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Hmmm...I'm probably missing something here, Nick, but:

In the first picture, based on eyeballing the midpoint of the PPF which would be the point (5, 5), the inflection point of the indifference curve you have drawn is somewhere around (4.5, 4.5). The diagram is a little misleading, because the y-axis point you have labelled as 4 is actually closer to (3.5, 3.5) I think.

There are other indifference curves in the same space of possibilities, representing different levels of total utility. One of them is the curve whose inflection point is (5, 5) - that is, the curve for which the PPF line is tangent to the curve at the inflection point. That is the production position consistent with the joint achievement of both the highest achievable level of total utility and full production. The two production positions for which your curves intersect in the first picture represent the achievement of full production but a lower level of utility.

I don't see why these points represent "equilibrium" positions. After all, you could draw another indifference curve representing an even more miniscule level of utility far to the left of the curve you have drawn, with the points of intersection at locations like (9.5, 0.5) and (0.5, 9.5). But an economy is not constrained to move along its indifference curve. So if the economy were in a situation in which it was achieving such a low level of utility while nevertheless maximizing production, it would readily move to a higher level of utility.

So why hasn't the economy you have imagined produced the highest level of total utility consistent with its production possibilities? Beats me - it's your picture. I guess there are many possible reasons for that kind of real-world inefficiency?

I meant to say "The y-axis point you have labelled as 4 is actually closer to 3.5, I think."


Paragraph 1. Ignore the fact that the first picture isn't drawn exactly to scale. (That my 4 is closer to 3.5). All that means is that my Paint skills are not very good.

But your other paragraphs get the point: something *seems* to be very wrong with that first picture. Why isn't the equilibrium at point {5,5} instead? At a higher level of utility, on a higher indifference curve?

A monopoly imposes a non-Pigouvian tax, distorting efficiency to its own benefits..Entropy ( 4th law of thermodynamics) also shift your preference. So graph 1 makes sense though it's not the clearest way of looking at the problem.
In the steady state, each apple and banana replaces one produced in the preceding period. That we started with one less apple is now irrelevant as it has receded in the past. It is equivalent to the hotel with an infinite number of rooms, each with 1 broken and 3 intact windows. The number of rooms and of each type of windows is the same.
At the steady state, there is no time and so no interest.The equilibrium is 5,5. But we're not there.
Hope I make sense.Otherwhise, it proves that commenting is not the best way to unwind after a 10-hour drive on a snowy mountain road...

Jacques: (A 10 hour drive can be tiring; on a snowy mountain road it can be exhausting, because of the concentration required. But I still sort of envy you driving it.)

I'm not sure if that makes sense or not. I'm not sure if my original post was very clear, or made sense, either.

Let me restate. You are a visiting economic anthropologist. You come across a society where nothing ever changes, and everyone is identical. You notice that the price of one apple is 1.5 bananas. You notice that people eat 4 apples and 6 bananas every day. You notice that it takes 1 hour of labour to produce 1 apple, and 1 hour of labour to produce 1 banana. And you find this puzzling. Why don't they produce and consume more apples and fewer bananas? Is there some hidden tax on apples? Does someone have a monopoly on apples, and restricts production to raise the price? Is there some hidden factor of production, some special type of land required for growing apples, that is in limited supply, so that only 4 apples can be produced? You draw the first diagram, and the equilibrium makes no sense.

Then you learn that it takes a one-year lag between producing and consuming an apple. Everything comes clear.

The preferences, by the way, are Ut = Log(At)+Log(Bt) and Lifetime Utility = Sum over all t (2/3)^t.Ut

BTW, is this a followup to your comments on the previous post? In my view, the "economic anthropologist" would have to properly specify the production technique for the economy, which looks something like:

w = pa'; pa' * (1 + r) = pa; w = pb

where w is the hourly wage (assuming that it takes an hour of labor to produce an apple), pa' is the "value", or "shadow price" of whatever results from this production process (say, whatever fraction of the value of an apple tree); pa is a price of an actual apple, and pb is the price of a banana. Alternately, you could think of "dated" labor, which has been expended in the past, as being more expensive than current labor. So you can write, more simply:

(w)(1 + r) = pa; w = pb

Then we can solve these simultaneous equations assuming that we have enough information on how the wage relates to the interest rate; which might even be determined outside the market system, such as by institutional influences or other exogenous factors.

