Agricultural Household Models Under Market Imperfections: Theory, Estimation, and Welfare Implications for Smallholders in Kogi State, North Central Nigeria

Classical agricultural household models assume separable consumption and production decisions under complete markets, a condition widely violated in smallholder farming contexts characterised by missing markets, transaction costs, and factor market imperfections. The theoretical and empirical implications of non-separability for welfare analysis and policy design in Nigerian smallholder systems have not been systematically examined in the recent literature. This study developed and estimated a non-separable agricultural household model incorporating labour, land, and food market imperfections using structural methods applied to primary data from 440 farming households in Kogi State. The theoretical model was derived from first principles to characterise shadow price formation and decision rule modifications under market imperfections. Full information maximum likelihood estimation was applied to structural model parameters. Results provided strong empirical support for model non-separability, with shadow wages estimated significantly above market wages for approximately 58 percent of households, consistent with missing labour market conditions. Policy simulation results showed that assuming separability when it is rejected leads to 25 to 40 percent overestimation of farmer supply response to price incentives. The study makes an original theoretical contribution to the agricultural household model literature in the Nigerian smallholder context, with significant methodological implications for extension and market development policy design. Keywords: agricultural household models, non-separability, market imperfections, Kogi State, shadow prices.