278 – Global wealth inequality

The charity Oxfam recently released a remarkable report on international wealth inequality. Based on data and analysis published by the Swiss financial company Suisse Credit, they highlighted that the aggregate wealth of the world’s richest one percent of people is about the same as the aggregates wealth of the other 99 percent.

This made my head spin, so I wanted to see the graph of wealth distribution. Using the Oxfam/Suiss Credit data, I put together an approximation of the Lorenz Curve for the whole world (Figure 1). To create a Lorenz curve, you rank all the people, from poorest to richest, and plot the proportion of the world’s wealth that they own. The graph shows the proportion of the world’s wealth that is owned by the poorest X percent.


Figure 1. The percentage of the world’s wealth that is owned by the poorest X percent of the population.


The figure reinforces the remarkable extent of inequality indicated in the headline 1%:99% fact.

For example, it shows that the least-wealthy 70% of people own just a few percent of the world’s wealth between them.

90% of people have a bit more than 10% of the wealth.

The wealth of the bottom 30% is roughly zero. If you look closely, you can see that the line disappears below the axis for the bottom group of people, indicating that they have slightly negative wealth.

At the other extreme, the wealth of the very richest people is astounding. You can’t make this out on the graph, but the richest 80 people in the world – with individual wealth ranging from $13 billion to $76 billion in 2014 – have as much wealth between them as the bottom 50% of people on the planet. That’s 80 people versus 3,500,000,000 people.

However, you might be surprised to learn that the story of the richest 1 percent is not all about billionaires, or even millionaires. To make it into the richest 1 percent, you need wealth of about $800,000. There are 1.8 million such people in Australia. Those of us who live in Australia (or in any developed country) would come across top 1 percenters on a regular basis – they are all around us. They are mostly not people living a jet-set lifestyle. Within a developed-country context, most of them would not be considered especially rich.

That is even more true of the top 10 percent. The wealth you need to make it into that group is only $77,000. As one of my colleagues commented, this reveals that the problem is not “those rich bastards”. It’s us!

slumsThis is not to say that the poor are not improving their lot. In many developing countries, the average wealth of poor people, and especially middle-ranked people, has improved over time (see here). It’s just that the wealth of people who are already wealthy is growing more rapidly, not just absolutely but relatively.

Another surprising result is that there are quite a few people from developed countries at the bottom end of the distribution. These are mostly people who have assets, and actually have a pretty good standard of living, but they also have large debts that leave them with negative net wealth. The collapse of house prices in the US associated with the Global Financial Crisis created many such people. Remarkably, about 7% of Americans are in the bottom 10% for net wealth. Only India has more people in this poorest group! Of course, this reveals that net wealth is not the whole story. An American from the bottom 10% is likely to have a much higher standard of living and much greater opportunities for improvement than an Indian from the bottom 10%.

The difficult thing, of course, is the question of what should be done about all this inequality. Oxfam has some proposals, but others have argued that inequality per se is not a problem, as long as the lot of the poor is improving. To me it seems that extreme inequality is a concern in its own right, particularly within a country, but that it would be hard to support measures to dampen inequality if doing so would make poor people worse off. This is a  can of worms, of course.

Further reading

Bellù, L.G. and Liberati, P. (2005). Social Welfare Analysis of Income Distributions: Ranking Income Distributions with Lorenz Curves, IDEAS page.

Credit Suisse (2014). Global Wealth Data Book, online here.

Oxfam (2015). Wealth: Having It All and Wanting More, online here.

News reports: here, here, herehere

277 – Perfection isn’t best

In whatever work we do, a common challenge is deciding how much effort to devote to a particular task. Additional effort will usually generate more output or better-quality output, but at what point does the cost of extra effort outweigh the benefits? It might be a lower point than you think.

A standard model from production economics provides some useful insights into this issue. The model represents a firm’s decision making about a production input. A classic example from agriculture is a farmer’s decision about how much fertiliser to apply to a wheat crop. I’ll go through this example and explain the insights it gives us. Later on, I’ll show how the same insights are often relevant to completely different types of work, such as writing a report or studying for an exam.

Looking at the fertiliser example for now, the question is, how much fertiliser should a farmer apply in order to get the outcome that is best overall?

The higher the rate of fertiliser applied, the higher the level of wheat production. However, the relationship between the input (fertiliser) and the output (wheat grain) is unlikely to be a straight line. It’s more likely to be shaped like Figure 1: as the level of input increases, the level of output increases but it tends to flatten out. Whatever its shape, economists call the relationship between an input and an output a “production function”.


Figure 1. A production function for fertiliser applied to a wheat crop.


