The dual economy: Lewis and Fei–Ranis

W. Arthur Lewis (1954) described a typical poor economy as dual. There is a traditional sector, mostly subsistence agriculture, where people share the product of family land and, because land is limited and workers many, some workers add little or nothing: their marginal product is zero or negligible. And there is a modern sector, a capitalist sector of factories, mines and plantations, which pays a wage and sells for profit. The wage in the modern sector must be somewhat above what a person earns in the traditional sector, to attract workers, which allows for the cost of moving and for the pull of the village.

Lewis’s claim is about the supply of labour. If there is a large pool of workers whose marginal product is zero, the modern sector can take any number of them without reducing farm output, and it can do so at a wage that does not rise as it hires. Labour is then in “unlimited supply”: the supply curve of labour to industry is horizontal at the going wage. That is the condition tested in the opening question.

Picture the modern sector’s labour market. Demand for labour is the marginal product of labour at the sector’s current capital stock: it falls as more workers are added to the same capital. Supply is horizontal at the wage w̄ while there is surplus labour. They meet at an employment level where marginal product equals w̄. At that wage the capitalists earn a surplus, profit: output minus the wage bill. Lewis assumes they reinvest it. More capital raises the marginal product at every level of employment, so the demand curve shifts out, employment rises, and the surplus grows again. The process feeds itself.

With a Cobb–Douglas modern sector, Y = A K^α L^1−α, the marginal product of labour is (1 − α) A (K/L)^α. Setting it equal to the wage gives employment L = K[(1 − α)A/w̄]^1/α. Capital then grows by K_t+1 = K_t + s(Y_t − w̄L_t), where s is the share of profit reinvested. While the wage is fixed, K/L is fixed too, so capital, employment and output all grow at the same rate, which depends on the reinvestment share. Output per worker in the modern sector does not rise; what rises is the number of workers in it and the share of the economy it accounts for.

The turning point. Eventually the pool of surplus workers is used up. Now taking another worker means taking one whose marginal product on the land is positive, and the traditional sector will release him only at a higher wage. The supply curve turns upward. This is the turning point (the Lewis point), where the economy leaves the stage of unlimited labour: wages start to rise, the share of profit in income eventually stops rising, and the economy behaves like the neoclassical models of the growth module. (Asked in UOH 2017: the transfer continues until the marginal product of labour is the same in both sectors.)

What drives the speed. Not the wage, which is held down, but capital accumulation: the larger the share of profit reinvested, the sooner the surplus is absorbed. A larger surplus pool takes longer. Lewis’s model is a model of growth by saving out of profits, which is why it is sometimes read as an argument for a high profit share. As the economy’s labour moves from zero-productivity to productive jobs, output, employment and the economy’s labour productivity all rise (UGC NET 2026 asks what reinvestment of the surplus over the wage brings: more production, more labour productivity and more employment, not a rise in prices).

The simulator is a Lewis economy with a Cobb–Douglas modern sector (capital share 0.4). The first chart is the labour market in the year you choose: the blue demand curve is the marginal product of labour at that year’s capital stock and the red line is the supply curve. The next two charts show employment and the wage over time. Try raising the share of profit reinvested and watch the turning point arrive sooner; shrink the surplus and watch the horizontal stretch shorten; make the wage rise steeply after the turning point and see employment slow.

Gustav Ranis and John Fei (1961, and the book of 1964) built the model out with a fuller picture of agriculture. Their traditional sector has a total product curve that rises with labour and then goes flat: beyond some number of workers the marginal product is zero. They also assume that farm workers earn a constant institutional wage, equal to the average product when everyone is on the land (a share of the common product, set by custom). Moving workers out of agriculture takes the economy through three phases.

