The Lewis Model

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"If an economy is a traditional backward economy then how does the economy transform itself into a modern industrial economy?"

Looking at this question, eminent economist and Nobel Prize winner Sir Arthur Lewis set about creating the first duel sector model of economic growth. His model compares the traditional sector versus the modern sector, or in simpler terms the rural agricultural sector versus the urban manufacturing sector.

First of all let me state what the characteristics are of such a backward rural economy according to Lewis.

* The economy is essentially a subsistence economy. That is production is primarily for self-consumption.

* There is no saving and no capital accumulation in the economy.

* The economy is not market based but rather the emphasis is on families supporting themselves and trading among other families. Or to put it more formally, organisation of production is family based, not market based.

* The most important of Lewis's assumptions that he makes about rural economies is that there exists "a surplus labour supply". To put this assumption into context imagine that there are 10 brothers and sisters working on their family farm and together they produce 150 units. Now, as the family own the land it therefore means all the family work there. But the reality of it is they could probably produce as much output with only six of them working there. So in reality there is a surplus of labour. To make this point more mathematically you can say that the marginal product of labour is equal to zero, or if it is equal to anything then it is negligible. Wage is equal to Average product in this case so in the farm scenario above each family member gets 15 products. And so therefore wage is higher than marginal product of labour.

If nothing happens to this economy then this will repeat year after year. Something has to happen for this economy to become a modern industrial economy. Capitalists will need to invest from the industrial sector and in Lewis's model this sector is assumed to located in the urban economy.

Now let me address the assumptions Lewis makes about the Urban industrialised economy.

* Production, in this case, is primarily for profit.

* Output of production is market based, not family based in the formal sector. That is, firms hire employees from the market on the basis of knowledge, experience, availability etc... rather than because they are related to someone who can give them a job. [Although undoubtedly this can still be the case, it's just not so much of a factor.]

* In order to maximise profits, capitalists will employ labour only up to the point where wage equals marginal product of labour.

* Finally, there is a diminishing product of labour with a given amount of capital.

To explain that last point further let's just assume that the capitalist sector can get all the labour it wants from the agricultural sector. Lewis says because there is surplus labour in the agricultural sector you can therefore get all the labour you want at a fixed wage. If this is the case then as more labour is employed the marginal product of labour goes down. For example if there is one machine, and one man can produce 200 units of output from it, then by adding a second worker you may be able to produce 380 units of output and finally by adding a third worker you can produce 480 units of output. You can see that by the time the third worker is added you are receiving much less than you would expect for a lot more in wage. Therefore firms will only hire up to the point where the marginal product of labour equals the wage.

Figure 1 Production Possibility Frontier for the Urban sector

Assuming capitalists do not consume their profit but rather want to reinvest in order to gain more we can see that from the PPF above, reinvesting shifts the PPF from N1, to N2.

Employment in this case raises from M1 to M2 as well. In fact, this will keep on until there is no surplus labour in the economy and eventually the capitalists will have to start paying higher wages in order to get more labour.

Now the majority of the people work in the industrial sector and the agricultural sector has now been modernised with wage equal to the marginal product of labour.

Now suppose as workers go to the industrial sector the wages rise. The profits of the capitalist will decrease. Therefore, for this theory to work the wage must be constant. With little profits the capitalist sector will be small with not much to invest.

The wage may rise due to trade unions demanding higher wages and government intervention may also cause wages to rise, which would again reduce capitalists' profits.

One reason endogenous to the model for rising wages would be the following. Clearly, the agricultural level will be getting smaller. However, the demand for food will still be there and this can only be met by the agricultural sector. Therefore the demand for food will increase but the supply will decline causing food prices to go up. So in order to buy food you will need bigger wages.

Therefore, as we have already established the wage must remain constant in order for the economy to grow so how can this be achieved? Only by increasing supply in the agricultural sector at the same time. Agricultural reinvestment is a pre-requisite for the industrial revolution. If it doesn't happen then the price of food will not remain constant.

A further way to look at the model is to use the above diagram. Here point a is considered to be the equilibrium. P.dxa/dna is the productivity or marginal product of the agricultural sector and dXm/dNm is the productivity of the manufacturing sector. Remember, migration occurs when there is a wage differential. So at point b we can see P.dxa/dna > dXm/dNm which implies the wage is greater in the agricultural sector than in the manufacturing sector, so people will migrate there until we reach point a. The reverse is also true. When dXm/dNm > P.dxa/dna then the wage is greater in the manufacturing sector and so the rural sector inhabitants will migrate to the urban sector from point c up until they reach point a.

Implications of the Lewis Model

* Saving and investment are vital for growth. You need capitalists in order to grow!

* Structural transformation of the economy is crucial if you want to grow.

* Income distribution will be uneven to start with. The share of wages will increase in the early stages causing the share of profits to fall. In the long run however, this should even out.

* Agricultural development is a pre-requisite to industrial development. Without agricultural surplus, the urban economy cannot grow.

* Rural to Urban migration is desirable and conclusive to development. Or in other words, urbanisation is a good thing.

The Todaro Model

Michael P Todaro studied Lewis model and then decided to create his own model by changing one assumption. Todaro decides that rural sector wages should be assumed to be determined competitively and that it is urban sector wages that are institutionally set.

What this implies to the Lewis model is that the urban wage is no longer roughly equal to the rural wage, but rather due to trade union pressure etc... it is a reasonable amount higher. This rigid minimum wage in the urban sector lies above the competitive rural sector wage causing a high rate of rural to urban migration. However, Todaro argues that this over urbanisation is bad as the probability of getting a job for these migrant workers is low.