The Disaster Profiteers: How Natural Disasters Make the Rich Richer and the Poor Even Poorer (28 page)

Figure 11 illustrates how a two-component economy might be affected by disaster.

Figure 11. Full recovery in two sectors of society and the growth of inequality.

Everything is as before except that there are two lines of predisaster growth, the upper one representing wealth and strong growth, the lower one representing the lower overall assets and slower growth. The growth rate on the lower line is smaller and the absolute level is lower. Just before the disaster, the inequality between the two is
d
and is widening. A disaster strikes as before. Now we see that the drop from the upper curve is much greater than that from the lower curve, but recovery is much faster. The lower sector loses less, but the recovery is much slower or perhaps not at all.

Now it is easy to see that after a short time, the gap between the two new growth curves has increased—
D
is now greater than
d
and is greater than what the gap would have widened to without the disaster. Inequality was sure to have increased anyway, but now it has increased all the more. The disaster has exacerbated inequality. But it's not the immediate effect of the disaster that matters, it's the effect of differing recoveries: A rich, capital-owning group appears to have lost a lot more than the poorer group, but in the end it gains at the expense of the poorer group.

TECHICAL APPENDIX II

Disasters in Neoclassical Growth Theory

Neoclassical growth theory is attributed to Robert Solow, and the ideas are often referred to as the Solow model, or the Solow-Swan model.
1
(Swan refers to T. S. Swan, who came up with almost the same model independently of Solow, both in 1956.) The ideas are contained in Figure 1.

The vertical axis is the output per person, usually designated
q,
but other letters also are used (
y
is common). Output per person is created by a so-called production function,
2
here written as
Af(k),
where
A
is the total factor productivity and
k
is the capital-labor ratio. So the horizontal axis is capital, and the curve shows how output depends on capital. That means that output is driven by capital (strictly, capital in relation to available labor). The upper curve that plots that function sometimes is called an L-curve for its shape. Near the origin (lower left corner), the curve is steep, meaning that for small additions of capital, large increases in production occur. It is almost flat in the upper right so that additions of capital achieve less; there is a diminishing return on marginal capital investment.

The lower curve, which is very similar, is the same function with
s
as the factor modifying the first curve,
sAf(k),
where
s
denotes the savings rate. Because no one ever saves everything,
s
is less than 1, and the second curve will always sit below the first. Then there is a straight line
(n + d)k.
Here
k
is the same as before,
n
is population growth rate, and
d
is the rate of depreciation of capital.

Figure 1. A standard depiction of the Solow-Swan exogenous growth model. All symbols are explained in the text. Reference 1 gives citations for the model.

The term
(n + d)k
is called capital widening; it is the amount of savings necessary to keep the capital-labor ratio the same despite depreciation and population growth. Those latter two elements can be thought of as having similar effects on growth—if the population increases greatly but the capital stock stays the same, then production per capita will drop because the model regards capital as the source of growth. In the opposite case, where the capital depreciates and the population is the same, productivity decreases as well. There is a point where this straight line meets the savings curve,
sAf(k);
that is the point when the economy is in equilibrium. At that point, per person capital is designated
k
E
.
We could associate
k
E
with an equilibrium output
q
E
.
In the standard theory, when the capital-widening line is below the savings curve (perhaps a more realistic way to say it is that
the savings curve exceeds capital widening), the economy grows. That is, output grows.

Using the graph and adding the effect of a capital shock, we see in Figure 2 that the capital shifted left to
k
D
,
the amount remaining after the disaster. We could say the capital loss is the difference between the equilibrium and the new capital,
D
k = k
D
–
k
E
.
The same could be achieved by making the capital-widening line steeper by increasing depreciation of the capital stock. That would push the dot that is the point of intersection of the savings function with the capital-widening line to the left as well and have the same effect on production. Here we can say it was lowered by an amount
D
q
to
q
D
.

Figure 2. The effect of a capital shock ∆
k
on output ∆
q
. Output has dropped by the amount ∆
q
, an amount that is determined by the shape of the growth curve that is governed by the utility function, explained above.