Your post is entitled "Capital and interest in the steady state." I see the interest and I see the steady state, but I didn't see the capital...at least not yet. More to come?

Merry Xmas.

Hi anon: yes, in part it's a followup from our discussion in comments on the previous post.

I would prefer to write the technology as:

A(t)=La(t-1) B(t)=Lb(t) and maybe include the resource constraint La+Lb <= 10

Because those equations are all in units an engineer would understand, and would be meaningful in any economy regardless of how the allocation of resources was determined. Those equations would make sense for a Robinson Crusoe economy, centrally-planned economy, a market economy (whether competitive or not), or whatever.

We would only get your equations in a market economy that was perfectly competitive and in steady state equilibrium, so we are already building in some "non-engineering" social science assumptions if we write them your way. And even then we are making an implicit assumption about preferences. Suppose that producing apples is a job that people don't like, and that producing bananas is a job they do like (maybe they even do it for fun). Then the wage would be higher for producing apples than for producing bananas (or maybe they produce bananas for no wage at all, as an enjoyable hobby like gardening).

If I start with my technology, and add in preferences, I can solve for Robinson Crusoe's allocation of resources, or a Utilitarian central planner's allocation of resources, or a competitive market allocation of resources (including the rate of interest and the relative prices).

"Then we can solve these simultaneous equations assuming that we have enough information on how the wage relates to the interest rate; which might even be determined outside the market system, such as by institutional influences or other exogenous factors."

Yes, but we would need to specify what that extra information is that relates wage to the rate of interest, otherwise we can't solve for r and Pa. In my model that extra information is preferences. With preferences I can solve for Robinson Crusoe, the Utilitarian Central Planner, or the competitive market.

2slugbaits: suppose you spend 1 hour to dig 1 hole in the ground, plant an apple seed, one apple tree grows, produces 1 apple next year, and then the tree dies. We would call those apple trees "capital", which has a 100% depreciation rate per year. But notice how my little story about trees doesn't change anything in the model. What we call "capital" is really just the time-structure of production.

Merry Christmas!

Each consumer wants to maximize the present value of his future fruit consumption. The present value of a future fruit consumption of (5,5) is greater than the present value of a future(6,4), based on the information given.

If the discounted difference in utility between (5,5) and (6,4) in the future in greater than the utility of the 6th banana in the present then he will rationally forgo the 6th banana now for a 5th apple in the future.

Ron: I had to read that 3 times, but I *think* you are right. I would just add one word to what you said:

"If the discounted difference in utility between (5,5) and (6,4) in the future in greater than the [marginal] utility of the 6th banana in the present then he will rationally forgo the 6th banana now for a 5th apple in the future."

Correct (I think). But given the preferences I have assumed, it isn't greater.

Ron: sorry. It actually reads very clear now. Must be because it's Christmas Eve.

The point: consider a capitalist economy that is productive enough to have a surplus product after reproducing means of production and wage goods. If the organic composition of capital varies among industries, prices of production are not proportional to labor values. A student of Ricardo should agree.

The coefficients of the following equations are in observed engineering units: 1*w=pb, 1*w(1+r)=pa. Since Nick takes bananas as numeraire, pb=1. pa is observed to be 3/2. It follows that w=1 and r=1/2.

Talk of utility-maximization may be fashionable. But it is not needed here.

Nick Rowe: "What we call "capital" is really just the time-structure of production."

Okay, but I just want to make sure we aren't going down slippery Austrian slopes.

I was trying to think about what assumptions one would need in order get to a steady state of (5,5) rather than (6,4).

In order to move to (5,5) they would need to sacrifice a 6th banana in one period. In return they get higher utility in all future periods.

