In two-tier price systems, yield uncertainty creates incentives to overproduce quantity-restricted outputs even when prices for surplus output are very low. These incentives arise from precautionary motives against expected losses from quota shortfalls. Using an approach augmented for multiple input applications, the likelihood of excess production and the relative importance of price changes in different markets are estimated for Icelandic dairy farms. The results indicate that the average farm plans to exceed its quota, and price changes in the surplus milk market are approximately three times more effective in generating supply response than price changes in the quota milk market.