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:

X_ij = A_ij . K_ij^0.5 . L_ij^0.5

where X_ij is production of product i in country j and K_ij and L_ij are capital and labour respectively used to produce product i in country j.  A_ij 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.