Based on your (implicit) assumptions they will stay forever on (6,4) which maximizes the present value of their income streams but leaves their total utility over all periods less than it could be if they moved to (5,5) (and assuming they live over enough periods so that the eventual utility gains outweigh the utility loss in the first period).

The utility-maximizing choice will always depend on their time preference but it does not seem unreasonable that that one banana sacrificed in period 1 may be a price worth paying for a life-time of higher utility.

Robert: "pa is observed to be 3/2."

Can you explain why Pa is 3/2? You have one equation (1+r)=Pa in two unknowns. (Or 3 equations in 4 unknowns, if you prefer).

How do you solve for the quantity of apples consumed and the quantity of bananas consumed if you don't know preferences? And if you do know preferences, you can solve for Pa and r as well.

And how do you even know that the wage for producing apples will be the same as the wage for producing bananas, if you don't make an assumption about preferences? Maybe people really like growing apples, and don't like growing bananas, so you have to pay them more to work at growing bananas. Maybe they even grow apples for fun.

I think that's the reason why talking about utility (or preferences) has been fashionable in economics for the last 141 years. It helps us explain stuff. If people didn't like apples as much, they probably wouldn't consume as many.

2slugbaits: I think I'm already halfway down that slippery Austrian slope! Isn't "the time-structure of production" Hayek's definition of capital? (I may be wrong/inexact on that).

Ron: I have (implicitly) assumed people live forever, or that they care about their kids as much as they care about themselves, so will happily plant apple trees for their heirs.

I can think of two changes to preferences that would cause the Indifference curve in the second picture to swivel around and make {5,5} the equilibrium: make them prefer apples to bananas; make them indifferent to delays in consumption (a 0% subjective rate of time-preference).

Nick: " make them indifferent to delays in consumption (a 0% subjective rate of time-preference).
Then, there is no time (there may be a thermodynamic time but economic agents just don't care, tomorrow is the same as today as yesterday). We are at the steady state. And the equilibrium is 5,5.
A day's rest and the thermodynamics stays the same...

Merry Christmas all, including the turkey who just fulfilled its karma...

"I think that's the reason why talking about utility (or preferences) has been fashionable in economics for the last 141 years. It helps us explain stuff."

The trouble with this view is that David Ricardo and other classical economists were well aware that all labor is not alike. Here's Ricardo, in his Principles (3rd ed.):

"In speaking, however, of labour, as being the foundation of all value, and the relative quantity of labour as almost exclusively determining the relative value of commodities, I must not be supposed to be inattentive to the different qualities of labour, and the difficulty of comparing an hour's or a day's labour, in one employment, with the same duration of labour in another. The estimation in which different qualities of labour are held, comes soon to be adjusted in the market with sufficient precision for all practical purposes, and depends much on the comparative skill of the labourer, and intensity of the labour performed. The scale, when once formed, is liable to little variation."

In other words, Ricardo argues that relative wages are stable enough that we can, say, pick one occupation as the "standard" quality of labor and scale the amount of labor accordingly in each production process. Alternately, one would think that we could have multiple "wages" w, w' ... in our production processes, each with its own coefficient in the equations; obviously, solving the system in order to determine long-run prices requires characterizing the relationship between three variables, namely (1+r), w and w'.

"I can solve for Robinson Crusoe's allocation of resources, or a Utilitarian central planner's allocation of resources, or a competitive market allocation of resources (including the rate of interest and the relative prices)."

Maybe OT, but would you get the same result from these different calculations?

I would not. Unless we allow for the risk of death, you wont maximize your stream of utility by the (4,6) combination - even though actual agents might choose that combination due to a physiological defect.

In t= 2, you will think that whatever happened in t=1 wasn't that important, and whatever happens in t=3 wont be as important, as the present.

In t= 3, you will think that whatever happened in t=2 wasn't that important, and whatever happens in t=4 wont be as important, as the present.


So, knowing the parameters, the utilitarian should restrict the agents behavior.

Ah Nick, you were the dissertation committee member I never had...

