Guest Post by Shaun Hingston — Allocation and Equality

Shaun Hingston posted a provocative comment on allocation and equality recently, and I asked him to expand upon it in a post. Here are his thoughts.

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Allocation efficiency is the ability to effectively allocate resources towards activities that increase one's welfare. If someone has more resources to manage than they did before, will they still allocate those resources with the same efficiency? I think not. As the amount of resources one has increases, so does the number of allocation errors. Therefore one's allocative efficiency falls, as the amount of resources they have increases.

Such a statement is intuitive. As the amount of stuff I have grows, the harder it is to keep everything running at the optimal level. Whenever a resource is misallocated, it is no longer producing the optimal amount of income. So, the number of misallocations grows as the amount of resources increases.

Assume a second person equally capable, but with less resources than the first, what course of action should be taken to ensure that the income from all the resources is maximised? For a given single resource item, is it more likely to be misallocated by the first or second person? Since misallocation is proportional to the amount of resources one has, the first person is more likely to mis-allocate the resource item. So to minimize the amount of mis-allocations, first person should give some of their resources to the second person. But how much resources should first person give to the second person ?

The objective is to maximise the income from resources, which is achieved by correctly allocating resources. The first person should continue to give resources to the second person until each person is equally likely to misallocate resources. Recall that mis-allocation is proportional to the amount of resources each has. So they are equally likely to correctly allocate when they have the same amount of resources. This means that the income from resources will be maximized when person one and two have the same amount of resources.

What about for a third person? The rule still holds. That is, the total resources should be divided equally between one, two and three. This will ensure that income from resources will be maximized. This rule will hold for any subsequent person. Therefore a community will achieve maximal income when resources are divided equally, assuming equal allocation ability.

Unequal allocation capacity

So far it is assumed that everyone has the same ability to allocate resources, which isn't true. The assertion doesn't hold when considering different allocation skill levels. Therefore one must consider the cost of education and allocation.

Lets consider the above scenario where the first person has more resources than the second person. Let's also assume the second person is less capable than the first person. From the community's perspective the first person can either use her energy to allocate resources or educate the second person. This is a simple profit/loss calculation. Calculate the cost of educating second person and the associated allocative gains, compared with the allocative losses incurred to educate first person. If people were immortal then on average the optimal decision is to educate second person.

For society as a whole, this obviously shows that the more time and effort spent on empowering people, the greater that society will be. Society may suffer a short-term fall in allocation efficiency, but it will result in a long-term allocation capacity increase, and consequently income.

From the community's perspective undereducated people are an obvious resource. Raising people through education will increase the communityÍs ability to allocate resources. This will lead to an increase in income and consequently prosperity for all.

Economic growth and inequality.

The businessman might argue the teacher should educate him instead of you. This assumes that the businessman is more capable of learning than you are. Indeed this could be true. However, it becomes harder to justify not teaching you as his wealth grows many times greater than yours.

The businessman has a huge amount of resources to allocate. So it is significantly more expensive to fund the education of a businessman than you. Allocative errors grow because the businessman is learning instead of allocating, a huge cost considering the amount of resources they must allocate. This huge cost must be justified by a corresponding improvement in allocation efficiency. In addition, the businessman's allocation efficiency increase must be greater than that achieved by educating you. The resources used to educate the businessman could be used to educate you or others. And since you do not have as many resources to allocate, then the time-cost is significantly less. Therefore even if it takes you significantly longer to learn the same topic, it may still be cheaper to educate you, many times over. Thus resulting in the greatest allocative efficiency.

The gap between the rich and the poor could be viewed as a way to measure the allocation and learning ability of the rich compared to the poor. A large gap can only be justified if the rich are allocating resources better and can be educated cheaper than everyone else. Given that allocative errors grows as the amount of resources one has increases, and education costs also rise as the amount of resources someone has increases, then today's gap is unlikely to reflect the true capacity each individual has. In fact as the gap grows, the errors will increase, which will detrimentally affect income. As the gap becomes ever greater, income from resources is sub-optimal. Society underperforms without any logical economic reason.

Shaun Hingston