Capital flows vs Kapital flows (very wonky)

This is only partly a response to Paul Krugman's posts. Mostly it's me trying to get my own head clear on something. This is a difficult topic, and this post is not as clear as it should be. So I don't expect many, or any, to fully understand it. I don't properly understand it myself. You have been warned.

What we call "international capital flows" (borrowing and lending across borders) aren't the same as what I shall call "international kapital flows" (flows of produced means of production -- like machines -- across borders). Yep. But they can go together, if kapital goods are tradeable goods.

But interest rates aren't the same as returns to kapital either. They are only the same in a one-good model, where the kapital good is also the consumption good.

I'm trying to bring some "kapital theory" into the picture of "international finance". And the easiest way to start out doing that is to start with a model with no kapital, only land. Land is just like kapital, except we have forgotten how to produce more. And when we do remember how to produce more land, so land becomes kapital, we get Dutch Capital Theory.

1 Capital flows in a world with no kapital.

Start with the simplest model. There is one consumption good, apples, that are produced by labour and land. There is one financial asset, bonds, which are bits of paper that promise to pay apples in future. There are zero transportation costs for apples and bonds.

Suppose the home country has a bad apple harvest, but the foreign country does not. Apples will flow from the foreign country to the home country, and bonds will flow in the opposite direction. The home country has a current account deficit, and a capital account surplus. If the home country is large the world interest rate will rise, because current consumption is less than expected future consumption. If the home country is small the world interest rate will stay the same. But arbitrage ensures the home and foreign interest rates remain equal to each other.

Now let's make the model slightly more complicated. The home country can only produce apples; and the foreign country can only produce bananas. But both countries consume both goods. In normal times the home country exports apples and imports bananas, the current account is balanced, and so is the capital account. If there is a bad harvest in the home country, the world price of apples will rise relative to the world price of bananas. And that relative price is expected to fall back to normal next year, because the bad harvest is expected to last only for the current year.

What happens to the rate of interest? Trick question. There are two rates of interest, because there are two sorts of bonds: promises to pay apples; and promises to pay bananas. We know that the apple rate of interest must rise above the banana rate of interest, because apples are expected to depreciate in price relative to bananas.

Would it be correct to say that the apple rate of interest is the home country rate of interest; and the banana rate of interest is the foreign country rate of interest? Not really. If consumers in the home country have the same preferences as the consumers in the foreign country, and so consume the same mixture of apples and bananas, it is the interest rate on a basket of fruit containing that representative mixture that matters for the consumers in both countries.

What happens to the rates of interest if the home country puts a tax on the rental paid on land? Nothing. Land is in perfectly inelastic supply, so production and consumption of apples does not change, so the price of apples and interest rates do not change. The only thing that happens is that the price of land drops. The price of land is determined by the present value of the flow of after-tax rents.

2 Adding kapital flows.

The land on which apples are grown cannot be transported across borders. (The borders can be transported across the land, but let's not go there.) But suppose it could. The land becomes machines, which can be transported just like apples. But the machines are not really kapital, because we still can't remember how to make new machines. There's a fixed world stock of machines.

Suppose the home country cuts the tax on machine rentals? The economy jumps immediately to a new steady state. The stock of machines rises in the home country and falls in the foreign country, and the stocks of bonds change in the opposite direction. Production of apples rises and production of bananas falls. The price of apples falls relative to the price of bananas. Thereafter prices do not change over time, nor does consumption change over time, so interest rates will not change as a result of the tax cut. If the home country is large, the world price of machines will rise in terms of apples, and rise in terms of bananas too. Because the after tax rentals on machines will rise. Wages in the home country will rise in terms of apples; wages in the foreign country will fall in terms of bananas.

Now let's add investment to the model, so new machines can be produced, and they really are kapital. The rise in the world price of machines means that more machines will be produced, so consumption of apples and bananas will be lower temporarily as machines and labour are reallocated to produce new machines. And then consumption will rise over time as output rises over time. So world interest rates will jump up initially, then slowly fall again over time. There is no reason to think there will be any difference between the apple rate of interest and the banana rate of interest, because production of both apples and bananas will be rising over time, at presumably the same rate.