Jacques: I think that is right, and important. If there is a time-lag in production, but nobody cares about that delay, it might as well not exist. It is as if there is no time, so the equilibrium must be at {5,5}. God invented time to stop everything happening at once. But if people don't care about when things happen, we might as well be in a one-period model.

(That 10 hours snowy mountain road has stuck in my mind. You must tell me where it is, so I can at least drive it vicariously by looking at the map.)

anon: here is my take on that passage in Ricardo:

Ricardo was a great economist, and no fool. He knew there were wage differentials, and he knew his theory couldn't properly explain them. (He could have explained some wage differentials, like human capital, but not all.) So he did what all sensible economists (and other scientists) do in such cases: he black-boxed it. Rather than waste his time getting bogged down trying to explain something that isn't central to his theory, he puts the problem in a black box, assumes that wage differentials don't change much over time, so he can get on with the rest of his theory.

Keynes did the same thing with the consumption function. He black boxed it in a "psychological law", so he could get on with the rest of his theory and not get bogged down.

That was the right decision for Ricardo at the time. But it isn't the right decision for us now, 200 years later. We can do a bit better. We can build preferences into our price theory. Why do some musicians get paid a lot higher wages than others? Part of the explanation is that people like their music better. Why do hockey players get paid more than equally skilled and trained cricket players? Partly because (in some countries) people like watching hockey more than cricket.

We can build both preferences and technology into the demand and supply functions, and explain how they both affect how prices and wages and interest rates are adjusted in the market.

So it's time to move on, and think about all the problems that we are black boxing in turn.

Nemi: that's close enough to on-topic. Robinson Crusoe would choose the same {4,6} allocation as competitive equilibrium. You could argue that a Utilitarian central planner might ignore that aspect of the agents' preferences, if he deemed time-preference to be irrational. (In a growing economy we could still get a positive real interest rate even without people discounting future utility if they have diminishing Marginal Utility of consumption, and so discount future consumption at the margin, because they will consume more in future.)

Bob: I enjoyed reading the big chunk of your thesis that I did read. Do you get the feeling that not many economists think about this sort of stuff nowadays?

Merry Christmas to all. Now I must go stuff the turkey.

Hmmm. I took 3 tries to post this comment. TypePad is playing up.

Yes, I agree that we'd rather explain the things that classical analysis punts on, such as the level and composition of output, or the relationship between wages and the rate of normal profit. But I'm not sure that talk of "preferences" is any less fuzzy than talk about "institutional factors, influences, etc.". It suffices to think about how important culture is in explaining which kinds of music and sports are preferred: a sociologist would probably say that talking generically about "institutions" and "influences" on the price system is more scientifically honest than assuming that every agent has preferences, as if such preferences could be directly measured.

From a modern perspective, it does seem strange that classical economics has so little to say about e.g. the composition of output, or the distribution of income. But its overall goal seems to be rather different, namely explaining prices while taking choices in allocation and distribution as a given for the most part. While this goal is clearly less ambitious, it may well benefit from greater generality and applicability than modern economic theory.

BTW, happy holidays everyone.


"as if such preferences could be directly measured"

Isn't it a key principle of neoclassical economics that preferences can't be directly measured? One can look at prices, look at behaviours, but what's in people's heads is important but unmeasurable by economists. Indeed, if one is strictly ordinalist in the Mengerian tradition, one can't even assign cardinal values to people's preferences for a particular product/service.

"a sociologist would probably say that talking generically about "institutions" and "influences" on the price system is more scientifically honest than assuming that every agent has preferences, as if such preferences could be directly measured"

I fail to see how "influences" is any more precise, and I think that the formulation of people's preferences is best kept (for the most part) outwith economics, mainly because it involves so many different subjects that economists can't master in addition to economics (e.g. psychology, anthropology, sociology, history etc.).

