This study estimates a multi-output production response model of Korean crop producers. In order to circumvent the problem that the estimation system based on the historical data usually violates the convexity property of the restricted profit function, our approach used a combined method of constructing an optimization model and estimating an econometric model with the data obtained from running the optimization model. A multi-region multi-output optimization model that describes producers’ responses to prices in detail was constructed, and many times of price shock experiments were conducted with the constructed optimization model. We estimated atranslog restricted profit function based on a series of simulation results. Our estimation results satisfied the convexity property for most of the simulation results, and derived significant own and cross price supply elasticities. It is found that flowers and fruits have relatively large price elasticities while rice has a relatively inactive price response. Our estimation results may be used for various types of agricultural economic modelling in Korea.