1. Assume perfect competition (reasonable assumption for analysis), no firm invests (I) today unless tomorrows revenue (R) is higher than the investment.
3. In perfect competition, I = R because both firms (or any number of n firms) will invest up to a point just below I > R.
This is wrong. Firms will invest to the point where their revenue equals the natural rate of interest, which is determined by peoples time preferences.
That is, firms do not only require that R>I to invest. They require that R>k*I where k would be the natural rate of interest. Money today is worth more than money tomorrow. Interest rates are the market price for time, and that price is not 0 as you assume.
Note that in my model, money is capped to 1 (divisible infinitely). We can't expand money. So there's no inflation. Not sure how we would get interest here.
Sorry but if money is capped then won't money today be worth more than money tomorrow? Think about it, if you could only ever have 1 dollar divided in between everyone in the world, wouldn't your portion tomorrow be worth more than it is today? Today I invest 50 bitcoins buying 1 ASICMiner blade, but I know I will never even get 50 bitcoins back (exponentially rising difficulty, more people getting asics, BFL to ship, etc). So I don't invest. No reasonable person would invest 50 bitcoins today to get some <50 bitcoins in the future. So I require R>I to invest. Wouldn't you?
How are there interest rates in a world where money is finite?
Interest is the price of time. Time is a scarce valuable resource, thus it will have a price as all scarce valuable resources do. You can have interest rates on the lending of any good. I can lend you a hammer, and demand 2 hammers in return, the second hammer being the interest. What that says is simply that the time I won't be able to use my hammer is worth an extra hammer, and it's up to you to either accept or refuse this offer.
It's simply more effective to lend money in most cases, and the same principle applies. If I lend you one bitcoin I will require more than 1 bitcoin in return. The time where I won't be able to use my bitcoin has value. That value is priced as the interest rate. In a market for lending I will look for those who give me the best offer.
Besides we already have interest in the bitcoin economy, see BitFinex. Explain why that would just dissappear if the supply got capped right now.
You are also confusing price with value. 1 Bitcoin today is always worth more than 1 Bitcoin tomorrow. 1 bitcoin today could actually be saved and used tomorrow, but the opposite is not true, so 1 bitcoin today gives you more options. 1 bitcoin tomorrow likely has a higher price though, but that is a different thing.
The interest you get from your bank deposits now are due to fractional reserve banking. Because your bank stores a fraction of your deposit, and gives out the rest as loans on which they charge interest on, you get interest on your dollar. If banks couldn't do fractional reserve banking, there would be negative interest on your bank deposit.
BitFinex can provide interest because the bitcoin money supply is still growing.
Consider the following:
1. Money supply = 1
2. N people in the world.
3. 1 of the N (lets call X) has 0.9 of the money supply and the rest divided evenly. 0.1/(N - 1).
4. Because X has a significant proportion of the money supply, capital has to come from X.
5. Only X can invest and improve the lives of the other N - 1 population.
6. X will only invest if he gets a positive interest.
7. X provides a loan of 0.1 to someone from N - 1 (lets call Y) with an interest of 10%. X requires a repayment of 0.11.
8. Because money is capped = 1, there is no way X will get back the loan + interest unless Y gets some of the 0.1 from the rest of the other (N - X - Y).
9. Now the whole world is left with 0.09 to be shared instead while X goes up to 0.91.
10. Repeat this process several times and X ends up with almost all the money supply in the world while you and I share a smaller and smaller portion of a smaller and smaller money supply for the rest of N - X.
This, I'm sure you agree is unsustainable.
If you think about the simplest example, I ask: why not buy an ASICMiner for 50 BTC? Simple because you know that investment (of 50 BTC) will never get you > 50 BTC. Similarly, when the bitcoin supply gets capped, investors would not invest, why? because there is no more money to get hold of in the next period. The only way to do this is some people in the economy consistently lose money until they are at 0 balance (supply is capped remember so in order for you to get investment + interest, someone else has to LOSE). Having a significant amount of people in poverty (0 money supply) I'm sure is not good for the welfare of the greater population. Unless of course you say you are a benevolent individual who freely gives his money away.
Sorry but 1 bitcoin tomorrow will be worth more, we can debate on the importance of choice today vs quantity tomorrow but if supply is capped, today 1 bitcoin buys you 1 pen but tomorrow 1 bitcoin buys you 2 pens because more pens are being made and bitcoin is limited.