My main problem with classical economics is a deduction from the work of Nancy Cartwright. Classical economics involves the wrong sort of unrealistic assumptions: it's one thing to make simplifying assumptions to make something computational or cognitively tractionable, but things like the labour theory of value are either misleading or have to be patched up, as Marx did, to the point of tautology. Unrealistic assumptions should not determine the theoretical output of the model. To take Sraffa as an example: constant returns to scale can help make things comprehensible sometimes, but if this assumption is necessary to the conclusions one draws from the model then one is in big trouble. (This is by no means purely an objection to most of CLASSICAL economics, of course!)

IIRC, Sraffa actually claimed that his model could abstract away from considerations of returns to scale without any loss in generality, and that reading it as a constant-returns model meant making a simplifying assumption. It's right there in the introduction to Production of commodities by means of commodities. I'm not saying that I full understand his claim, but it makes some sense given that neo-Ricardian analysis is so narrowly focused on relative prices.

Screpanti and Zamagni, who are Neo-Ricardians, go into this issue in some detail in their 'Outline of the History of Economic Thought'. I find it very hard to follow, but they conclude in their analysis of Sraffa's model that there is not a basis for thinking that removing the assumption of "constant returns could preserve the most important properties of Sraffa's theory".

They forgive him because they endorse a methodological principle that theories should be judged only for their results within their prescribed scope, which is a convenient methodological principle for a Neo-Ricardian. I disagree; so do Screpanti and Zamagni, when it comes to assessing many economists not called 'Piero Sraffa'.

@nick rowe. The classic book explaining wage differentials from a classical/marxian perspective is Howard Botwinick's wage disparity under capitalist competition.

anon: I would put it like this: "preferences" are "black-boxed" in neoclassical theory. We just cross our fingers, and hope they are stable, even though we know that ultimately they aren't always. (Though one could make the same argument about technology too. Not to mention institutions.) Yep. There's always stuff being black-boxed, and always a few brave people trying to open up those black boxes. It's good that we can build preferences into the theory, but it doesn't stop there.

Is aged wine expensive because of storage costs or impatience?

Primed: probably both. Plus maybe a bit of risk of theft/damage/spoilage/whatever. Plus maybe we aren't in steady state, so the demand for aged wine might be bigger, and the price higher, than it was expected to be when it was put in the barrels.

primed: if it's felt to be better, the customer is willing to pay storage costs, spoilage, whatever. Only if the wine is "better".

Nick: the QC-138 between Sept-Îles and Québec City. It doesn't go very high except in the Charlevoix area but it constantly goes up and down, sometimes it's carved in clifffaces, there is the only mountain tunnel in the province, it winds around itself so much that sometimes you go west in the morning and have the sun in your face, the humidity from the Gulf of St-Lawrence ensures there is always enough stuff for snow. There are areas where you are more than 100 kms away from the nearest tow truck or ambulance ( and 200 from even a small hospital). Some stretches have no cell coverage. Once, I got a tow truck through a satellite phone...
Last Sunday morning, a truck lost its brakes in the hill leading down to the Tadoussac ferry wharf and maneouvred straight onto the ship, slamming into another truck already on board. 10 hours of unending fun. But the view of the mountains and the St-Lawrence...Is there a more beautiful river in the world?
From the french version of "O Canada": "Sous l'oeil de Dieu, près du fleuve géant, le Canadien grandit en espérant...". My family has lived on its banks since 1660...my cousin in the thirteenth degree still works the ancestral land on Orléans Island. His ice cider is beyond words.

Jacques Rene reminds me that I had forgotten to include the demand side analysis of the price of aged wine!: "primed: if it's felt to be better, the customer is willing to pay storage costs, spoilage, whatever. Only if the wine is "better"."

If it weren't felt to be better, none of my supply side stuff would count for anything, because none would be produced, except by mistake, and if it were produced by mistake, its price would be no more than the price of young wine. Unless buyers too bought it by mistake.

QC-138 looks beautiful on the map, and from your description. Its existence affects my labour supply curve. Should I retire, so I can enjoy driving a road like that, while I'm still young enough?

