Von Neumann's Machine

Magical & thermodynamical, non-classical & stochastical!

Are you a physicist and want to learn intermediate microeconomics as quickly as possible? Here you go.

Minute 18

• Goods = vector space
• Price = covector
• Expenditure = their inner product
• Foliate the vector space by hypersurfaces convex to the origin with codimension 1. Indifference surfaces / isoutility surfaces.
• (no local minima/maxima, ever-increasing)
• Look at the inverse images, given a particular choice of price = budget constraint. Affine hyperplanes of codimension 1, translated from the origin, which are all based on the kernel of the pricing vector.
• The central dogma: agents spend up to their budget constraint reaching the highest level surface intersecting with the convex hull.
• People buy the unique basket whose tangent space at the basket to the indiffference space is equivalent to the kernel of the pricing vector in force.
• The space of all such baskets, given any income level but the same pricing system, is called the Engel curve.
• Minute 34: income vs substitution effects
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Minute 31. For the economists in the audience. This is a really good point. We measure the inflation from period to period by some formula like

$\large \dpi{200} \bg_white \frac {\text{Prices}_{t+1} \ast \text{Quantities (consumption choices)}_t} {\text{Prices}_t \ \ \; \ast \text{Quantities (consumption choices)}_t}$

What’s up with multiplying something from timepoint 2 against something from timepoint 1? That doesn’t really make sense does it. If prices changed in the next period then that induced a response in purchasing behaviour.

Not to mention that e.g., hats have fallen out of fashion for men since a century ago—so the price of hats no longer merits a high weight in the basket of what price increases are killing the budgets.

What we really want to do is use a connection. That gives us parallel transport across timepoints.

(Source: pirsa.org, via isomorphismes)

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