Buying & Selling

When you own your goods

So far income \(m\) just dropped from the sky. More realistically, a consumer starts with an endowment — a bundle \((\omega_1,\omega_2)\) they already own (hours of time, a crop, savings) — and trades at market prices. Their “income” is whatever that endowment is worth: \[ m = p_1\omega_1 + p_2\omega_2. \] So the budget constraint is \[ p_1 x_1 + p_2 x_2 = p_1\omega_1 + p_2\omega_2, \] and it always passes through the endowment point — because consuming exactly what you own is always affordable. A price change rotates the budget line around \((\omega_1,\omega_2)\).

The consumer is a net buyer of good 1 if \(x_1 > \omega_1\) and a net seller if \(x_1 < \omega_1\). The powerful twist: when a price rises, an endowment-holder isn’t simply worse off. A seller of that good gets richer; a buyer gets poorer. That’s why the response to price changes here differs from the fixed-income case.

The sim uses Cobb–Douglas demand with endowment income: \(x_1 = a\,(p_1\omega_1 + p_2\omega_2)/p_1\).

Try it. Slide the price of good 1. The budget line pivots around the endowment ■. Watch the optimal bundle ● move — and watch the consumer flip between net buyer and net seller of good 1.

What to notice

  • Every budget line passes through the endowment ■ — consuming what you already own is always feasible, so a price change can only rotate the line, never shift it off that point.
  • Raise p₁ enough and a buyer of good 1 becomes a seller: good 1 is now so valuable it’s worth selling some of your stock rather than buying more.
  • A higher p₁ makes a seller of good 1 richer (endowment worth more) — the endowment income effect that’s absent from the fixed-income story.