Shadow price and reduced cost analysis for optimizing cropping patterns using linear programming in Madhya Pradesh

Abstract

This study focuses on analyzing the shadow prices and reduced costs associated with optimizing cropping patterns in Madhya Pradesh using a Linear Programming (LP) approach. The research utilized secondary data from 2005-06 to 2019-20, sourced from the Directorate of Economics & Statistics, Government of India, and the National Sample Survey Office (NSSO). The LP model was implemented through Microsoft Excel Solver to maximize farm profitability under cash and labor constraints. The shadow price analysis revealed that while cash constraints for Kharif and Rabi crops remained non-binding, labor availability emerged as a critical limiting factor influencing profitability. The highest shadow price for Rabi labor was Rs. 203.3 per hectare (2016-17), and for Kharif labor Rs. 182.4 per hectare (2017-18), indicating years of severe labor shortages. Reduced cost analysis showed that crops such as Mustard and Lentil occasionally featured in the optimal cropping pattern, whereas Cotton, Paddy, and Maize consistently exhibited high negative reduced costs, rendering them unviable under existing resource conditions. The findings highlight that efficient land and resource reallocation based on LP optimization can substantially enhance profitability, minimize input wastage, and support sustainable agricultural planning for farmers in Madhya Pradesh.