This article explores supply response models in a rational expectations framework with endogenous risk by using a multivariate generalized autoregressive conditional heteroskedasticity model with Cholesky decomposition. This approach allows the incorporation of price volatility as a risk factor into the supply response of a primary commodity sector that is composed of several markets of homogenous products. The model is applied to the Greek meat sector, which is composed of four major meat categories, that is, beef, lamb, pork, and broiler, and thus the model for the entire market includes supply and demand equations for all the four meat markets, which are estimated simultaneously. The empirical results confirm that price volatility is a significant risk factor in Greek meat production and also provide useful implications about the cost factors of production. Furthermore, the empirical findings show that the last reform of the Common Agricultural Policy seems to have had a negative effect on beef and lamb production in Greece.