Summing Budget Lines Does Not Derive the Demand Curve

It's a common exercise in undergraduate economics to sum individual budget constraints to derive a market demand curve, but this is wrong.

1. Budget constraints are immune to changes in individual preference, but demand is not.
2. Budget constraints do not include economic cost, but quantities demanded do include preference and economic cost information (see point 5)
3. Budget constraints respond to change in market price due to market change in demand, but those price changes most be viewed as exogenous when we know they aren't.
4. Quantity demanded occurs at the tangent of an indifference curve and a budget constraint; real demand is a necessarily discontinuous collection of such points
   1. A demand curve should be thought of as a regression of such points which is necessarily fictitious but still very useful in estimation.
   2. Demand curves as regressions should also be \"fat\" with confidence at each estimated point.
   3. The idea of the representative consumer is preserved in this statistics-oriented approach.
5. In this correct approach we can model good 1 vs good 2 or good 1 vs All Other Goods
   1. But these goods prices are accounting prices, not economic prices
   2. If we use price level for the price of AOG, issue 4.1 stands for AOG analysis
   3. The quantity demanded preserves the economic calculation because the utility curve becomes an All Other Information curve.
      1. In this framework, neoclassical economics models a change to the individual information state as a change to preference, not price
   4. Real demand (the discontinuous collection, not the curve) contains preference and economic opportunity cost and calculation
   5. The real demand curve (the best statistical estimate of real demand) is our best estimate of preference and opportunity cost and calculation
      1. But, our best estimate is an aggregated fiction; so tread lightly and more lightly when applying market findings at lower or higher levels of aggregation