a good state.
`Price Elasticity = Change in Quantity / Change in Price`

### Money Supply

M1 Money: The amount of highly liquid money in circulation. The cash that people have, the money in the bank accounts that could be withdrawn at any time (demand deposits). Cashiers cheques, and quite a few other sources. M2 Money: The less liquid money, plus the M1 money. This would include additional sources of money such as savings account, and time deposits (money that cannot be immediately withdrawn).

Banks:Middle Men between depositors and borrowers. Store a portion of deposits from people, this amount varies from country to country. For an example, let’s say that it’s 10%. You deposit \$10000 into a bank account. Joe B then goes to the bank for a loan, and they loan him 90% of your money, so \$9000. Then Joe B buys a tractor from John for \$9000, and John deposits the money into his bank account. Johns bank can then lend out \$8000 to a new person, and it keeps going round and round. We will pick up the thought of final amount of money, and reserve requirements later. You may now be asking yourself, what if you want your money back? The bank does not have it. That is the cause of bank runs, where the first people who withdraw their money from the bank get it, while the late people get nothing. To prevent this, in the US, as in most countries with fractional reserve banking, there is a central bank who has the ability to print money, or monetize the debt. That central bank would then lend money to Joe B’s bank from the “Discount Window”, at the “Discount Rate”, so they could pay him out. The discount rate is purposefully set high to discourage banks from doing this, the banks should be borrowing from each other at a lower rate. The central bank is also known as the lender of last resort. Whenever a new loan is made, the M1 will increase. You can see by this, that the rate of change of the M1 Money would be a good indicator of economic activity. You can lookup this up on the Bank of Canada web site. Another thought you might have, is where does the money for interest come from? That is a great thought. The money for interest must come from new loans, essentially going around in a circle, travelling through the economy. It’s like musical chairs, the music playing is people taking out new loans. At the point when the new money being created by the act of lending drops below the amount required to pay the interest on all the loans, there could be a short period of deflation when that cash to pay the interest becomes more valuable. What would follow, is monetization of the debt from the central bank, then inflation again, once everyone’s money becomes worth less (including the principal amount of all of those loans). We will pick these thoughts up again later, when I go through some data from Statistics Canada, and see how this all plays out.

Velocity of Money: How quickly money circulates through the economy.
`Velocity = nominal GDP / money supply`
Basic Equation of Money: Money Supply * Velocity = Price Level * Real GDP Investment Decisions: Investment Decisions are forward looking, based upon expected rates of return. This is because investment decisions depend primarily upon perceptions of future economic conditions. As an example, the TSX follows the Canadian GDP fairly closely. Exports: Determined by the purchasing power of other countries. Trade Deficit:
` Imports - Exports = Domestic Investment - Private Domestic Saving - Government Savings`
Therefore, if you are running a trade deficit, it means the person you have the deficit with is investing in your country, anticipating future returns.

### Unemployment

Natural Unemployment: Remaining rate of unemployment even in a healthy economy. An interesting observation, is even though the population has increased, there is no trend in the unemployment rate of most developed countries. Unemployment has two main causes: Frictional Unemployment: This is the result of the period of time it takes for employers and employees to find each other. This could be due to the time it takes to advertise a job, interview candidates, and for the final candidate to move to the location where the job is. Frictional unemployment is higher in societies with a large proportion of young people who more frequently change jobs/fields while they find the best fit for them. Structural Unemployment: Unemployment cause by a mismatch between the education/training that a work force should have, and what they do have. An example of this, is when the space program downsized, and there were many unemployed aeronautical engineers. Phillips Curve: Shows the relationship between unemployment & inflation. If one goes up, the other goes down. Similar to the function of 1/x. Worked well in the past, but recently this relationship has broken a bit. Economists used to use this to guide policy decisions, and strike their ideal balance between inflation & unemployment. Stagflation: When an economy has high inflation & high unemployment. Meaning the economy is not following the Phillips Curve. Inflation: High inflation reduces labour productivity. It disrupts normal business, as it makes it more difficult to perform transactions, and economic evaluations.