I think I've got that right. But don't ask me to even try to do the math!

3. Paul Krugman's model. [I can't find the link dammit, so apologies to Paul if I've misremembered and misrepresented it] Thanks MF.

Paul gets different results from me. I think I understand why. I think Paul assumes that the kapital good used in the home country can only be produced in the home country; and the kapital good used in the foreign country can only be produced in the foreign country. Kapital cannot flow across borders; only the two consumption goods can flow across borders, and each country produces a different consumption good. But at the same time Paul is assuming each country has a simple "Neoclassical" production function Y=F(K,L)=C+dK/dt. And if we take that simple "Neoclassical" model literally, it means the kapital good produced in each country is the same as the consumption good produced in each country. Which makes it a problem to assume that the consumption good can be traded but the kapital good cannot. Why can't the home country import machines?

I don't think this is an unsurmountable problem. The technical assumption is not that the consumption and kapital good are literally the same; only that the Marginal Rate of Transformation between the two goods is always one, so they always have the same price. (That's what you need to get the result that the Marginal product of Kapital is always equal to the real rate of interest on the good that kapital produces.) Maybe some sort of "putty-clay" version of the model might work OK.

I'm not sure I'm right about all this. And yes I know it's not explained fully or clearly enough. But I'm tired, my brain hurts, and it's finally sunny outside, so I'm just going to post it.

Comments

[Market Fiscalist]

I think this may be the link:

https://krugman.blogs.nytimes.com/2017/10/05/the-transfer-problem-and-tax-incidence-insanely-wonkish/

[Nick Rowe]

MF: thanks!

[Roger Sparks]

I can't see any need for an interest rate in this series of thought experiments!

Maybe this lack-of-need flows from my thinking that 'interest' is identical to 'rent'. Both are payments for surrendering the privilege of use for some time period.

The only difference is that 'interest' is a monetary charge on a monetary instrument while 'rent' is monetary charge made for surrender of a physical object. Both are time-period based.

Now let's advance to the two commodity framework. A crop reduction on either commodity would force adoption of a new pattern of consumption. If both sides had rich and poor consumers, the burden of change would probably fall mostly upon the poor. It seems to me that controlling individuals on each side could agree to replace the short commodity with a oversupply in the future but we would need to add a storage component to the framework.

Once we had a storage component in our framework, we could think of an interest rate that moderated the draw-down and refill rate of that storage. The interest rate would likely be different on each side, depending upon who was storing or drawing each product. The intensity of the interest rate would serve to expand or contract the size of the rich/poor designation. After all, real changes are required to meet real supply fluctuation--promises are nothing more than promises.

We can continue and begin to think about Kapital. It seems to me that this additional component represents a wide variety of components, not a narrow class of machines. Kapital would represent knowledge, tools-in-place, local unique resources, and a whole host of social-economic interplays. Any interest charge would more clearly represent a penalty/privilege cost. I can't think of any reason why interest rates should be the same in every nation unless the do-as-your-neighbor-does syndrome is in-bedded into the economy.

[Nick Rowe]

Roger. There is no money in this model. There's an interest rate of 4% per year if you have to promise to repay 104 apples next year to get 100 apples this year. Sorry, but you won't get this post.

[Lord]

Where does the tax raised or spent go? Is debt reduced or increased? Or does it shift interpersonal consumption without affecting consumption at all? The former should shift rates, the latter possibly not.

[Nick Rowe]

Lord: simplest assumption is that tax revenue is redistributed as lump-sum transfer payments.

[Majromax]

> Kapital cannot flow across borders; only the two consumption goods can flow across borders

Krugman I think would take issue with this description. In his article, he says:

>> And because markets for goods and services are still very imperfectly integrated – most of GDP isn’t tradable at all – it takes large signals, big moves in the real exchange rate, to cause significant changes in the current account balance.