Suppose the planned level of fertiliser in Figure 1 is low – say 20 kg/ha. As the graph shows, if the farmer increased the rate from 20 to 40 kg/ha, there would be quite a large increase in wheat yield. On the other hand, if the planned fertiliser rate was 120 kg/ha, increasing it by another 20 kg/ha would increase yield by only a small amount. At 200 kg/ha, a further increase in fertiliser would make no difference to yield (in this example).

There have been countless thousands of fertiliser trials conducted around the world, and the great majority show a shape like Figure 1 – steep at low fertiliser rates, flat at high rates.

One possible answer to the question, “what is the best rate of fertiliser?” would be, “the rate that gives the highest yield”. In Figure 1, the yield is maximised at 200 kg/ha.

The problem with this answer is that it ignores the cost of the input. Clearly, fertiliser is not costless.

Figure 2 shows the farmer’s revenue from the harvested wheat crop and the cost of the fertiliser that has been applied (all calculated per hectare). The revenue curve is the crop’s yield (from Figure 1) multiplied by its sale price (which I’ve assumed is $250 per tonne in this example). The cost curve is the cost of fertiliser ($1.90 per kg) times the rate of fertiliser applied.


Figure 2. Revenue and cost from wheat production at different fertiliser rates.


At any fertiliser rate, the benefit to the farmer (the profit) is the revenue received minus the cost of fertiliser. On the graph, the profit at a particular fertiliser rate is the vertical distance between the revenue and cost line at that fertiliser rate. You can see that if no fertiliser was applied, the benefit would be $300 per ha (the distance between the red and blue lines at the points where they hit the vertical axis, where fertiliser rate is zero). If the fertiliser rate was 80 (where the dashed line is), the vertical distance between the red and blue lines is a bit over $500, so 80 is clearly a better option than zero. At rates above 80, the revenue and cost lines get closer together, meaning that the overall benefit is less than at 80. In fact, 80 is the best possible input level in this example. It gives the highest profit to the farmer.

Figure 3 shows the farmer’s profit at different fertiliser rates. It is the difference between the two lines in Figure 2. In this graph it’s easy to see that the maximum profit is generated at 80 kg per ha of fertiliser.


Figure 3. Profit from wheat production at different fertiliser rates.


It’s also easy to see that the fertiliser rate that maximises crop yield (200 kg/ha) is not the rate that maximises profit. The reason for this is that, at rates above 80 kg/ha, the revenue from the additional grain isn’t enough to cover the cost of the additional fertiliser. In fact, at 190 kg/ha, increasing the fertiliser rate up to 200 kg/ha gives basically no additional yield at all, only additional costs (see Figure 1).

Figure 3 also shows that the profit function is quite flat in the vicinity of the optimum (80 kg/ha). Any rate between say 60 and 100 kg/ha gives very nearly as much profit as does 80 kg/ha. (See PD#88)

As promised earlier, let’s look at other types of outputs and inputs and see how this model is relevant. Economists have found that the shape of Figure 1 (or something like it) is relevant to many types of physical production processes. Just Google “production function” and you’ll see that this is the default assumption in the absence of evidence to the contrary. In all these cases, the optimal input level is less than the level that maximises output, and there is a range of input levels that are almost as good as the optimum.

What about work that doesn’t create physical products? In most developed countries, the service sector constitutes 70 to 80% of the economy. How relevant are the above conclusions to activities in that sector, like analysing some data, writing a report, marketing a product, or designing a building?

My proposition is that the shape of the production function in Figure 1 is very often relevant to these sorts of activities as well as to physical production processes. Consider the process of writing a report. It’s a common experience to find that one can prepare a report to a reasonable standard with a moderate amount of work, but further improvements in the standard of work take increasing amounts of work. As the report approaches perfection, there is a risk of continuing to work on it almost indefinitely without any real improvement in its quality. Clearly, this is just like the fertiliser example, with the main difference being that I’m focusing on the quality of the output rather than its quantity.

If that’s so, then it must also be true that the ideal level of effort to put into this type of work is less than the amount needed to produce a perfect report. Aiming for a 98% or even 95% perfect job (rather than 100%) will produce an output that is good enough in the majority of cases, and will allow you to move on more quickly to other work. For some people, adopting this as a conscious strategy can greatly increase their efficiency at work, especially people with strong perfectionist tendencies.

Of course, sometimes 95% really isn’t good enough. If a report is particularly important and will be carefully scrutinised, you might decide to aim for 99.9%, but even in these special cases, it is unlikely to be optimal to aim for 100%.

Further reading

Pannell, D.J. (2006). Flat-earth economics: The far-reaching consequences of flat payoff functions in economic decision making, Review of Agricultural Economics 28(4), 553-566. Prepublication version here (44K). IDEAS page here.