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?