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.