Von Neumann's Machine

Magical & thermodynamical, non-classical & stochastical!

isomorphismes:

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
 

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

ratio of past price to now price

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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