Speaking of ice cider, aged wine, stability of preferences, and Quebec traditions: my depanneur said there used to be lots of cider produced and consumed in Quebec 40 years ago. He rattled off half a dozen different brands. But that when they were allowed to sell wine the cider market fell away to almost nothing. I was complaining about the high price of the single brand of cider he had for sale, told him I thought that Quebec should be cider country, like the west of England, because apples grow well here, plus many ancestors came here from Normandy which is also cider country, so he was explaining that it used to be cider country, and why it wasn't any more. Perhaps cider will return. This needs more research.

Students often forget the other side. "I deserve a better grade, I worked so hard!"

You can't retire, you would still blog, it's the nature of the beast...

Take the 138 from Montréal, it's called the Chemin du Roy, the oldest road in North America
Past Québec City, go round Oréans Island,
known simply as "the Island". "Le tour de l'Île, 42 milles de choses tranquilles" said the poet Félix Leclerc, "Round the Island, 42 miles of quiet things".
Go through Charlevoix and don't forget Coudres Island
The North shore will add another 800 kms...

Cider came with the ancestors.(My mother's came in 1635 and my father's in 1651.) I am from "familles souches" (root families, those who came from 1608 to 1705)on all sides. With urbanization and Prohibition the craft was lost.

From the Wikipedia article,
obviously written by a fellow survivor...(The Grand Sec...banned as cruel and unusual punishment)

"When cider became legal again, Quebecers were served a cider produced industrially, which was disliked very much by many and gave it a bad reputation. Makers were unable to supply to the demand and inundated the market with products that had no maturity.[11] A whole generation experienced the Grand Sec d'Orléans,[12] which to many, evoked what is most undrinkable when it comes to alcohol. Sales declined after a few years, and cider, barely gotten out of its "dark age", was plunged back into it."

Today, it's back and various growers now provide very high quality products. A few favorites:


and of course, allow me this plug for the aforementionned distant relative


available at some SAQ, on the other side of the Ottawa river.

Tasting note and serving suggestion are there on that link.

The things we learn on this blog.

The main reason aged wine is expensive is selection: only high quality wines tend to be stored for long periods. A year increase in age-at-release is associated with a return of about 20%, which is much too high to be largely attributable to storage costs or interest.

W. Peden, interesting. But I see Neo-Ricardian/Sraffian "economics" as mostly about their price theory, or "theory of value". Heterodox economists obviously disagree, and endeavor to build a complete economic theory, so they tack on lots of details to their basic model in order to explain output levels, the split between wages and profits and whatnot--but all of these added details/theories are half-baked to say the least.

BTW, I think this explains why neo-Ricardians and related theorists are (or used to be, at any rate) so harshly critical towards mainstream economics: they're uncomfortable about not really having a consistent alternative, so they're kind of forced to make the case that mainstream econ is actually _logically unsound_, as opposed to being merely affected by some pathological cases.

At the end of the day, I'm not sure I'd want to reject the principle that limiting your conclusions lets you make broader assumptions, and vise versa. I think it's sensible, and I don't see a problem with it applying to both mainstream and Sraffian models.

Thanks for the great answers!

I had implicitly assumed perfect competition or monopolistic competition and IIRC price in that case would just be a function of marginal cost. In my question, and in the context of this post, I was merely wondering to what extent the marginal cost increases due to time-preference (and I lumped everything else - spoilage, theft, etc. as storage costs). The 'not-in-steady state' answer was really interesting but wouldn't that suggest an equal likelihood of too low prices?

In hindsight, I agree perfect or monopolistic competition is a bad assumption for wine and so demand matters and markups are correlated with quality which in turn is correlated with the wines selected for 'aging'.

primed: demand matters in perfect competition (and monopolistic competition) too.

Take a very simple, extreme (and false) model of the wine market, just to illustrate the point:

All wine is identical. Wine can be produced with land only (ignore labour and aging). There is only one million acres of land that can grow wine, and that land is useless for any other purpose. Each acre of land produces 100 bottles of wine per year. The rental market for that land is perfectly competitive. The market for wine is perfectly competitive. Each individual firm that produces wine can rent land at $R per acre per year. The Marginal Cost of one bottle of wine is 0.01R per bottle. If the price of wine is $P per bottle, and given perfect competition, so price = MC, we know that P=0.01R. But what determines R?