So the disaster does lower economic output, at least in the short run. It is fairly obvious also that the loss of output will be greater in this model for greater capital losses. Your position on the upper curve when a disaster happens matters a great deal. Imagine that the capital-widening line was
less steep, caused, for instance, by a reduction in population growth rate,
n.
(Other things could cause the line to be less steep, of course.) The black dot in the center of the diagram would then move to the right and be on a flatter part of the curve. The amount of output loss is a direct function of the shape of the curve. If I moved everything to the right, the same
D
k
will have much less effect on output. That's shown in Figure 3. What the figure expresses is that the loss of capital matters a lot less when an economy already has a lot of capital; the same point that was made in Appendix I using different graphics. And it is essentially the opposite of the effect of additions of capital in the Solow-Swan system: The marginal return on capital is smaller when you start with a great deal of capital; the marginal loss also is small when you have a great deal of capital to start.

Figure 3. The same amount of capital loss occurs in this depiction, but the drop in output is much less because returns to capital are much more modeled on where the utility function is very flat.

If you look at Figure 2, which shows the first way we considered production loss resulting from capital loss, you see how this might come about. Although you have fallen to a lower position on the production curve, that
part of the curve actually has a steeper upward slope. The slopes are the dot-dash lines.

Even though you have dropped to a position of lower production, you are now at a place on the growth function where output growth is more rapid for a given capital input, just as capital additions should be more effective in poorer economies. So capital was lost, but growth rate increased. That increase means you will experience a growth spurt from any new additions of capital (from disaster recovery assistance, say) and quickly get back to where you were. That quick recovery matches the thinking about getting back to the predisaster growth trajectory discussed before. In Figure 4 we see it is because the economy has moved to a state where returns to growth from capital input are greater.

Figure 4. The effect of output on capital loss is the same as in Figure 2. Note that the slope of the utility function designated by the dash-dot line is actually steeper where output is, in an absolute sense lower.

The Solow-Swan growth model predicts that poor countries should be growing very rapidly; many, however, simply are not. In fact, many are mired in stagnation, and some are even going backward. Jeffrey Sachs, the
outspoken economist and director of Columbia's Earth Institute, thinks that it is because at extremely low levels of capital accumulation, capital-based growth doesn't work anymore. For additions of capital to be utilized effectively, a country needs some basic infrastructure of roads and ports and factories and a minimally literate, reasonably healthy population of workers. Sachs suggests there is a threshold of capital below which returns to capital may be low. Figure 5 is from the same study by Sachs and others. This curve is now S-shaped instead of L-shaped, with a very steep high-growth section in the middle and regions of low growth at the beginning and the end.

Figure 5. Depiction of the Solow-Swan exogenous growth curve, but with a modification near the initial point of the graph to include slow growth at low capital levels that induce a poverty trap.

The critical capital threshold is
k
T
.
Below that level, individual savings are
below
the capital-widening line, which means the economy is going nowhere, even with positive (but not high enough) capital investments. Sachs (and he is not alone) argues that economies on the wrong side of the critical capital threshold
k
T
will experience poverty traps, which generally are defined as “any self-reinforcing mechanism that causes poverty to persist.”
3
Many mechanisms can cause poverty traps. The health trap is perhaps easiest to grasp. People who are ill cannot work to earn income; if they are young, they cannot go to school to gain skills. That means that illness will likely lead to income reduction. But if you live in a poor country, you are much more likely to become ill because of poor levels of sanitation and low levels of health services. So poverty will cause you to be ill, but then your illness will cause you to be poorer still. The gray area on the diagram is the region of the poverty trap. Sachs's argument is that, in this region, savings rates are just too low relative to population growth for places in this condition to get ahead.

Figure 6. The same magnitude of capital shock ∆
k
is shown in poverty trap scenario. The output loss is now very large and has the potential effect of sending an economy from outside a poverty trap into such a trap.