Brilliant Simplicity

some examples

There are two different ways in which brilliant scientists contribute to their science. One is by doing something difficult and complicated — a physicist inventing the theory of relativity, an economist solving the problem of general equilibrium. The other is by seeing something simple and important that nobody else had seen, the sort of thing that, once seen, appears obvious, can be explained in a paragraph or two.

As I will demonstrate.

Harold Hotelling

The distinction between simple and complex brilliance occurred to me reading a piece on the median voter theorem. There are, as the discussion pointed out, lots of possible complications, but the central idea, due to Hotelling, is simple. Two parties are competing for votes from an electorate with a one dimensional distribution of views, right to left. Given the choice between two candidates, each voter votes for the one whose position is closer to his. If the right wing candidate takes a position to the  right of the median voter his opponent can take a position just to his left, get more than half the votes, and win the election. The only stable equilibrium is both candidates in the center. The same result holds for other situations with the same logic, such as two competing barber shops on a street.¹

A second example from Hotelling is his analysis of the economics of depletable resources. Imagine that there are lots of oil wells with different owners, all of whom want to maximize their profits. For simplicity assume there is no cost to pumping the oil out. If the price of oil is going up over time at more than the interest rate, an owner of an oil well makes more money by leaving the oil in the well today and pumping it in the future than by pumping it now and putting the money in a bank. If it is going up by less than the interest rate, he makes more by pumping it now. Pumping it now lowers its price now, raises its future price after the well is exhausted. Keeping it in the well now to pump later has the opposite effect. Hence, in a world where the owners correctly predict future prices, the price of oil rises at the interest rate.²

Many years ago I heard a talk by an ex-cabinet member that touched on the problem of running out of resources, imagined as a surprise, the day when you put the key in your car’s ignition, turn it, and the car doesn’t start because there is no longer any gasoline. Hotelling’s analysis of the problem shows why that is the wrong way to think of it, why, if we ever run out of oil, it will be a long process of gradually rising price and gradually falling consumption.

Ronald Coase

Coase got, and deserved, a Nobel prize in economics for two articles, each embedding one simple and important idea.

One, The Nature of the Firm, answers the puzzle of why firms exist and what determines their size.

If, as Mises and others argued on their side of the calculation controversy, economic calculation requires a market and prices, is impossible in a centrally planned economy, why is the actual market made up largely of firms, miniature socialist economies within which coordination is by centralized control?

Coase’s answer was that, while there are costs due to the difficulty of rational planning in a centralized system, there are also costs to transactions in a decentralized market.

The main reason why it is profitable to establish a firm would seem to be that there is a cost of using the price mechanism. The most obvious cost of “organising” production through the price mechanism is that of discovering what the relevant prices are. … The costs of negotiating and concluding a separate contract for each exchange transaction which takes place on a market must also be taken into account. (“The Nature of the Firm”)

That explains both the existence of firms and their size. Costs of centralized coordination increase with the size of the firm, the number of layers between the president and the factory floor. Firms expand until the cost of coordinating additional production within the firm becomes higher than the transaction cost of getting it done outside of the firm on the market.

It is a simple argument — on which the modern theory of the firm is based.³

The other and even more famous article was “The Problem of Social Cost.” The argument is usually, and misleadingly, summarized as the Coase Theorem, which holds that if there are no transaction costs any initial allocation of rights will be bargained to an efficient outcome since as long as inefficiency exists there is a potential transaction to eliminate it that is in the interest of both, or all, parties. It follows that, absent transaction costs, inefficient outcomes due to problems such as externalities or adverse selection do not exist. Coase’s point was not that inefficiencies do not exist but that they are due to the existence of transaction costs, which are for the most part ignored in standard price theory. It follows that to redo price theory properly requires a theory of transaction costs, something we do not yet have.

Thomas Malthus

Malthus’ best known contribution to knowledge was a simple and elegant theory of population, intended as a disproof of the optimistic views of some of his contemporaries. It starts with the observation that humans like sex and sex produces babies. He concluded that, unless there were substantial costs to rearing children, population would increase at something close to the biological maximum, leading to exponential population growth that would overcome any plausible rate of increase in human productivity. Looking around him at the end of the 18^th century he observed that  most people were poor enough to make the cost of supporting an additional child a substantial burden. He concluded that if that was not the case, if, as Godwin and Condorcet, the authors he was responding to, expected, the future saw a sharp rise in the standard of living of the masses, the pressure of population increase against a fixed supply of land would push standards of living back down.

