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If a market is competitive then it will produce on its own devices an equilibrium that is socially desirable (if one accepts the principle of economic efficiency). Adam Smith referred to this general idea (albeit in a different context) as the Invisible Hand. He said
Every individual...generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry he intends only his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention (Smith, 1776; p.243).
Smith's idea is that people acting in their own self-interest may produce unintended consequences which, surprisingly, can serve the social good. In the example above, individuals through competition with one another push the market price towards its equilibrium value, and this value is socially desirable. However, to do this was not the intention of the individuals involved. They were just competing with one another and trading with sellers for their own private benefit.
How does this analysis help with the problem of affordable housing? From an economic point of view, affordability is a meaningless concept. It is simply not a social objective for things to be affordable, rather the government should seek to promote competition in the housing market and then leave the market to its own devices.
This conclusion of economics is striking and quite at odds with other perspectives on this problem. I will argue that affordability is an important problem, and that something fundamental is missing from the economic approach to housing. Within economics what is missing is some notion of equity, or a concern for how the gains from trade are distributed across different people. To illustrate this point, imagine that the equilibrium price of a house in a competitive housing market is ?200,000. Then those who are willing to pay ?200,000 or more for a property will get one, and the situation will be efficient from an economic point of view. However, this might not be the ethically appropriate way to allocate houses to people. The reason is fairly obvious. What someone is willing to pay for anything is constrained by their income. A rich person might be willing to pay more for a house than a poor person, but this does not mean that it is better that the rich person gets the house as opposed to the poor person. This is sometimes referred to in economics as the equity-efficiency trade-off. This is the idea that less efficiency is the price we have to pay sometimes if we want to ensure a more equitable distribution of goods across people (Landsburg, 2002; Ch.8). Policies designed to promote affordable housing fall into this category.