Automation and Real Wages

Economists generally work on the basis that improvements in technology lead to higher real wages.  Conventional production functions (when combined with other assumptions) invariably produce this result.  Looking at the Cobb-Douglas production function, as the most common example, an increase in total factor productivity raises labour's marginal product.  With the normal assumptions about competition, this leads to higher real wages.

Although I have no problem with using such things at times, I am wary of simple aggregate production functions.  It seems clear to me that technological developments can lead to reduced real wage levels, even without considering how such developments might impact on monopoly power.

Although I'm sure others have produced models that illustrate this, I'm not aware of any and, in any event, I like to experiment with things myself, so I have constructed a little model of production in which technological innovation leads to a fall in real wages.

There is a single good produced by a combination of labour and capital.  There are two possible production techniques, each of which requires a fixed quantity of labour and a fixed quantity of capital to produce a fixed quantity of the good.  These quantities are set out in the table below:

	Output	Labour Input	Capital Input
Technique A	12	1	1
Technique B	24	1	4

Total labour and total capital are fixed.  There is perfect competition and no demand deficiency.  This has two implications:

1. The use of each techniques will normally be such that will ensure full employment of both labour and capital.  However, if the ratio of available labour to available capital is too extreme, then all production will use a single technique (whichever maximises use of the abundant factor) and some of that abundant factor will be unutilised.  This possibility is ignored here - it is assumed that available labour and capital always lead to some combination of possible techniques.

2. The real wage will be at a level that ensures the return on capital is the same for each technique.  If it were not, suppliers of capital would switch technique which would lead to shortages or surpluses in the labour market.  With the numbers here, the real wage works out as 8 units of output per unit of labour.

Marginal productivity is not well defined for each individual technique.  However, given the above conclusion about how the techniques are combined, there is a marginal productivity of labour at an aggregate level.  It is relatively easy to show that this is equal to the real wage.

If we take factor supplies of 12 units of labour and 24 units of capital, we get the following output matrix:

	Labour Used	Capital Used	Production
Technique A	8	8	96
Technique B	4	16	96
Total	12	24	192

We now want to consider the innovation of a new technique involving a more intensive ratio of capital to labour.  For this to be beneficial overall, it must yield a higher return on capital given the prevailing real wage.  The details of this new technique are:

	Output	Labour Input	Capital Input
Technique C	30	1	5

Technique C dominates technique B at all levels of the real wage, so the latter is completely abandoned.  Since the relative factor input ratios have changed, there is also a change in the amount of resources devoted to technique A.  The new levels of production are shown below:

	Labour Used	Capital Used	Production
Technique A	9	9	108
Technique C	3	15	90
Total	12	24	198

The change in techniques also impacts on the real wage, which must settle at a new level to continue to equate return on capital across techniques.  In fact this involves a fall in the real wage to 7.5.   

The interesting thing here is that although labour productivity (labour's average product) has increased, its marginal product has decreased.  Real wages have therefore fallen, even though output per head has risen.  The corresponding change is that the return on capital has increased.

My belief is that, on the whole, technological progress results in higher overall real wages.  However, I do not think we can assume that all new innovations will do this.

Comparative Advantage With Labour Inflexibility

My last post adapted Ricardo's model of comparative advantage to include internationally mobile capital.  However, what I think is much more important is the ability of labour to be redeployed between industries when production patterns are disrupted by trade liberalisation.

So I thought I'd have a go at a version of Ricardo's model that included just that.

The Model

There are two countries: England and Portugal, and three goods: wine, cloth and cars.  Each country consumes all three goods and can produce all three.  Each country has its own currency. 

Labour is the only factor input and there are constant returns to scale.  Prices are set at a fixed mark-up to unit cost, with the same mark-up in both countries and all industries.  Within each country, a single fixed nominal wage applies to all industries.  (For simplicity, the nominal wage per unit of labour, grossed up for the mark-up, is set here at one unit of the local currency, so the price of local produce is simply equal to the requisite labour input.)

Labour cannot move between countries.  Within a country, labour can generally be redeployed between different industries, with the single exception that labour currently employed in car production cannot be redeployed to wine or cloth production.  The number of labour units required to produce one unit of goods varies between industry and country as follows:

	Wine	Cloth	Cars
England	1.00	1.00	1.00
Portugal	0.80	0.90	0.95

There is free trade in wine and cloth but (at least, initially) no trade in cars.  In each case of wine, cloth and cars, Portugese made versions are perfect substitutes for English made ones and there are no transport costs so, where there is free trade,  everyone just buys the cheapest.  However, wine, cloth and cars are imperfect substitutes for each other with a constant elasticity of substitution.  All income is spent currently on consumption, with a weighting in both countries of 0.45 on each of wine and cloth and 0.10 on cars.  The exact specification of consumer spending is given in the technical note at the end of the post.

As there is no saving, trade must be balanced, which is achieved by a variable exchange rate.

(To get the numbers to show what I want, I have assumed a slightly higher labour supply in England than Portugal.)

1. No International Trade in Cars

Because of the comparative advantages in wine and cloth, England ends up importing all its wine and Portugal all its cloth.  Both countries produce their own cars.

