Monday, 1 May 2017

Comparative Advantage And Offshoring



In a recent post Lars Syll quotes Steve Keen on Ricardo's model of comparative advantage.  Keen thinks you can "prove" that the idea that free trade benefits all is a fallacy by considering the following:

"Ricardo’s model assumed that you could produce wine or cloth with only labour, but of course you can’t. You need machines as well, and machinery is specific to each industry. The essential machinery for making wine can’t be used to make anything else, if its use becomes unprofitable. It is either scrapped, sold at a large loss, or shipped overseas. Ditto a spinning jenny, or a steel mill: if making steel becomes unprofitable, the capital involved in its production is effectively destroyed …"

Now, I think there is a lot to be said on the topic of trade, including a case to be made that certain protectionism can benefit all in particular circumstances.  But I found Keen's statement rather odd, because it is not obvious to me that the message in Ricardo's model has anything to do with whether or not there is machinery, whether it has specific use and whether it can be offshored.  So, I thought I'd look at what Ricardo's model might look like with those modifications.  


The Model

There are two countries: England and Portugal.  Each can produce wine and cloth.  The production function in each case is Cobb-Douglas with equal weightings on capital and labour:

Xij = Aij . Kij0.5 . Lij0.5

where Xij is production of product i in country j and Kij and Lij are capital and labour respectively used to produce product i in country j.  Aij is a factor specific to each industry and country intending to reflect the different skills of labour (and is not therefore a technology that can be transferred between countries).

The capital stock consists of a fixed supply of machines.  Machines are either wine machines or cloth machines; they cannot be transferred between these uses.  However in some scenarios, they can be transported between countries.

Labour cannot move between countries, but it can be used in either industry within a country.  The labour stock in each country is fixed and assumed to be fully employed.

Each country has its own currency.  The nominal wage is fixed in local currency units.  Products are sold at marginal cost.

For simplicity, households in each country are assumed to want to consume wine and cloth in equal quantities.  This means factor allocation must ensure equal global output of the two products.

The matrix of the values for A is as follows:


England
Portugal
Wine
1.0
1.2
Cloth
1.0
1.1

Factor endowments are as follows:


England
Portugal
Wine machines
1,000
1,000
Cloth machines
1,000
1,000
Total labour
2,000
2,000

Portugal has a natural absolute advantage in both products, but England has a natural comparative advantage in cloth.  Unlike in Ricardo's model, however the marginal comparative advantage varies with the allocation of inputs, because of the production function.

Various scenarios are considered below:


1. No Trade

England will employ equal amounts of labour in each industry; Portugal will need to employ more in production of cloth than wine to compensate for the lower labour productivity in that industry.
 

Portugal

England

Wine
Cloth

Wine
Cloth
Factor Usage





Machines
1,000
1,000

1,000
1,000
Labour
913
1,087

1,000
1,000






Products





Output
1,147
1,147

1,000
1,000
Traded
0
0

0
0
Consumed
1,147
1,147

1,000
1,000






Local price
1.59
1.90

2.00
2.00

The relative price of each product is different for the two countries.


2. Free Trade But No Free Movement of Capital

England increases its employment in cloth production, where it has a comparative advantage, and Portugal reduces its cloth employment.  Prices move in each country so that the relative price of each product is the same.  The exchange rate settles at the level which equates the price of each product between the two countries.
 

Portugal

England

Wine
Cloth

Wine
Cloth
Factor Usage





Machines
1,000
1,000

1,000
1,000
Labour
994
1,006

907
1,093






Products





Output
1,196
1,103

952
1,045
Traded
-49
44

49
-44
Consumed
1,148
1,148

1,001
1,001






Local price
1.66
1.82

1.90
2.09






Profit per machine (€)
0.99
1.01

0.79
0.95






Exchange rate (€/£)
0.87










Portugal's Balance of Payments (€)





Wine exports
81




Cloth imports
-81




Net
0





Expressed in a common currency the profit per machine is higher in Portugal in both industries.

Both countries benefit from increased consumption, although the gain is surprisingly small.


3. Free Trade With Free Movement of Capital

Here we allow machines owned in one country to be used in production in the other country - a kind of offshoring.  This acts to equate the profitability of machines in each country (but not between industries are all the machines are single use).  In fact, profitability is not equalised in wine production because there is a boundary condition when all wine production moves to Portugal.
 

Portugal

England

Wine
Cloth

Wine
Cloth
Factor Usage





Machines
2,000
335

0
1,665
Labour
1,668
332

0
2,000






Products





Output
2,192
367

0
1,825
Traded
-1,044
781

1,044
-781
Consumption
1,148
1,148

1,044
1,044






Local price
1.52
1.81

n/a
2.19






Profit per machine (€)
0.83
0.99

n/a
0.99






Exchange rate (€/£)
0.83










Portugal's Balance of Payments (€)





Wine exports
1,589




Cloth imports
-1,415




Investment income received
660




Investment income paid
-834




Net
0






Although in the last scenario, cloth machines were more profitable in Portugal, wine production shifts so extensively that this position reverses and it becomes profitable to relocate cloth machines to England.

