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Concept of poverty trap

In the developing world, many factors can contribute to a poverty trap, including: limited access to credit and capital markets, extreme environmental degradation (which depletes an areas agricultural production potential), corrupt governance, capital flight, poor education systems, disease ecology, lack of public health care, war, or poor infrastructure. Nations like this include Sierra Leone and the Democratic Republic of the Congo.

Jeffrey Sachs, in his book The End of Poverty, discusses the poverty trap and prescribes a set of policy initiatives intended to end the trap. He recommends that aid agencies behave as venture capitalists funding start-up companies.

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Venture capitalists, once they choose to invest in a venture, do not give only half or a third of the amount they feel the venture needs in order to become profitable; if they did, their money would be wasted.

If all goes as planned, the venture will eventually become profitable and the venture capitalist will experience an adequate rate of return on investment. Likewise, Sachs proposes, developed countries cannot give only a fraction of what is needed in aid and expect to reverse the poverty trap in Africa.

Just like any other start-up, developing nations absolutely must receive the amount of aid necessary for them to begin to reverse the poverty trap. The problem is that unlike start-ups, which simply go bankrupt if they fail to receive funding, in Africa people continue to die at a high rate due in large part to lack of sufficient aid.

The Solow model did not assume that technical progress was exogenous that is, determined outside the model. Rather, the model made the assumptions necessary to produce a model of an economy with a dynamic equilibrium, a path to which, in the long run, the economy would settle down.

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The implication of those assumptions was that technical progress had to be exogenous to the model. The technical problem is that the assumptions necessary to produce a model with an equilibrium implies that payments to the standard factors of production labour and capital exhaust the total product.

Nothing is left over to pay entrepreneurs or innovators. But if innovators cannot be paid at all in equilibrium (given the assumptions of the model), then nothing including policy of any kind can affect their incentives to innovate.

This problem of reconciling purposive economic innovation that results in greater productivity of all factors with formal economic models was long standing. It was clearly recognised by Joseph Schumpeter and Frank Knight, but Solow’s clean algebra and exposition just made it stark.

Thus, the model predicts that a high saving rate is positively related to the growth in output per worker and the growth of labour force is negatively related to the growth in output per worker after corrected for the rate of technological progress and the rate of depreciation of capital. The basic testable model

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Equation (1) predicts that states with low initial output per effective worker possess faster transitional growth rates than the states with higher initial output per effective worker, conditioned upon the values (s, n, g, and a). The transitional equation for the Solow- Swan model augmented with human capital is given by

Further equation (2) implies that human capital is also positively related to the growth in output (income) per effective worker.

In the single cross-section analysis the above testable equations (1) and (2) are estimated under the assumption that the production structure is common to all countries (states).

If we assume the Solow model Martin, 2004. It presents the standard formalisation of this framework. We introduce Richard’s production function as follows:

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All parameters are greater than zero f(0) > 0 means that there is some free production, A is the limit of f (k) when k goes to infinity. The function is always increasing in k, it is convex when k > k in f and concave when k > k in f. The point k = k in f is the inflection point which represents the change from increasing returns to decreasing returns. Instead of the classical Inada conditions

We now have that the first condition is the same but the second becomes f'(0) > 0. The fundamental equation is now:

From equation (2) we can obtain four cases of equilibrium.

**Case 1:**

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This case appears when the fundamental equation has only one equilibrium point. This can occur when the technology always presents decreasing returns.

**Case 2:**

The inflection point is greater than zero, economic growth rate presents fluctuations before reaching the unique stable steady state, which is obtained at high level of production. One example is obtained with the following values of parameters:

**Case 3:**

The inflection point is greater than zero but the economy presents several equilibriums. It is easy to check that under our assumptions there are only three equilibrium points. Two of them are locally stable and the one in the middle is locally unstable.

The first equilibrium that is greater than zero is a poverty trap. Only increasing the output could allow to leave the poverty trap. In this case, the following values can give this result,

**Case 4:**

This case appears when we have only one equilibrium but 8 + ris very large compared to marginal returns of f (k). The economy reaches a stable state but production level is very low. In this case, the depreciation rate is destroying production.