Very few economists are aware of Dutch Capital Theory (DCT to us insiders). It was invented by my ancestor Nick van Rowe, over a century ago, but has been suppressed by a conspiracy of silence and ignorance ever since. Think of this as a teaching post.
Start with a very simple economy. Land is the only resource, all land is identical, and the quantity of land is fixed. Each acre of land produces 4 tons of wheat per year, without labour, fertiliser, seed, or anything else. Wheat cannot be stored from one harvest to the next. There are no other goods. There is a fixed population of identical people, who own the land. All markets are perfectly competitive. Nothing ever changes.
The annual rent on land would be 4 tons of wheat per acre per year, obviously.
What determines the price of land? What determines the rate of interest, if you borrowed wheat and promised to pay it back next year?
The answer is simple: preferences. More specifically: time-preference. If people are very patient the rate of interest will be low and the price of land will be very high. If people are very impatient the rate of interest will be very high and the price of land will be very low.
There is a very simple relationship between: the price of land P (measured in tons of wheat); the annual rent on an acre of land R (measured in tons of wheat per acre per year); and the rate of interest r (the extra tons of wheat per year you have to pay as interest to borrow one ton of wheat).
It's P=R/r. Or you can think of it as r=R/P. Arbitrage ensures that equation holds true. If r>R/P, the rate of return on owning land and renting it out would be less than the rate of interest, so everybody would want to sell land, driving P down. If r<R/P, the rate of return on owning land and renting it out would be greater than the rate of interest, so everybody would want to buy land, driving P up.
Or you can set the price of land equal to the Net Present Value of the rents, and get exactly the same answer, if you assume that rents are never expected to change and interest rates are never expected to change.
If you want to do some math, to show the exact relationship between preferences and the rate of interest, you can do so.
Assume V(t) = U(C(t)) + B.U(C(t+1)) + B^2.U(C(t+2)) + etc.
Where U(C(t)) is the Utility you get at time t from Consumption (of wheat) at time t. And B (which is a number between 0 and 1) is a subjective discount factor that measures how patient you are. We can rewrite B as 1/(1+i) where i measures your degree of impatience, or "rate of time preference proper". If i=0 then a person who is consuming the same amount of wheat every year is indifferent between consuming an extra ton this year and an extra ton next year.
The equilibrium condition is that 1/(1+r) = B.MU(C(t+1)/MU(C(t)), where MU(C(t) is Marginal Utility of Consumption at time t. Since consumption equals production in equilibrium, and production is constant every year, this reduces to 1/(1+r)=B. Or, more simply, r=i.
In this very simple model, where production and consumption never change over time, the rate of interest is determined by, and equal to, the rate of time preference proper. r=i.
The rate of interest cannot be determined by the marginal product of capital, because there isn't any capital in this model.
The rate of interest cannot be determined by the Marginal Physical Product of land. Because MPPL = 4 tons of wheat per acre per year in this model, and the rate of interest could be anything, depending on preferences. They don't even have the same units. Because the rate of interest will have the units 1/years, and MPPL will have the units tons/acre.year.
It is easy to complicate this simple model in lots of ways. Introduce lots of different goods in addition to wheat. Introduce lots of different types of land, some of which are better than others at growing different crops. Introduce labour into the production function. Introduce lots of different types of labour. Introduce monopoly, Etc. But, as my Dutch ancestor showed, none of these complications make any difference whatsoever to the basic insight of Dutch Capital Theory: that the rate of interest is equal to and determined by the rate of time preference proper, because 1/(1+r) = B.MU(C(t+1)/MU(C(t)) is still true. Provided consumption never changes over time.
It's when consumption starts changing over time that Dutch Capital Theory gets a little bit more complicated.
Lets look at some things that might cause consumption to change over time.
1. The sea level falls, so new land appears every year. Suppose the stock of land grows at 1% per year. Then production and consumption of wheat will grow at 1% per year. So the marginal utility of consumption will be falling over time. So the rate of interest will be greater than the rate of time preference proper. How much greater depends on how quickly Marginal Utility of Consumption diminishes as consumption increases.
2. Suppose there is a once in a lifetime flood, that reduces the stock of land temporarily for just one year. So production and consumption of wheat will be lower this year than next year. So the Marginal Utility of Consumption will be higher this year than next year. So the rate of interest on one-year loans of wheat will be higher this year than next year, and will be higher than the rate of time preference proper.
3. Once you have understood the effects of sea-level changes in 1 and 2, it's quite easy to figure out how more complicated patterns of actual and expected changes in the sea level will affect the rate of interest. Just plug them into the formula 1/(1+r) = B.MU(C(t+1)/MU(C(t)) to get the answer.
"Hang on Nick" I hear you saying. "What's any of this got to do with Capital Theory? You still don't have any capital in the model. You've only got land!"
And that would be the point at which my Dutch ancestor would deliver his punchline:
"Yes we do! "Capital" is just a strange name for land that we drained ourselves, instead of waiting for God to reduce the sea-level. Saving and investment is just like having a flood this year, and so consuming less wheat, barley, or whatever, this year, and a lower sea level and more land next year. It's just 1 and 2 together. Or maybe a more complicated pattern like 3, if you have to rebuild the dikes every few years. And growing new land is a business just like growing wheat or barley or any other business."
My Dutch ancestor was right, of course. But he did leave one thing out. The quantity of new land produced each year would be where the Price of land equals the Marginal Cost of producing new land. So the position of that Marginal Cost curve would also affect how much new land gets produced each year, which would also influence the current and future production and consumption of wheat, barley, and whatever. It's not just preferences that determine interest rates. Unless consumption never changes from year to year.