The individual firm producing wine takes R as given, so has a horizontal MC curve, which is its supply curve. But the market supply curve for wine is vertical at 100 million bottles per year. (The market MC curve is vertical). There is a downward-sloping market demand curve for wine, that crosses the vertical supply curve at (say) $10 per bottle. So P=$10 per bottle, and R=$1,000 per acre per year. If the demand for wine increased (the demand curve shifts up) P will increase, R will increase, and each individual firm's horizontal MC curve will shift up.

If you relax some of my assumptions, so that some land and/or labour has a comparative advantage at producing wine, but is not totally useless at producing anything else, you get an upward-sloping (rather than vertical) market supply curve for wine. The market LRMC curve for wine will be upward-sloping even if the individual firm's LRMC curve is horizontal. An increase in demand for wine will cause the individual firm's MC curve to shift up.

P=MC in perfect competition. This does not however mean that MC determines P. It is equally true (and equally false) to say the P determines MC. Rather, P and MC are co-determined simultaneously by demand and supply (preferences, technology, and resources endowments).

anon: "BTW, I think this explains why neo-Ricardians and related theorists are (or used to be, at any rate) so harshly critical towards mainstream economics: they're uncomfortable about not really having a consistent alternative, so they're kind of forced to make the case that mainstream econ is actually _logically unsound_, as opposed to being merely affected by some pathological cases."

A couple of reflections on that:

Decades ago I did some reading on CCC trying to understand that claim that neoclassical economics is logically unsound. I came to the conclusion that it wasn't logically unsound. But I have some sympathy for the critics making that claim, because, well, I got the impression that the people defending neoclassical economics didn't really understand neoclassical theory of capital and interest either. How many neoclassical economists still think that MPK determines r? MPK doesn't even have the same units as r, and it certainly doesn't determine r (except in special cases where the price of capital goods is always equal to 1 because the technology for producing capital goods is identical to the technology for producing consumption goods so the Marginal Rate of Transformation between C and K is always 1).

(Which is not to say there aren't other problems with neoclassical theory, because there are).

Some (not all) of the critics seem to be rather angry. This may be because they sort of realise their own models don't present a good alternative (because it *is* hard to explain stuff if you don't put preferences in the model). It might be politics. It might also be because they see themselves being shut out of academia. It might be because they think their own insights are being ignored. It might be because they think that CCC proved that neoclassical economics is logically unsound and that neoclassical economists are deliberately ignoring that critique. Or all of the above.

I have tried to engage them a bit, over the last year or so. Not very successfully.

Some day I will probably write another post, saying that neoclassical theory does not (should not) say that MPK=r, and laying out the relation between MPK and r in neoclassical theory. It will be as much for students of neoclassical economics as for the critics.

Weird thing is: this is not at all my area of economics. Plus I'm really bad at math, which makes it harder for me. But nobody else seems to be willing to do it.

Why is it a problem that r=MPK? That is the equilibrium demand for capital. The equilibrium supply for capital is determined by the household's Euler equation, typically given by the marginal utility of consumption today being equal to the expected discounted utility of consumption tomorrow, i.e. MU(t) = beta E[MU(t+1)*(1+r(t+1))]. beta is the subjective discount factor and R the rate of return including principal and depreciation. That is not too different from w=MPL as the demand for labor and the supply is given by preferences. You can also add adjustment costs and what not, then the firm's problem becomes more complicated (notably dynamic) and r is not equal to the MPK. It seems I am missing the point.

Till: quick version (in which will probably screw up the math):

Ignore depreciation, to keep it simple. Let Pk be the price of capital goods in terms of consumption goods. Let MPK be the extra units of consumption good produced per extra machine (it's in physical units). Let the consumption good be the numeraire for the real rate of interest r. The equilibrium condition is:

1.) 1 + MPK(t)/Pk(t) + [Pk(t+1)-Pk(t)]/Pk(t) = 1 + r = Marginal Rate of Substitution between C(t+1) and C(t).

