So what you are basically saying is that in the long run the price will be driven close to the lowest average price -- right?

Yes; in the long term the producers that have higher-than-average Costs will be driven out of the market.

Still not quite, as once you recognize that "perturbations" will happen, you need to engage in some risk management (zero mean does not imply zero volatility). In your scenario the chicken producer seems to be fine with the 50% chance of going bankrupt at the delivery time which isn't a good assumption to make.

I'm modeling risk management as part of the typical Cost of doing business, along with things like interest rates, opportunity costs of capital, chicken feed, other inputs, etc. Separating out risk management as a stand-alone variable doesn't seem to change anything.