Charles I. Jones writes,

By the end of the 20th century, per capita income in the United States was more than 50 times higher than per capita income in Ethiopia and Tanzania. Dispersion across the 95th-5th percentiles of countries was more than a factor of 32.

We have discussed this ad nauseum on this blog, talking about explanations such as institutional differences, IQ differences, and so on.

This paper is more about mechanics: can we develop a plausible mechanism for getting a big multiplier, so that relatively modest distortions lead to large income differences? The modern institutions approach builds up from political economy. This is useful in explaining why the allocations in poor countries are inferior — for example, why investment rates in physical and human capital are so low — but the institutions approach ultimately still requires a large multiplier to explain income differences…The political economy approach explains why resources are misallocated; the approach here explains why misallocations lead to large income differences. Clearly, both steps are needed to understand development.

Jones starts out with intermediate goods–goods that are useful in production but which are not part of final consumption.

Inferior highways that result from corruption can reduce output in a range of sectors, including construction. But this in turn further reduces the output of highways. In the model below, this multiplier depends on 1/(1−σ), where σ is the share of intermediate inputs in gross output. This share is approximately 1/2 in the United States and in
other countries, delivering a multiplier of 2.

However, Jones continues, a large multiplier by itself does not explain underdevelopment. That is because with large multipliers, one would expect to find a “magic bullet” that leads to rapid development, based on the large multiplier. Instead, development proves difficult. This suggests that a combination of factors is involved, including what Jones calls “weakest links.” (I tried to tell this sort of story in What Causes Prosperity?.)

In any production process, there are ten things that can go wrong that will sharply reduce the value of production. In rich countries, there are enough substitution possibilities that these things do not often go wrong. In poor countries, on the other hand, any one of several problems can doom a project. Obtaining the instruction manual for how to produce socks is not especially useful if the import of knitting equipment is restricted, if cotton and polyester threads are not available, if property rights are not secure, and if the market to which these socks will be sold is unknown.

Jones’ final point is that when the elasticity of substitution is high,

GDP depends disproportionately on the highest levels of productivity
in the economy.

Imagine an economy in which people want to listen to recorded music. If some key intermediate input is missing, such as reliable electricity, output will be low. At the upper end of the income spectrum, where intermediate inputs are available and there are many different ways to deliver music, the high-productivity method will dominate music listening. So if downloading music is much more efficient than buying tapes, an economy that has all the intermediate inputs necessary for downloading will have much higher music listening per person than will an economy that is missing a crucial input.