You say “Basically Hayek could see which way the wind was blowing and tried to resist it by banishing money”.

Perhaps I am taking this quote out of context but the whole point of Hayek’s theory was that in a monetary economy , if the money rate differed from the natural rates then distortions could take place.

Hayek didn’t like Wicksell’s “basket of goods” approach because he saw that there is no fixed set of goods that reflects total spending through time – but I’m not sure he ever came up with a good alternative explanation of how the money rate in a monetary economy could fully encapsulate all the various own-rates in a barter economy. And I agree that once you factor in the effect that risk and uncertainty have on interest rates then his theory starts to feel unworkable.

]]>In the example that you gave, I think you are missing two items – time and quantity of goods.

You gave the example of cucumbers versus tomatoes. Suppose the price of cucumbers is $1.00 per pound and the price of tomatoes is $1.00 per pound. Also, suppose that it takes 2 months for a pound of cucumbers to mature and be sold but 4 months for a pound of tomatoes to mature and be sold. Meaning that in a four month time period, half as many pounds of tomatoes are grown and sold.

The own rate of interest is calculated as follows:

%INT = Own Rate of Interest

%RINT = Real Own Rate of Interest

Qt = Pounds of tomatoes that can be grown and sold in a given time period

Qc = Pounds of cucumbers that can be grown and sold in a given time period

Pt = Price per pound of tomatoes

Pc = Price per pound of cucumbers

Tt = Time period for tomato growth and sale

Tc = Time period for cucumber growth and sale

T = Time period for loan

%INT = [ Qt * Tt * Pt ] / [ Qc * Tc * Pc ]

If both the tomato and cucumber markets always clear then:

Qt * Tt * Pt = Qc * Tc * Pc

The relative price of a pound of tomatoes and a pound of cucumbers can change without affecting the own rate of interest between the two as long as either the production time or the quantity produced and sold per time period also changes.

The own rate of interest is a nominal variable. The real own rate would be:

%RINT = [ Qt * Tt * Pt ] / [ Qc * Tc * Pc ] – [ Pt / Pc ]

Here even if the relative prices are unchanged ( Pt / Pc = 1), a productivity improvement in the growth of tomatoes versus cucumbers (or vice versa) combined with a change in the quantity of pounds of tomatoes versus cucumbers will change the real own rate.

Fisher is wrong about a unique real own rate because he does not allow for improvements in productivity that are not homogenous nor does he allow for the outmoding of goods.

]]>1) I also think that your definition of own interest rate is inverted. If tomatoes cost $0.9 today, and forward price is 1$ (i.e. I pay one dollar today for delivery of one tomato tomorrow – this is not what finance people usually mean by forward price, maybe that’s the source of confusion?), I can transform one current tomato into 0.9 future tomatos, so own rate of interest is -10%.

2) Even in a stationary equilibrium, interest rate doesn’t have to be zero. For example, in a simple Ramsey/Kass/Koopmans growth model with zero growth in steady state, quantities and prices (relative to the numeraire consumption good) are constant, but the interest rate is still positive, determined by rate of time preference. The “current forward price” would be equal to discounted future spot price, so it would be not the same as spot price itself.

3) But even if rate of time preference is zero, I’m not sure about the example with cucumbers and tomatoes. The fact that one has positive and the other negative own interest rate doesn’t necessarily mean there is a corner solution. The differences in own rates are caused precisely by expected appreciation/depreciation of spot prices, so a good with higher own rate will also experience decline in its “purchasing power”, and from an investor’s point of view, the two will cancel out.

]]>He also raises another point: even for the Wicksell natural rate to work we have to abstract from risk let alone uncertainty. I wrote a paper on this some time ago. The natural rate implicitly rests on the EMH.

Overview:

http://fixingtheeconomists.wordpress.com/2014/05/17/the-natural-rate-of-interest-does-not-exist/

]]>If the current price of cucumbers is $1.1 and its forward price is $1, I would say there is an equilibrium lending rate of 10% in cucumbers, i.e. repayment of 110 cucumbers for every 100 cucumbers loaned.

If I was the lender, I would pay $110 for 100 cucumbers which I would lend to you. At maturity, you would then deliver me 110 cucumbers (principal plus 10% interest), which I would sell for $110. Alternatively, I could buy 100 tomatoes for $90, lend them to you, get back 90 tomatoes (principal minus 10% interest) and sell them for $90. So I’m indifferent between lending cucumbers, tomatoes or dollars.

Maybe, I’ve misunderstood how you are defining the own rate of interest.

]]>I think there is still some confusion here. Sraffa was not trying to prove that the natural rate as such was nonsense. But merely Hayek’s exposition of it. Hayek was trying to do an analysis in a pure barter economy and did not want to introduce money. Sraffa argued that in order to do this you have to take price-levels — as Wicksell had done — and this led to the selection of an arbitrary numeraire which was effectively the same as introducing a money standard. Sraffa says this quite explicitly:

“This, however, though it meets, I think, Dr. Hayek’s criticism, is not in itself a criticism of Wicksell. For there is a ” natural ” rate of interest which, if adopted as bank-rate, will stabilise a price-level (i.e. the price of a composite commodity): it is an average of the “natural ” rates of the commodities entering into the price-level, weighted in the same way as they are in the price-level itself.” (p51)

Hayek was trying to avoid introducing a monetary standard in this debate because he didn’t like the implications of this. Specifically he knew that it would lead to Keynes’ analysis in the Treatise on Money which would later develop into the liquidity preference theory of the General Theory. Basically Hayek could see which way the wind was blowing and tried to resist it by banishing money. Sraffa called him on this and he couldn’t answer.

Here is a full overview:

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