The Lucas (1978) asset pricing model seems to be one of the workhorse models in finance / asset pricing models. It also seems to be the case that the environment, with claims to $n$ (exogenous) productive units traded, features complete markets. I have also seen another version of this model with the agent trading a single stock and a single bond that the instructor told me had complete markets.
To me, this is not obvious at all -- the agent does not have access to Arrow securities for each state, or something of that sort. In fact, in the original paper, the states are continuous, and this makes it even harder for me think about market completeness.
Can anyone tell me why (or perhaps why not) this model features market completeness?
Any help would be greatly appreciated (or pointers to relevant links would work). Thanks!
Edit #1: ----------------------------------------
Just to clarify, while I understand that in equilibrium the net holdings (of all the identical agents) must be zero, my concern was that having access to AD securities vs. not having access may have asset pricing implications. What I mean by this is that although the outcome in terms of asset holdings must (almost by construction) be equal in any case, but perhaps the presence of AD securities may distort the prices of other assets (e.g. equity claims "trees").
Intuitively, perhaps the price of trees must be different in the presence of AD securities to offset the agent's desire to hold the AD securities in equilibrium. My next logical step in determining whether or not this is the case, was to think about whether the markets were complete or not in the first place -- if markets were already complete, then the additional AD securities are "redundant" is some sense, and prices should not change. If markets are incomplete, my initial intuition was that this may possibly have consequences (not in asset positions, but in prices).
To me, this is not obvious at all, and something I would really like to see a proof of.