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

What’s up with multiplying prices from timepoint 2 against quantities 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.

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