(Notice: the capital gains term [Pk(t+1)-Pk(t)]/Pk(t), and notice that MPK is divided by Pk.

And 2.) Pk(t) = Marginal Rate of Transformation between Investment goods and Consumption goods at time t. (The opportunity cost of producing one more machine today in terms of foregone consumption, which is the slope of the PPF between Current Consumption and current Investment.)

If you substitute for Pk(t) and Pk(t+1) into the Left Hand Side of the first equation, it becomes Irving Fisher's equilibrium condition:

3.) Marginal Rate of Transformation between C(t+1) and C(t) = 1 + r = Marginal Rate of Substitution between C(t+1) and C(t).

[Edit: the interpretation of that equation is that the rate of interest is co-determined in equilibrium by technology (the left hand side) and preferences (the right hand side). In general, the MRT between C(t+1) and C(t) is not a constant, because the PPF between C(t+1) and C(t) is not a straight line.]

The simple aggregate Neoclassical model is C+I=F(K,L), and K(t+1)-K(t) = I

That simple model assumes the PPF between I and C is a straight line with slope of minus one. That pins down Pk=1. That means my equation 1 reduces to:

4.) 1 + MPK = 1 + r = MRS between C(t+1) and C(t)

[Edit: which reduces to MPK=r, and since K is not a jump variable, since it is a stock and I is a flow, that means MPK is not a jump variable either, so MKP determines r for given K.]

But that straight line PPF between I and C is a very special assumption, that only holds if the capital good and the consumption good are produced with the same technology with the same factor intensity. In general, that PPF between I and C will be curved, so the slope of the PPF will depend on preferences for consumption vs saving, and so Pk will depend on preferences too.

[Edit: and Pk is a jump variable if preferences change.]

The adjustment cost model is one crude way to get a curved PPF between I and C.

Where's Bob Murphy? He's very good on this stuff. He sent me a very good paper of his, where he showed where Samuelson was getting it wrong, by ignoring that capital gains term. And you can only ignore that capital gains term in steady state equilibrium, where Pk is constant over time.

Till: put it another way: MPK will equal the rental rate per machine (just as MPL is the rental rate per worker). But the rental rate per machine is not the same as the rate of interest, unless the price of a machine is always equal to one. But it won't always equal one (or any constant), except under very special assumptions about technology.

The rental on land will be equal to the Marginal Product of Land. But the price of land is not pinned down by the technology of producing new land. You need to bring in preferences as well to pin down the price of land.

Of course, Nick. Your example is so clear, I am honestly surprised that I mistakenly thought demand wouldn't matter - I should really think more before commenting.

primed: I'm glad you commented before thinking. Because maybe a lot of people don't get that point even with thinking. So it gave me a chance to explain it.

A modest proposal for slightly complicating the simple aggregate neoclassical production function:

Replace "C+I=F(K,L)" with "F(C,I,K,L)=0".

Then Pk/Pc is not pinned down by technology.

And r = (F3/F2) + percentage rate of change of (F2/F1). (If I got the math right).

You can impose Homogenity (constant returns to scale) if you like, and rewrite it in per worker terms as "f(c,i,k)=0".

That would get rid of an awful lot of pointless arguing. Because the original can be written as F(C+I,K,L)=0, which makes it additively separable in C and I, which is a very special assumption.

Nick, I agree. It's quite interesting that, taking the neo-Ricardian model, you ought to need only a single "preference" to determine the wage-profit split (provided that you take the level and composition of output as given, as the neo-Ricardian model does), but the interpretation is not entirely trivial (IMHO): the wage-profit split balances the capital-labor ratio on the margin of production with the consumption side's choice between labor supply and abstinence. If w was fixed to be higher and r lower, then capital accumulation would decrease and labor supply would increase, hence some workers would not be employed given the technique of production; on the other hand, if r was higher and w lower, then the accumulated capital would offer more employment than the available labor could fill.

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