HO and the Ricardian models are both true given their assumptions. So the interesting question is what exactly is it that generates the difference in the results here. In other words, at what point does the rabbit get put in the hat.
I must admit that while I read the post carefully I didn't bother working through all the maths. So what follows is pretty much a guess. A good one, though, I think.
At first I thought it was the activity analysis vs. smooth production functions, but I'm fairly certain that's a red herring, in the same way that the same issue is somewhat of a red herring in the whole aggregatin' capital controversy (i.e. it's pretty damn hard to aggregate capital even with smooth production functions). Because, admittedly, I'm not too familiar with activity analysis, I though the essential absence of consumers somehow prevented the prices from doing some adjustin' they were supposed to be doing in order to restore the standard Ricardian results. But you're right, it's not it, the main textbooks make the same assumptions regarding prices in a small open economy.
Also, the standard gains-from-trade-argument is really just an extension of the two fundemental theorems which are fairly broad, and given some assumptions on production technology (more below) should apply whether the model is smooth production functions or linear activity. So it ain't it.
I'm guessing the rabbit hops in when the intermediate good gets introduced - the fact that one of the goods is produced from another. Basically, the presence of the intermediate, and the way that production technology is specificed introduces a non-convexity. The individual production of each good is still constant returns to scale, but the existence of intermediate introduces a sortof global increasing returns into the production set. I think you can get still the same result with (particular) smooth production functions and an intermediate.
It's true that standard undergrad textbooks are pretty blase about it. Usually they just say "we assume non-increasing returns to scale" whereas to be precise they should say "no increasing returns and no intermediates" or "convex production SET" (that Devil's Bible, Mas-Collel actually makes this point explicitly). But really, they're undergrad textbooks so you can't expect too much technical details. Also, though it's been awhile, I seem to recall that Markusen's book on international trade does mention the problem with intermediates though in a more general context of increasing returns.
Like I said my familarity with Saffrian models, or linear activity models in general is fairly limited. So do all reswitching examples work like this? If the various activities form a convex cone (so the production of the intermediates is restricted in a particular sense) can you still get reswitching?
Anyway, if my guess is correct, then the long complicated five posts could be just shrunk down to "the presence of intermediate goods can introduce non convexity in the production set which can play havoc with the standard Ricardian and HO results on gains from trade". Though I'm not sure if the label "comperative advantage" can still apply in this case.
I do not know that the Heckscher-Ohlin and Ricardian models are both true given their assumptions. The HO model is often set out with one of the factors of production called "capital". These expostions are invalid (false).
I agree that the loss from trade in this example is not driven by the discrete nature of technology or by the non-specification of consumers' utility functions. I do not know what the referent is for "aggregatin' capital controversy".
I do not see increasing returns to scale in my example. I know of nobody who has explained the loss from trade in the theory illustrated by my example from supposed increasing returns to scale.
The example does not exhibit reswitching and is not a reswitching example.
Metcalfe and Steedman explain that a positive interest rate acts like a factor market distortion. I tried to explain the substance of this point by comments on the contrast between the slope of the PPF and the switching price of ale.
Re HO and Ricardian model. It depends on what your definition of 'capital' is, which is I guess what all the fuss' about. However if you just call it the 'I-don't-think-that's-really-capital' factor, then the results are true.
Increasing returns isn't the correct term. Nonconvex production set is what I'm guessing.
I think Metcalf and Steedman emphasized reswitching as necessary for this kind of result then later folks realized that reswitching wasn't it. But like I said, I'm not too familiar and it's been awhile.
Ok - I think I found the MS article and will read up on it (JIL May '77)
You state that the interesting properties do not result from the fact that capital and consumption goods are the same yet they can be traded when used for consumption but not when used for capital.
Admittedly I haven't worked through the algebra myself but it seems as if this point is important.
Firms would want to produe Ale and trade it for Corn because they have a comparative advatage.
Yet you have restricted this possibility because they are forced to be autarkic in the production of input corn.
As such the price of domestic corn should differ from the price of international corn since they are not substitutes.
However, it looks as if you've assumed that all corn trades at the same price.
It is worth noting that in your example domestic corn is fundementally more valuable than international corn because the home country has a comparitive advatage in the production of Ale.
That is, world wide wealth is increased more by an additional unit of domestic corn than an additional unit of international corn because domestic corn has the property that it can be used to make cheap Ale.