It was an elegant theory and a pretty good description of the history of mankind up to the time Malthus wrote. Since then real incomes in the developed world have increased by more than an order of magnitude. I discussed why the predictions of the theory failed to hold, starting about when Malthus created it,  in a post to my old blog.

Malthus was also a co-inventor of the Ricardian Theory of Rent, an important step in the development of modern economics, but it got named for Ricardo, who used it but was not the other inventor. Ricardo was, however, the inventor of Marshallian quasi rents, named after Alfred Marshall who reinvented the idea most of a century later. Both namings conform to Stigler’s law, which holds that scientific laws are never named after their actual inventor — and was not, of course, invented by Steve Stigler, after whom it is named.

Milton Friedman

An important question in economics is what determines how much an individual consumer spends. The natural answer is his income. To see why that is the wrong answer, consider someone whose income changes substantially over time, a student in a field that requires extensive training or someone with the kind of job that varies, year to year, between feast and famine.  If you make a hundred thousand dollars this year and expect that it might be only ten thousand next year, you don’t spend all hundred thousand, instead save some of it to pay for food and housing in the next bad year. If you are a medical student with an income close to zero you don’t live on the street and starve, you borrow against your future income as a well paid physician.

How then should we model consumption  in our economic theories to take account of both saving and borrowing? Milton Friedman’s answer was that your consumption depends not on your current income but on your permanent income, your best estimate of the present value of your income summed over the rest of your life, allocated across time by saving when your income is high, borrowing when it is low. That is the Permanent Income Hypothesis, the earliest part of the work for which Friedman got the Nobel Prize.

Darwin

Leaving economics for biology,⁴ consider the theory of evolution. Given random variation of heritable characteristics, those characteristics that increase the individual’s reproductive success will become more common over time. The result is to produce organisms that appear to have been intelligently designed for reproductive success.

That simple insight is the basis of modern biology. It also provides a non-religious explanation for the design of living creatures, which answers one of the strongest arguments for the existence of God and so has contributed to the decline of religious belief over the century and a half since Darwin published.

Where to Armor a Bomber

During the second world war, my father was part of the Statistical Research Group, a team of statisticians and mathematicians applying their talents to solving military problems. One of the important ones was the problem of where to armor a bomber against the effect of anti-aircraft shells. Put armor everywhere and the plane is too heavy to get off the ground, no armor and even a small shell fragment can bring it down.

The obvious solution is to build lots of bombers, punch random holes in different parts of them, and see which ones crash. It occurred to someone at the SRG that the experiment was currently being done over large parts of western Europe with bombers provided by the US air force, holes by the German anti-aircraft. Set up a mock bomber somewhere in England and put black patches  on it to mark the location of holes in bombers that come back from raids. The parts without patches are where you want armor, since they correspond to where the holes were in the bombers that didn’t come back. An elegantly simple solution, once you think of it.

Another idea from the group, simple in concept but mathematically more difficult in application, is sequential analysis, described in a post on my old blog under the subhead “A Statistical Digression.”

Complex Brilliance

Examples include the work of David Ricardo and Alfred Marshall in economics and Isaac Newton in physics, none of which can be explained in one or two paragraphs. For Marshall the best source is probably his Principles of Economics. Ricardo also wrote a principles book; readers who want to attempt it may find  the lecture notes from my old History of Economic Thought class helpful. For Newtonian physics see any good physics textbook.

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1. Discussed at greater length in Chapter 19 of my webbed Price Theory under the subhead “Alternative Approaches.”

2. A more detailed explanation can be found in Chapter 12 of Price Theory under the subhead “Depletable Resources.”

3. Harold Demsetz, another prominent economist, used to claim that he should have gotten the prize since he had written many more articles based on Coase’s ideas than Coase had.

A good discussion of the historical tradeoff between centralized and decentralized organization is Markets and Hierarchies by Oliver Williamson.

4. The fields are not unrelated. Thomas Malthus certainly and Adam Smith possibly were among Darwin’s intellectual influences.