A Brand of Inequality

I don’t blog very often now (which is excellent news for anyone who reads my newsfeed - Facebook is classy enough without my thoughts making their way into the congealed soup of 9gag gifs and duckface drivel). However, occasionally something comes alone which I feel deserves a response. In this case, that response is to Daniel Katz’s take-down of the now famous Russell Brand interview by Jeremy Paxman. 

While Katz’s unsheathed barrage is entertaining and thought provoking, my eyebrows rivaled Paxman at his trivial treatment of inequality. 

Katz begins the argument by taking a case of trickle down economics and follows it up by arguing that poverty isn’t such an issue in advanced economies because even the poorest will earn well above the arbitrary international poverty line ($1.25 USD at purchasing power parity, the “condition so limited by malnutrition, illiteracy, disease, squalid surroundings, high infant mortality, and low life expectancy as to be beneath any reasonable definition of human decency.”) as if relative poverty didn’t exist.

While it would be worth two of Paxman’s eyebrows to discuss this issue here, I’ll instead be a good economics student and give a simple  model which illustrates intuitively why we should be concerned about inequality at the policy level. 

We’re going to assume a couple of simple things:

1. A person’s utility is determined by their income. 
2. Utility is a decreasing function of income. 
3. Each individual has an identical utility function.

Utility is an economic concept which can be understood in a couple of ways: as a person’s happiness, the ability to affect their desires, their welfare. 

The first assumption is simple enough: a person’s happiness depends on their income. 

The second assumption is again fairly simple: we are happier with more income, but our happiness increases at a slower rate as our income increases. Going from $0 to $10,000 makes us happier than going from $90,000 to $100,000, or $990,000 to $1,000,000. This is a fundamental result from the branch of economics happily called Happiness Economics. 

The third assumption: people react to income as a whole identically. This is not strictly true - a monk in Tibet probably has a different view of money than a French aristocrat - but it’s the best way to think about it. By treating everyone by a single representative individual, we can ignore the effects of age, gender, ‘whether they prefer a rainy day at the beach or a sunny day at the park’, favourite colour, and whatever other spurious factor you could think of. 

In this, I’m disagreeing with Nietzsche: 

“In a better social order the hard work and misery of life will be allotted to the man who suffers least from it, that is, to the dullest man, and so on step by step upwards to the man who is most sensitive to the highest, most sublimated kind of suffering, and therefore suffers even when life is most greatly eased.”

Whether an aristocrat or a penniless philosopher, there is no reason to suppose that you’ll like money any more or less than anyone else. 

These three assumptions lead to the social welfare function:

Welfare = U₁ + U₂ + ... + U_n 

Where U_k is each individual’s overall happiness or utility. 

What we find is income is optimally distributed when we have complete equality (when the marginal utility of each individual is equivalent).

Before we start a revolution

There’s a fourth assumption: that the total amount of income is fixed. Katz actually addresses this point arguing that wealth is not a zero-sum game. When income is completely equal (a doctor, and an economics student being paid the same regardless of their actions), economic incentive is removed. 

The incentive to become a civil engineer, or work as a labourer, is removed entirely when we have pure income equality, to the point where doing it would be out of pure altruism or interest. It might be cynical, but a society with pure equality would (almost certainly) lead of a collapse of income and overall welfare. Pure inequality (all income belonging to a single individual) would similarly lead to a collapse of incentive. Some inequality is required to act as incentive for individuals to increase welfare as a whole. 

That’s not even close to say that we should ignore the issue of inequality. Inequality is only beneficial to the point that it leads to an increase of overall social welfare. If we pretend that inequality is an issue that doesn’t require explicit intervention, then we implicitly imply that any action to reduce inequality will reduce social welfare overall. It’s an overly optimistic view of current inequality which itself deserves a pair of Paxman’s Eyebrows. 

I’ll finish this post with a thought experiment, which I hope shows the difference between economic efficiency and social welfare.

If society could choose between a billionaire receiving an million dollars, or five hundred individuals receiving a thousand dollars each, which would make society society better off?