Optimal multi-period crop procurement and distribution policy with minimum support prices

Governments of many developing countries offer minimum earnings to farmers through crop Minimum support price (MSP), which guarantees minimum revenue to farmers who cultivate the crop. The crop procured by a government through MSP is later distributed among poor consumers at subsidized prices through public distribution systems (PDS). Thus, governments combine MSP with the PDS scheme to simultaneously ensure farmers' welfare and tackle poor consumers' hunger and nutrition problems.However, improper implementation of the schemes causes burgeoning stockpiles in government ware-houses, which eventually causes a substantial increase in operational costs and food wastage. In this paper, we characterize the optimal joint MSP and PDS policy over a finite horizon for two objectives: (i) minimize the total cost and (ii) maximize the net value after accounting for farmers' benefit.Using the data over 15 years, we show that the optimal policy can substantially reduce operational costs (by about 85%) and improve the net value (by about 1.8 trillion INR). We use a linearly constrained quadratic stochastic dynamic program formulation to model the problem. We derive a simple and efficient joint MSP and PDS operational policy that provides the optimal quantity of crop that should be disbursed through PDS in the current period and the optimal MSP that should be announced for the subsequent period.Our policy is easy to compute and implement and can help policymakers efficiently implement MSP and PDS programs jointly. Our model provides a basic framework to solve the joint MSP and PDS problem and can be modified to incorporate other aspects through additional constraints.