## Numerical Illustration

Economists like to use numerical models because it helps them to calibrate more specifically how much it will cost to accomplish a particular goal, in this case the goal of breaking a poverty trap. Here's a numerical illustration of how the poverty trap works, and though a bit tedious, it show's how financial planning can be used to identify the overall magnitude of official development assistance that will be needed to end poverty. To keep things simple, I use an illustration based entirely on household savings and investment, without worrying about taxation and public investment.

Figure 1: The Basic Mechanics of Capital Accumulation

Figure 1: The Basic Mechanics of Capital Accumulation

Suppose that an economy requires \$3 of capital for every \$1 of annual production. Suppose also that the capital stock depreciates at a rate of 2 percent per year. For each \$1 million of capital this year, about \$835,000 will remain at the end of a decade, after ten years of depreciation. We'll suppose that the economy currently has 1 million poor people, each with capital of \$900. This results in annual income of \$300 per person (\$900 capital divided by three). The total GNP is therefore \$300 million (\$300 per person times 1 million people). The population is growing at 2 percent per year, so at the end of the decade there will be about 1.2 million people.

Suppose now that the society is too poor to save. Each year the population lives hand to mouth, consuming whatever meager amount is produced. The starting income of \$300 is just barely enough to meet basic needs. At the end of a decade, the capital stock will have partly worn out. Instead of \$900 million in capital, there will be only \$750 million in capital. In the meantime, the population will have grown from 1 million

Figure 2 : The Poverty T

y T raP

Figure 2 : The Poverty T

y T raP

to 1.2 million. Instead of \$900 of capital per person, there is now only \$628 of capital per person (\$750 million in capital divided by 1,2 million population). Instead of each person being able to produce \$300, each person will now produce only \$209 (\$628 of capital divided by three). Households will be sinking into extreme poverty, without the income to meet basic needs.

In another illustration, suppose now that for whatever reason, the economy begins with the same population, but with a capital stock that is twice as large, equal to \$1.8 billion. Per capita income is also twice as large, \$600 per capita. As before, households need \$300 per person per year to meet their basic needs, and do not save anything out of incomes of \$300 or below. On all income above \$300 per person, they save 30 percent. Thus a household earning \$600 per capita saves 30 percent of \$300 (\$600 income minus \$300 basic needs), or \$90 in annual saving. Economywide saving is therefore \$90 million.

This year, the capital stock is \$1.8 billion, or \$1,800 per capita. What about next year? I have assumed that 2 percent of this year's capital stock, or \$36 million, will depreciate by next year. But there is also new savings of \$90 million. The net change of the capital stock is a rise of \$54 million (\$90 million minus \$36 million). Next year's capital stock is therefore

Figure 3: The Role of ODA in Breaking the Poverty Trap

Figure 3: The Role of ODA in Breaking the Poverty Trap

Depredation

\$1,854 billion (\$1.8 billion plus \$54 million). This amount of capital produces a GNP of \$618 million (\$1,854 billion divided by 3). The population also grows by 2 percent, and so stands at 1.02 million. Per capita income is equal to \$606 (\$618 million divided by 1.02 million). Per capita income has increased by 1 percent (in comparison with \$600), and will increase each year through the decade. Actually, the growth rate will rise gradually over time, reaching more than 2 percent per annum toward the end of the decade as household incomes rise further above the \$300 threshold of basic needs. If you use a spreadsheet to repeat the calculations for ten years rather than one year, the GNP per person at the end of the decade is \$687, up 15 percent during the decade.

Voilà. With the same economic structure as the first economy, but starting with twice the capital stock, the economy grows rather than declines. The reason is that at an income of \$600 per person, the economy is wealthy enough to save for the future; at \$300 per person, it is not. Therefore, starting at \$600 per capita, the economy finds its way onto a sustainable growth path, whereas starting at \$300 per capita, the economy sinks into further misery.

This is not all. As capital accumulates from the income base of \$600 per person, and the ratio of capital per person increases, not only does the economy grow, but the economy is likely to get an extra boost from increasing returns to scale of capital. An economy with twice the capital stock per person means an economy with roads that work the year-round rather than roads that are washed out each rainy season; electrical power that is reliable twenty-four hours each day, rather than electrical power that is sporadic and unpredictable; workers who are healthy and at their jobs, rather than workers who are chronically absent with disease. The likelihood is that doubling the human and physical capital stock will actually more than double the income level, at least at very low-levels of capital per person.

A graphic illustration of increasing returns to capital is the case of roads like the one that connects the port at Mombasa, Kenya, with the landlocked countries Uganda, Rwanda, and Burundi. The transport costs on this road are extremely high because the road is in very poor condition on various stretches. From time to time, transport is disrupted entirely when the rains wash away bridges and sections of the road. Suppose that, at some point, around half the road is paved and usable, and the rest is unpaved and impassable, with alternating sections of paved and unpaved roadway. Repairing the missing sections would amount to doubling the kilometers of paved road, but would much more than double the economic benefits of the road, since it would become usable along its entire length. This is an example of a threshold effect, in which the capital stock becomes useful only when it meets a minimum standard.

Thus targeted investments backed by donor aid lie at the heart of breaking the poverty trap. Donor-backed investments are needed to raise the level of capital per person. When the capital stock per person is high enough, the economy becomes productive enough to meet basic needs. Households can thus save for the future, putting the economy on a path of sustained economic growth. In my illustration, foreign aid (over several years) that raises the capital stock from \$900 per person to \$1,800 per person would enable the economy to break out of the poverty trap and begin growing on its own. It would also enable the economy to benefit from increasing returns to capital.

Without donor funding, alas, the necessary investments simply cannot be financed. No matter how hard a government might try—through taxes, user fees, or privatization—the poor households at \$300 per person simply do not have enough income to meet their basic needs and at the same time finance the accumulation of capital. They need the \$300 just to eat and provide clothing, shelter, and other basics.

### Differential Diagnosis and Capital Accumulation

In a simple illustration, or model, as economists call it, it is easy enough to talk about capital as a single item, something that can be doubled or halved fairly straightforwardly. Much of the complexity of real economic strategy, however, is that capital comes in numerous, almost unlimited, forms. Suppose that an economy successfully negotiates an extra \$1 billion in foreign aid. Should that go to building roads, or schools, or power plants, or clinics, or to pay doctors, or teachers, or agricultural extension officers? The answer, in general, is yes to all of the above. The mix will differ markedly country by country. At the core of an effective investment strategy is a rigorous differential diagnosis. The differential diagnosis should build on the appropriate division of labor between the public sector and the private sector, as shown in figure 4.

The public sector should be mainly focused on five kinds of investments: human capital (health, education, nutrition), infrastructure (roads, power, water and sanitation, environmental conservation), natural capital (conservation of biodiversity and ecosystems), public institu-

Figure 4: Private and Public Investments in Capita]

Figure 4: Private and Public Investments in Capita]

## Rules Of The Rich And Wealthy

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