We still have free trade so prices are equalised as before, although there is no price for domestically produced English wine.

The balance of payments now includes remission of profits based on the number of machines used overseas and their profitability.  (There are no net capital flows for the transfer of machines between countries because the purchase price cancels out the equity investment.)

The overall benefit from the free movement of capital is much greater than for free trade alone, but it is heavily skewed in England's favour.  This might seem odd given that production in England has actually fallen (based on scenario 2 prices) but it reflects the net foreign income flow.

There is also a shift in functional income distribution, arising from the equalisation of machine profitability and a shift of the exchange rate in Portugal's favour.  Overall, real wages fall for English workers and rise for Portugese ones, whilst profits rise for English capital owners and fall for Portugese ones.  These are the expected results of offshoring.


Conclusion

This model is certainly not intended to constitute a proof.  But I find it helpful in thinking about how the ideas in Ricardo's model might apply with internationally mobile capital.  And on the whole, I'd say that these particular issues do not really change the conclusions.

Keen also mentions scrapping of machinery.  This does not occur in my model, because the particular production function ensures that capital is always useful.  In fact, I suspect that machinery obsolescence does not change the analysis either, but I do think that under-employment of labour is very relevant.  This in my view provides much better grounds for critiquing the real-life application of comparative advantage.

21 comments:

  1. "But I found Keen's statement rather odd, because it is not obvious to me that the message in Ricardo's model has anything to do with whether or not there is machinery, whether it has specific use and whether it can be offshored."

    Nick,

    I think Keen's point is that free trade can destroy things.

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    1. Maybe. I wasn't trying to address Keen's article as such - I just wanted to explore the ideas he was raising about capital flexibility.

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  2. About the word "offshoring": it's usually referred to a home company which moves production abroad. Such as Apple manufacturing phones in Asia.

    Ricardo's ideas had less about offshoring. It kind of argued about different producers producing things in their home country only (implicitly) -- although opening trade would lead to a change in production patterns, which he thought will be good for everyone.

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    1. That's pretty much what I had in mind by offshoring here. So in my scenario 3, I imagine that English wine firms are setting up Portugese subsidiaries and funding them. The subsidiaries use the funds to buy the wine-making machines from their English parent companies and start making wine in Portugal with Portugese labour, remitting profit back to England. Without the machines, English wine production is closed down.

      I agree that Ricardo's model has anything to do with offshoring (neither does Heckscher–Ohlin). Obviously, that's not such a good model of international trade today. That was one of the things I wanted to look at. (But, equally, I'm not suggesting that this model is a good representation of all the issues involved with globalisation. I can think of a number of things I would want to try to incorporate if I wanted to show the problems with trade liberalisation.)

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  3. This comment has been removed by the author.

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  4. The biggest limitation in the real world application of Ricardo's comparative advantage system, is that the prices for the two goods are set by the ratio of hours spent in production by two particular trading partners. The prices for the two goods result to be a precise particular figure, a price ratio, that suits trading between the two parties , and so that is why on those terms the system works. But in the real world, prices for two internationally traded goods are arrived at independently in an international market of many participants, so put it bluntly comparative advantage is a useful concept , but not directly applicable where a free trade market place is accessed, and goods are traded at market prices, rather than an arrangement between two parties.

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  5. I don't see why the comparative advantage model would not work with multiple nations. But I do agree that actual prices (which are what really drive trade) do not entirely reflect actual comparative advantage.

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    1. It would not work because it would require one or both of the parties to forgo buying at a lower price someone else was offering the goods at on the market.

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    2. If a country were to switch from production of a quantity of domestically consumed product, to production of products for export , comparative advantage has nothing to say about whether or not it will garner enough funds from the sale of the exports to import the goods it requires for domestic consumption that it is no longer producing itself.

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    3. Models illustrating the implications of comparative advantage usually require that the terms of trade can alter so as to eliminate any imbalances. But I'd agree that they don't generally say anything about whether this will happen in practise.

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    4. The fact is more fundamental than that.

      Comparative advantage says nothing about trading in the international market for goods.

      To see this, the first thing to notice and acknowledge is that there are no prices in the comparative advantage thesis.

      Once you see that , then you can see that it us actually a narrative about two partners working in bilateral cooperation with the exclusion of trade.

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    5. The comparative advantage thesis is that Country A swaps an hour of labour with an hour of labour from Country B, and the goods exchanged depend on the countries relative talents. The actual goods are immaterial to that principle, and in the real world Country A and B will be buying those goods from whoever has the lowest price , a third party. And so comparative advantage is intellectually interesting but not an imperative principle that works for a country in world market trade.

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    6. The only thing Ricardo's model shows is that, where two nations have comparative advantage in different products, then there are welfare gains that can be obtained from trade in those products. It does not tell you whether trade will actually take place or, if it does, on what terms.

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    7. Hi, your not seing what I am pointing out and so I will put it bluntly.

      Comparative advantage has nothing to say about free trade, period
      Comparative advantage is not compatable with free trade because free trade is carried out with prices that do not represent the hours spent in production of the goods.
      It can not work in a market where goods are freely traded. But for some reason , probably historically educational, some economics commentary refers to the concept as if it were something that promotes free trade. Thats the fallacy , there is no need to add variables or conditions to comparative advantage to show that.

