Is the economy linear programming or is it gradient descent?

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This will be bad take, but also fun. There will be no thinking before typing, and no second draft.

There is a good tradition of people knowing that in a functioning economy, prices for goods are just the Lagrange multipliers of the constraints of that economy. Many people are aware of this fact, and more still would make much better decisions if they knew. You can learn this from any good text on linear optimization, such as The Best Uses of Economic Resources by L.V. Kantorovich.1Never mind that this text is from 1965 or that more recent textbooks don’t emphasize this view much. No good text will completely ignore this perspective though, often an example of a farmer or the Diet problem is discussed.

The linear optimization perspective aligns well with the typical Effective Altruism mindset: prices represent exchange value, so to be good we should allocate our money to maximize to maximize value produced per dollar spent. If a thing is very cost-inefficient, don’t spend anything on it. If everyone behaved that way, we would collectively solve the optimization problem that is our economy. The result would be an economy producing the most utility possible.

The convex optimization perspective on the economy contrasts with a more recent view implicitly held by many people: everything is gradient descent, the best algorithm is always gradient descent. Machine Learning? Gradient descent. Bandit problems? Gradient descent. Maximum flow? Gradient descent. Online algorithms? Gradient descent!

If prices carry gradient information2actually inverse Hessian times gradient would probably be a closer match but who cares about telling a coherent story not me then we should spend money on a good proportional to one over its price. If everyone spends their money that way, we will descent our loss function as quickly as possible, arriving at the optimal economy maximizing utility in little time.

If prices are Lagrange multipliers, you should be frugal and spend most of your money on bed nets and stuff. If prices are gradient thingies, you can and must buy some of that expensive tasty vegan white chocolate. I just did exactly that. Yum yum yum.

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