Suppose that $$q$$ is a k-tuple vector of prices for the k assets whose quantities are given by the k-tuple $$\theta$$. I have just read that in the Radner Sequential Trade Equilibrium (not sure if this goes by another name), where the trading of assets occurs in period t=0 (as opposed to t=1), the period-zero budget can be expressed as $$q*\theta$$, where $$*$$ denotes the inner product, and that this budget is non-positive.
In Radner's model each actor starts with an initial endowment, an asset vector $$\omega$$. You can trade this to any asset portfolio $$x$$ that has lower or equal value, so $$x * q \leq \omega * q.$$ Denoting asset trades by $$\theta = x - \omega$$, you can also express this as $$\theta * q \leq 0.$$
• So in the initial stage t=0, I've been assigned some quantity of each asset, and I can trade with some second party to possibly change the quantities I possess and these new quantities I end up with are the vector $x$, correct? Also, am I right to say that the only reason trade occurs is because there is uncertainty about which state will be realized in t=1? – Dion Apr 16 '19 at 21:08