      Comparative advantage requires two partners to cooperate and agree to arrange that the goods traded reflects the hours spent by each country to produce those goods. They trade one for one by hours a labour, note hours of labour not currency, and that understanding and prior definition by the two parties of what an hour of labour produces in each country and will be traded is unique to the two parties, and so cannot be extended to the international market where trade is conducted with market prices that dont relate to the hours spent in production.
      That is inherent in the maths of comparative advantage and explicit, it only takes 15 minutes to work through it from the figures of cloth and port on Ricardo's original example.

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    8. Part of the problem here is that I'm not sure I understand exactly what you think the claims of the theory of comparative advantage actually are. It's quite possible I agree with you. As far as I am concerned comparative advantage is just a description of the relationship between production possibility frontiers. And Ricardo's model is only what I said in my last reply.

      When you say "Comparative advantage is not compatible with free trade..", do you mean that you disagree that there is such a potential welfare benefit? Or are you simply saying that you don't think that patterns of trade under free trade follow comparative advantage. If the latter, then I'd say they don't follow it exactly, but it is influential.

      However, the description in your final paragraph sounds odd to me. Although Ricardo's model does not contain enough to need explicit prices, I have never imagined it as a barter model. It is easy to write out a model showing the same principles but with explicit prices. My own model in this post uses prices. Even if a nation is a price taker in international markets, it will still be influenced by comparative advantage. Global demand and supply will determine the price of international goods. The price-taker nation then decides which goods to produce and export and which to import. It will choose to produce those that it can produce most cheaply relative to world prices, i.e. those in which it has a comparative advantage.

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    9. Choosing to produce those that it can produce most cheaply relative to world prices is not comparative advantage , that is absolute advantage. Comparative advantage is where the producer specialises in what they are good at regardless of the production cost relative to what other can do and what they are selling at.

      In your example you state that England has a comparative advantage in cloth but your figures show 2000 input and 1000 output for cloth production and the same for wine production so there is no comparative advantage.

      Yes you use prices but those are labour theory of value prices where as in the modern world trade works by the subjective theory of value, or simply whatever the producer chooses to quote to get market sale.

      I think the claims of comparative advantage are what Ricardo said they were ie mutually beneficial trade can occur between two parties even if one is less efficient than the other in both products.

      It doesn't say anything about multinational trade without contractual obligations to exclude third parties.

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    10. "In your example you state that England has a comparative advantage in cloth but your figures show 2000 input and 1000 output for cloth production and the same for wine production so there is no comparative advantage."

      You can't make statements about comparative advantage in relation to one country in isolation - it's meaningless. Comparative advantage is about how one nation's production possibility frontier compares with the rest of the world.

      Take my numbers in the No Trade scenario and imagine that Portugal now represents the rest of the world. The world price for wine is €1.59 per unit and for cloth €1.90 per unit. These come from the production functions I have assumed, but it doesn't really matter where they come from - let's just take it that those are the prices in world markets.

      In England, it costs the same to produce one unit of wine as it does to produce one unit of cloth. It doesn't really matter how many machines, labour hours or anything else is involved - the point is it uses exactly the same resources to produce one unit of each.

      So the question is which makes more sense for England:
      1. Produce only the wine and cloth it needs itself.
      2. Produce only cloth. Sell the excess in world markets for €1.90 a unit and use the proceeds to buy wine at €1.59 a unit.

      The answer is the second one, and that's England has a comparative advantage in cloth, i.e. it can produce cloth more efficiently than wine, compared with the rest of the world.

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    11. Thanks for explaining that . That is informative.

      If you do a Google search for comparative advantage, the examples don't put it in those terms. In fact a lot are flat out wrong. So thanks.

      In summary -

      The comparative advantage of producing a product = (international price ratio)/(domestic price ratio)

      Simple!

      Cheers!
      Thanks for the chat.

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  6. The physical cost of moving industrial equipment or other goods from one place to another is the amount of energy consumed as work and wasted as heat.

    Modern societies tend to subsidize energy production and ignore spill-over costs on the natural environment. This means prices are distorted anyway.

    If economists are truly concerned with the efficient use of resources then they must study thermodynamics in addition to social policies that generate price structures in various geographic locations. The assumption that a price system optimizes efficiency is a fallacy when one recognizes that there is no absolute price of any physical unit of energy or other goods. The property system allocates control over goods to the will of an individual or to a group of agents (managers) operating a firm and this is not necessarily driving any sort of efficiency measured in scientific terms but may optimize "utility" of human desire in the mind of a living or dead philosopher.

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    1. I talked about moving machinery because that was what Keen was talking about. And I assumed no cost in relocation (whether monetary or environmentally), which I'd agree is unrealistic.

      However, it doesn't require movement of existing machines to have the same result. Allowing existing machines to depreciate and locating new investment elsewhere has the same effect over time. Also, with a lot of offshoring the capital relocated is actually intellectual property, which can be moved at no cost.

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