	England					Portugal
	Wine	Cloth	Cars	Total		Wine	Cloth	Cars	Total
Labour	0	1,081	119	1,200		913	0	87	1,000
Goods
Produced	0	1,081	119			1,142	0	91
Traded	563	-548	0			-563	548	0
Consumed	563	533	119			579	548	91
Expenditure
Domestic	548	533	119	1,200		463	450	87	1,000
Exports		548	0	548		450			450
Imports	-548			-548			-450	0	-450
Income	0	1,081	119	1,200		913	0	87	1,000
Prices	Wine	Cloth	Cars	Index		Wine	Cloth	Cars	Index
Domestic	1.000	1.000	1.000	1.000		0.800	0.900	0.950	0.856
Import	0.973	1.095	n/a			0.822	0.822	n/a
Consumer	0.973	1.000	1.000	0.988		0.800	0.822	0.950	0.823
Exchange rate (£/€)	1.217

Expenditure and prices are shown in the local currency.

The domestic producer prices shown are the prices that would be paid for domestically produced product, even though there is no actual production in industries with import penetration.  The index for these prices is weighted by consumption preference, so it is the price index that would apply with no trade.  This is higher for both countries than the actual consumer price index, showing that the trade in wine and cloth benefits both nations.

The nominal wage (expressed in the local currency) is the same in each country, so the fact that the consumer price index is higher in England implies that real wages are lower in England than Portugal.

2 After Trade Liberalisation in Cars

At the prevailing exchange rate, England can produce cars more cheaply than Portugal.  This means that Portugal starts to import cars and closes down its own production.  By assumption, these workers cannot be employed elsewhere, so overall income in Portugal is reduced.  This reduces demand for cloth imports but, because of the additional import of cars, demand for foreign exchange is increased overall.  This causes the exchange rate to change, worsening the terms of trade for Portugal (making Portugese cars cheaper but still not as cheap as English ones).

	England					Portugal
	Wine	Cloth	Cars	Total		Wine	Cloth	Cars	Total
Labour	0	982	218	1,200		913	0	0	913
Goods
Produced	0	982	218			1,142	0	0
Traded	607	-460	-102			-607	460	102
Consumed	607	522	116			535	460	102
Expenditure
Domestic	562	522	116	1,200		428	397	88	913
Exports		460	102	562		485			485
Imports	-562			-562			-397	-88	-485
Income	0	982	218	1,200		913	0	0	913
Prices	Wine	Cloth	Cars	Index		Wine	Cloth	Cars	Index
Domestic	1.000	1.000	1.000	1.000		0.800	0.900	0.950	0.856
Import	0.927	1.043	1.101			0.863	0.863	0.863
Consumer	0.927	1.000	1.000	0.966		0.800	0.863	0.863	0.833
Exchange rate (£/€)	1.159

England responds to falling cloth exports by redeploying labour to production of more cars.

Conclusions

The main result here is that, if trade liberalisation results in job losses and those workers cannot be employed elsewhere, then overall output will be impaired.  This is perhaps not entirely surprising.  But there are some more interesting points here:

Trade liberalisation results in production of cars switching to England even though Portugal can produce cars with fewer labour units and thus has an absolute advantage in car production.  The reason is that English wages are lower when expressed in a common currency.  The lower wage offsets the less efficient production (less efficient in an absolute sense, not a comparative one).

In this example trade liberalisation in car production not only results in unemployment for Portugese car workers, but actually reduces the real wages of Portugese wine workers.  This is because the increased demand for imports worsens the terms of trade.  Although they can now buy cheap imported cars, cloth has become more expensive.  Everyone in Portugal has lost out.

The same is true here even if we relax the assumption that Portugese car workers cannot be employed in other industries.  As a natural importer of cars, Portugal benefits when international trade in cars is restricted, even though that means that cars are more expensive there.  However, it is still better off than if there were no trade at all.

Reducing the nominal wage in Portugal makes no difference, as it simply leads to an offsetting exchange rate movement.  However, relative wages between industries do matter.  I have assumed that the same wage applies across industries, so that wages for Portugese car workers remain the same as for wine workers, even when they cannot be employed elsewhere.  If they were to fall (relatively), then Portugese car production could be preserved.

This change in relative wages is what standard economics says should happen.  It all comes down to opportunity cost.  The opportunity cost of Portugese car production is in fact zero, because the car workers have no alternative use.  Portugese car production is lost, because the cost to producers does not reflect the true opportunity cost.

Although trade liberalisation in the car industry is damaging in this example, that does not imply that introducing measures to restrict existing trade will be beneficial.  In fact any such measures would reduce welfare here.  If we extend the assumption on labour inflexibility, then such measures may be even more damaging as workers made unemployed from exporting industries might not be employed elsewhere.  It is the fact of change that matters here, not whether it is liberalisation or protectionism.

However, being able to adapt to change is crucial to an economy's ability to develop and grow.  Even without trade, progress involves old products and procedures dying out and being replaced.  Job losses and job creation is an inevitable part of that.  Whilst there is a strong case for factoring in the dynamic consequences of trade liberalisation, that cannot be an excuse for avoiding the need for flexibility, if an economy is to secure long-term growth.

Technical Note

Consumption of good i in each country is given by  

C_i = a_i . (P_i / P )^-σ . Y / P

where: a_i is the weighting,  C_i is number of units consumed, P_i is the price of good, Y is nominal income and P is the price index, which is given by:

P = { sum for i [ a_i . p_i^(1-σ) ] }^1/(1-σ)

σ is the price elasticity of demand, set at 2 for both countries.