Expanding the Solow Growth Model. Would preventing starvation be beneficial to the overall income?

Contents

1. INTRODUCTION: STARVATION AND PRODUCTION

2. THE MODEL

3. IMPLICATIONS

4. LIMITATIONS

5. CONCLUSION

APPENDIX

REFERENCES

1. Introduction: Starvation and Production

“Starvation, clearly, is the most telling aspect of poverty”, writes Amartya Sen (1981, p. 12). The need for nutritional intake is probably the most fundamental physical need of human beings. Still, although many people have never experienced starvation, almost one billion in the world are suffering from malnourishment in our world (United Nations World Food Programme, 2015). This is surely an undesirable condition itself. This paper, however, further expands on the problem of malnourishment, by arguing that it decreases the effectiveness of labor and thus has a negative effect on total production and growth. There is wide evidence in the academic literature on the damaging effects of malnourishment, ranging from restricted human development, especially of children (Guerrant, Oriá et al., 2008; Morgane, Mokler et al., 2002), to increased mortality rates (Pelletier, Frongillo Jr et al., 1995). These papers have shown that starvation negatively affects both physical and mental abilities, which gives reason to assume decreased effectiveness of labor as a result of malnourishment. According to the United Nations, we will define those suffering from malnourishment as the „people whose dietary energy consumption is continuously below a minimum dietary energy requirement for maintaining a healthy life and carrying out a light physical activity’’ (Patel, 2012).

By focusing on the relationship between starvation and production I do not want to encourage seeing the poor as only a means to an end (higher growth). Sen describes this viewpoint as “we have a problem of poverty to the extent that low income creates problems for those who are not poor“ (Sen, 1981, p. 9). The proposed model is intended to demonstrate that preventing starvation may be beneficial to overall income. It does not claim that reducing hunger does not have other values. As we are dealing with a global problem, the model will represent the world economy as one economy, so that national income = global income.

2. The Model

The following model will propose an addition to the Solow growth model. We will keep the basic setting of the Solow model, where output is total income and the factors of production are capital and labor. Each factor of production yields diminishing returns to scale when the other factor is being held constant. Everyone works, so there is no difference between the total population, the labor force and total employment (L).

However, in our new model, the population is divided between rich workers [Abbildung in dieser Leseprobe nicht enthalten] and poor workers [Abbildung in dieser Leseprobe nicht enthalten]. The important new factor I am adding to Solow’s model is β, which is the effectiveness of poor people’s labor. It depends on how well nourished the poor people are. We assume that workers will spend all of their income on food first until they reach a level where starvation is absent. Once this level is reached, they spend their income on whatever other needs and desires they have. Let f be the required income per poor person to buy enough food to be well nourished. Any consumption level below f will indicate some degree of starvation. Let e be a measure of equality in the distribution of income, i.e. the percentage of national income which can be consumed by the poor. The distribution of Income can thus be formalized as

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where is the total consumption of the poor,¹ [Abbildung in dieser Leseprobe nicht enthalten] is the total consumption of the rich and are total savings from national income in a given period. To get the consumable income per poor person, divide by the number of poor people !.² The effectiveness of poor workers results from the relationship between consumable income per poor person[Abbildung in dieser Leseprobe nicht enthalten]and required income to be free of hunger f. We get:

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The lower the consumable income per poor person relative to f, the lower the effectiveness of the poor’s labor. If = f, the poor are well nourished and [Abbildung in dieser Leseprobe nicht enthalten], i.e. the poor work just as effectively as the rich. However, we define that per definition cannot exceed 1. In our model, an increase in the effectiveness of labor is not possible anymore, once the poor have reached an income level that covers their nutritional needs. Also, we assume that the rich never suffer from hunger, because of the accumulated wealth in their countries. So even an equal distribution of consumption (e.g. e = 0.5, when [Abbildung in dieser Leseprobe nicht enthalten], which could result in suffering from hunger among the poor (e.g. because of a general low level of C), could never lead to malnutrition among the rich.

We can now adjust the Solow model to our case. The total production (national income) function will be given by

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where capital K is facing decreasing returns to scale ( < 1), or, on a per capita basis,

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As in the Solow model, the change in k will be given by:

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Where s is the saving rate, and d is the depreciation rate of capital.

You might have noticed that there is a causality running both ways between Y (or respectively the resulting consumption C) and β . We solve this problem by determining that β always depends on the Income of the last period. A simple way to conceptualize this is by thinking of the income being paid out only at the end of a period , so that the resulting consumption will actually take place in the following period [Abbildung in dieser Leseprobe nicht enthalten]. The β in period [Abbildung in dieser Leseprobe nicht enthalten] thus depends on the output Y in period , but affects the output in period + 1 and so on.

The effect of β on output per person is shown in Figure 1. Everything else being held constant, a higher β will result in a higher y.

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Figure 1

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¹ Two letters behind each other indicate that they are multiplied with each other, e.g. = ×.

² We are making the assumption that eC is distributed completely equally among the poor, and (1-e)C is distributed completely equally among the rich. Surely in reality not all of the poor get the same income, but you can think of it as an average. Similarly, in reality can be seen as the average effectiveness of a poor worker, taking into account that hunger affects people differently.