### Current Data

Let's look at how this applies to the current time, by downloading data from Statistics Canada, and producing graphs. You already saw the graph of the M1 supply from the year 2000, predicted to the year 2030. Let's look at a larger time span from 1980 to current. Let's check if it's a function of the natural exponent. I think it is. Now if you have R, you can type:
`model <- lm(log(M1Plus) ~ (unixTime ), data=dfname) `
That will find the m and b to make that line fit the y=mx+b equation, which will be:
`M1 =  e^(unixTime * 2.5*10^-9 + 9.98)`
The amount of money in circulation increases at about 8% per year. It is unlikely that hyperinflation would occur. Hyperinflation is defined as more than 50% monthly increase in prices. If you are getting worried, then look at this graph of a calculation out to 2050 (at an 8% increase per year). So, prices and wages will continue increasing, and episodes of deflation will be short lived. Why does the system need to be this way? It has to do with human psychology. People save money thinking they have security in that money, it makes people feel safer. If there was no money creation like this, and people saved money, we would all hoard tons of money, and the economy would slow to a halt. On the other hand, if the money you have saved up is continually becoming worth less, then you will spend it sooner, increasing the velocity of money, and making the economy run closer to it's potential capacity.

Now this part is my opinion. Because it appears the growth of money is related to e^x, the rate of growth is constant. With the parameters R found above, this works out to 8% per year. There could be error in that because I only used 40 years of data, and the slope has not started increasing too much yet. However, if we find ourselves in a credit crisis, when there is not enough money in circulation to pay off all the interest (would happen anytime the economy slows down too much, and rate of money growth/M1 change drops). This would lead to short term deflation when money is needed to pay the interest, followed by inflation assuming the central bank monetizes the debt (prints money, gives it to the banks in return for the loans that cannot be paid back). You can visit the bank of Canada web site, and view the holdings of the banks in Canada. Currently they have \$5.5 Billion in currency, and \$1.2 Trillion in mortgages, \$1 Trillion in business loans to non-Canadians, \$330 Billion in business loans to Canadians. It is easy to see how the \$5.5 Billion could run out, because \$2 Trillion * 2% Per Annum interest /12 = \$3.3 Billion per month. So if people stopped taking out new loans, there is enough money to last for almost 2 months, just to pay the interest on mortgages, and business loans. An easy way to think about this, is if M1 growth falls below the interest rate, then we are running on savings, and have a limited time before there is a banking crisis. You can watch the M1 growth here.

Thinking again about the growth of money, and how that is related to the economy, can we see a relationship between the M1 growth and the stock market? To find out, I made a graph of the money change, with red highlights anytime the TSX had a <-10% YoY change. I don't really see a relationship, so then what is the stock market related to? I picked the stock market to look at, because when we think of recession, what do most people think of? Looking at what I wrote above about investment decisions, you can see that investment decisions should be based on future earnings. I think GDP should give us the best idea of a companies future earnings: Looks like there is a relationship. Now if I make a scatter plot of GDP and TSX close, what does it look like. These charts would lead me to believe in the efficient market hypothesis, and that the stock market is a markov chain. That means you cannot predict the future using past information, any more than you can predict the future using current information. I'm sure that there are some exceptions to this, although I have not found them yet. Most machine learning algorithms that I have seen, which make trades based on past prices have a success rate of barely over 50%, so there definitely are some exceptions. We looked at the TSX and how it is affected by change in M1, but how is it (and GDP, since we know it's related somewhat to GDP) affected by the total M1 amount? There is alot of noise in the stock market. In the GDP graph, there is a more clear relationship: As M1 increase due to debt, the GDP increases, and the stock market increases. How about house prices, they are often referred to as Real Estate, meaning they are real and should be a good stay against inflation. Looks like there is a fairly straight line relationship between the value of mortgages and the amount of money in circulation (which is increased by new mortgages, so this makes sense). That's why it makes no sense that governments brag that they improved housing affordability by making it easier to take on new debt, because all that does is increase the cost of houses (except the the first few people who buy in, it's kind of like the opposite of a bank run). The real reason for high cost of housing is limited supply, due to limited land in the areas that are highly desirable to live in. Calgary is fixing this problem by building more high rises, which has reduced office rent downtown (in addition to people leaving due to a slower economy). Here is an article from 2016 showing a 30% in downtown rental costs in 2016. All that to say even though the costs of housing will increase with the money supply, there will be local variations due to jobs.

Speaking of which, does wage change with money supply? Well like I wrote earlier, wage is also dependent upon productivity. I will get a chart of that later.

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