HO and the Ricardian models are both true given their assumptions. So the interesting question is what exactly is it that generates the difference in the results here. In other words, at what point does the rabbit get put in the hat.
ReplyDeleteI must admit that while I read the post carefully I didn't bother working through all the maths. So what follows is pretty much a guess. A good one, though, I think.
At first I thought it was the activity analysis vs. smooth production functions, but I'm fairly certain that's a red herring, in the same way that the same issue is somewhat of a red herring in the whole aggregatin' capital controversy (i.e. it's pretty damn hard to aggregate capital even with smooth production functions). Because, admittedly, I'm not too familiar with activity analysis, I though the essential absence of consumers somehow prevented the prices from doing some adjustin' they were supposed to be doing in order to restore the standard Ricardian results. But you're right, it's not it, the main textbooks make the same assumptions regarding prices in a small open economy.
Also, the standard gains-from-trade-argument is really just an extension of the two fundemental theorems which are fairly broad, and given some assumptions on production technology (more below) should apply whether the model is smooth production functions or linear activity. So it ain't it.
I'm guessing the rabbit hops in when the intermediate good gets introduced - the fact that one of the goods is produced from another. Basically, the presence of the intermediate, and the way that production technology is specificed introduces a non-convexity. The individual production of each good is still constant returns to scale, but the existence of intermediate introduces a sortof global increasing returns into the production set. I think you can get still the same result with (particular) smooth production functions and an intermediate.
It's true that standard undergrad textbooks are pretty blase about it. Usually they just say "we assume non-increasing returns to scale" whereas to be precise they should say "no increasing returns and no intermediates" or "convex production SET" (that Devil's Bible, Mas-Collel actually makes this point explicitly). But really, they're undergrad textbooks so you can't expect too much technical details. Also, though it's been awhile, I seem to recall that Markusen's book on international trade does mention the problem with intermediates though in a more general context of increasing returns.
Like I said my familarity with Saffrian models, or linear activity models in general is fairly limited. So do all reswitching examples work like this? If the various activities form a convex cone (so the production of the intermediates is restricted in a particular sense) can you still get reswitching?
Anyway, if my guess is correct, then the long complicated five posts could be just shrunk down to "the presence of intermediate goods can introduce non convexity in the production set which can play havoc with the standard Ricardian and HO results on gains from trade". Though I'm not sure if the label "comperative advantage" can still apply in this case.
I do not know that the Heckscher-Ohlin and Ricardian models are both true given their assumptions. The HO model is often set out with one of the factors of production called "capital". These expostions are invalid (false).
ReplyDeleteI agree that the loss from trade in this example is not driven by the discrete nature of technology or by the non-specification of consumers' utility functions. I do not know what the referent is for "aggregatin' capital controversy".
I do not see increasing returns to scale in my example. I know of nobody who has explained the loss from trade in the theory illustrated by my example from supposed increasing returns to scale.
The example does not exhibit reswitching and is not a reswitching example.
Metcalfe and Steedman explain that a positive interest rate acts like a factor market distortion. I tried to explain the substance of this point by comments on the contrast between the slope of the PPF and the switching price of ale.
Re HO and Ricardian model. It depends on what your definition of 'capital' is, which is I guess what all the fuss' about. However if you just call it the 'I-don't-think-that's-really-capital' factor, then the results are true.
ReplyDeleteIncreasing returns isn't the correct term. Nonconvex production set is what I'm guessing.
I think Metcalf and Steedman emphasized reswitching as necessary for this kind of result then later folks realized that reswitching wasn't it. But like I said, I'm not too familiar and it's been awhile.
Ok - I think I found the MS article and will read up on it (JIL May '77)
You state that the interesting properties do not result from the fact that capital and consumption goods are the same yet they can be traded when used for consumption but not when used for capital.
ReplyDeleteAdmittedly I haven't worked through the algebra myself but it seems as if this point is important.
Firms would want to produe Ale and trade it for Corn because they have a comparative advatage.
Yet you have restricted this possibility because they are forced to be autarkic in the production of input corn.
As such the price of domestic corn should differ from the price of international corn since they are not substitutes.
However, it looks as if you've assumed that all corn trades at the same price.
It is worth noting that in your example domestic corn is fundementally more valuable than international corn because the home country has a comparitive advatage in the production of Ale.
That is, world wide wealth is increased more by an additional unit of domestic corn than an additional unit of international corn because domestic corn has the property that it can be used to make cheap Ale.