1. Phase 1. The marginal product is zero. Workers can leave with no loss of output, and the supply of labour to industry is horizontal at the institutional wage. This is Lewis’s case.
2. Phase 2. The marginal product is positive but below the institutional wage. Output now falls when a worker leaves, and since the remaining workers still draw the institutional wage, the food surplus that feeds the industrial workers shrinks. The relative price of food rises and industrial wages must rise: the shortage point marks the start of this phase.
3. Phase 3. The marginal product is at least the institutional wage. Agriculture is commercialised: workers are paid what they produce, as in the neoclassical model. The commercialisation point marks the start of the phase.

Two lessons follow. First, agriculture matters: industry can grow only if farm output keeps pace, through a farm surplus or imports, so balanced growth between the sectors is needed. Second, agricultural productivity (the green revolution of Lesson 14) is a condition of industrial growth, not a side issue. In the chart, 100 workers on the land produce a maximum of 10 units; the first 40 can leave without loss, and the next 18 leave at a positive marginal product below 0.1, the institutional wage.

Disguised unemployment means that more workers are employed in an activity than the output requires, so that some of them could be withdrawn without reducing output. Exam papers give several descriptions and treat them as one idea: the marginal product of labour is less than the wage, or is zero with a positive wage, or more people are engaged in an activity than the number required for it (JNU 2016 and 2020 take all three as true). It is found mostly in self-employment, especially family farming, not in organised wage employment, since an employer does not pay a wage to a worker who adds nothing (UOH 2016 and 2018). A textbook definition also includes workers with a job of very low productivity and pay (UOH 2011).

Ragnar Nurkse (1953) saw in it a hidden source of saving: workers who are not needed on the land could be set to work on roads, irrigation and buildings, and fed from the food they were already eating, so capital could be formed without cutting anyone’s consumption (UOH 2015 asks who suggested this: Nurkse, not Lewis or Rostow).

Is there really zero marginal product? Theodore Schultz (1964) argued that it is not. In Transforming Traditional Agriculture he used the influenza epidemic of 1918–19, which killed many people in India, to ask whether output fell when the labour force shrank. He read the fall in sown area as evidence that labour was not redundant. Amartya Sen (1967) disputed the statistical test in a reply published in the same journal. Sen (1966) also showed that a dual economy can have dualism, a gap between the sectors, without any surplus labour. The weight of opinion is that surplus labour exists in some places and seasons but is smaller than the model assumes. The model survives because the turning point can be reached without exact zero marginal product, so long as labour is cheap.

The dual economy gives a simple reason for Kuznets’s inverted U (Lesson 1). Suppose everyone starts in the traditional sector at a wage of 1. If one worker at a time moves to the modern sector, where the wage is r, the Gini coefficient is zero at the start, rises as a gap opens between a few high earners and many low earners, reaches a peak when about half have moved, and falls back to zero when all have moved. With p the share in the modern sector, the Gini coefficient is p(1 − p)(r − 1)/(1 + p(r − 1)). Five workers and r = 4 gives 0, 0.300, 0.327, 0.257, 0.141 and 0 (JNU 2016 asks the direction: it rises, then falls). Use the chart to see how the peak moves with the wage gap.

The Lewis model is a story of one kind of development, and its assumptions can fail.

• Labour-saving technology. If modern firms install machines that need few workers, employment grows more slowly than capital and the surplus is absorbed slowly or not at all.
• Capitalists may not reinvest. The model assumes they put the profit back; if they spend it or send it abroad, the engine stalls.
• Urban unemployment. The model has no unemployment in the city: whoever moves gets a job. In fact migrants queue for scarce jobs, which is the Harris–Todaro model of Lesson 4.
• Rural wages may rise earlier, because of better farm technology or because workers leave, before the surplus is exhausted.
• Agriculture. Without a farm surplus to feed the new workers, food prices rise and the wage must rise (Fei and Ranis).

Questions on the Lewis model, the turning point, disguised unemployment and the dual economy. Questions on rural–urban migration are in Lesson 4; those on Nurkse’s other work are in Lesson 5.