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A Bit of Finance

If there is an asset that will produce $100 of profit in ten years, how much is it worth today?  The price depends on the interest rate that you can get on other assets.  If the market rate of interest is five percent, then every asset (once you adjust for risk) should yield that same rate of return.  In this case, that would make the asset worth about 61.39.  You wouldn’t pay more for this because you could get a better rate of return on some other investment and if the price were lower than this, everyone would want to buy it so they would bid the price up.  Next year, the value will be higher since the $100 will not be as far off.  In fact it will be about 64.46 or about 5% more.  This is pretty basic stuff but the thing we need to notice is that the change in the value of an asset over some period of time when it doesn’t produce any direct benefits or costs should be equal to the market interest rate.  This logic can also be extended to situations like resource extraction (see Hotelling’s rule).

With this in mind, let us consider a particular asset–money.  Historically, money has served two main purposes.  It has been a medium of exchange which streamlined trade by reducing transaction costs and it has been a store of value.  The most appropriate materials for these purposes have been precious metals for several reasons.  Among them, are the facts that they are durable and the quantities of them are fixed by nature.  This is important precisely because it prevents the value of money from falling over time.  To see this consider an economy where money actually does grow on trees.  I have always found this an amusing expression because things that grow on trees don’t tend to be free.  If we went to the store and bought our groceries with cashews, it wouldn’t change the nature of the economy very much except for one thing.  As we got better at producing other goods, cashews would become more valuable.  When this happened, people would devote more resources to growing cashews which would increase the quantity of them and put downward pressure on their value.  Now it isn’t true that this is impossible with gold.  Surely some gold is harder to mine than other gold and as the value of it increases, people will go after the harder to mine stuff but the marginal cost is surely increasing at a much faster rate than it is for cashews or almost any other agricultural or manufactured commodity.  The effect of this is that when the production of their goods goes up, the quantity of gold in the economy doesn’t increase as fast.  This means that gold gets more valuable in the sense that it can purchase more real goods. 

Now consider how the interest rate is determined in a free market.  Investments exist that will provide some positive rate of return over some amount of time.  In order to get this return though, someone must forego the ability to consume over that period of time.  People aren’t willing to give up this opportunity for free but they are willing to give it up for some amount of return.  If there is a project that returns enough to get someone to give up the ability to consume over the amount of time it takes for it to come to fruition, they will negotiate some rate of interest that is mutually beneficial and the investment will take place.  This will go on until all remaining projects have a rate of return lower than the amount the marginal lender would require to invest.  The marginal rate of return determined in this market will be the real interest rate.

To see the relationship between this market and money, we have to think of money as an asset–that is, as a store of value.  This means that productive investment must compete with the holding of money.  So if there were no direct benefit to holding money (and there were no risk involved in other investments), the value of money would have to be increasing at the same rate as the real interest rate determined in the market for investment.  If it were increasing faster, nobody would invest in anything because they could just hold money.  If it were increasing slower, nobody would hold money because they could do better by investing.  In other words, there would be deflation.  In this case, there would be nothing destructive about the deflation.  It would be a sign of economic growth. 

In reality, the two things we assumed above (there is no direct benefit to holding money or risk involved with investing) are not true.  In fact, there is likely to be some risk premium involved with investment which is greater than holding money.  The odds of a project failing are most likely higher than the odds of your gold being stolen from your safe deposit box.  In addition to this, if you hold money, you are able to spend it at any time, whereas, if you invest it, you cannot consume until the investment matures (at least not without liquidating the investment which may carry some cost).  In this sense there is some risk associated with demand uncertainty that also comes with investment.  If your car breaks down next month, it will be easier to get it fixed if you have cash in the bank than if you have stocks.  This is what Keynes called “liquidity preference.”  Essentially, liquidity preference is just an additional form of risk premium though, so I will lump these together.  The risk premium on investment will mean that the return on holding cash will be somewhat lower than the return on investment.  If this risk premium is large, there might be inflation, however, this seems unlikely to me.  At any rate, in a free economy with real money, the rate of inflation and the rate of interest are determined by the market int his fashion. 

The thing that drives this wedge between the rate of return on money and the rate of return on other investments (liquidity preference) is represented in the equation of exchange by velocity.  Presumably, people have an increasing marginal cost of velocity.  To see this, consider the case of the Weimar Republic where people had to take their paychecks (often a wheelbarrow full of cash) and immediately take it to the store and buy food because it would be worthless the next day.  This is a state of very high velocity.  Certainly, this would be pretty annoying.  The reason they do this is because the value of money is decreasing rapidly so the cost of holding it is very high.  People would prefer to hold more cash which would mean a lower velocity.  As the cost of holding cash increases, they will hold less but as they hold less, the price they are willing to pay to hold it goes up.  This price is the risk premium on investment.  So if something (exogenously) causes the demand for cash balances (supply of loanable funds) to increase (decrease), this will cause velocity to decrease and the risk premium on investment to increase.  If something causes the demand for investment to increase, the risk premium will increase and velocity will increase.  This framework allows us to distinguish the relationship between interest rates and investment assumed by Keynes and the relationship assumed by his predecessors.

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