Mathematical Modeling for Demand and Supply Estimation for Cotton in Maharashtra

The output supply and input demand are closely interlinked to each other. Therefore, any change in input and output prices affect the input demand and output supply simultaneously. The present study used cross sectional cum time series data of Vidarbha region of Maharashtra state for cotton crop for the ten years from 1999-00 to 2008-09 were collected from the Agricultural Prices and costs Scheme, Department of Agricultural Economics and Statistics, Dr. PDKV, Akola by keeping in view to estimate input demand and output supply by using normalized Cobb-Douglas profit function. The analysis of input demand equations has shown that the demand elasticities with respect to own prices have the expected negative signs indicating that the results are in accordance with theory of demand. One per cent increase in own price, holding other prices constant, will reduce human labour employment at 1.296 per cent, bullock labour demand 1.343 per cent, fertilizer demand 2.093 per cent and seed demand 1.665 per cent in cotton crop. The absolute value of own price elasticity of human labour, bullock labour and seed price have been found greater than unity, indicating an elastic response of input utilization to their own price. It can be also observed from the study that own prices had negative Impact on supply of cotton. The profit function for cotton was decreased in prices of Farm yard manure and prices of seed. Among the variable factors, normalized seed price in general had the highest negative impact on variable profit for cotton crop followed by farm yard manure price. The study also shows that assuming no change in fixed factors or the level of technology, the input-output price structure has resulted in an appreciable change in human labour employment, bullock labour employment, fertilizer, farm yard manure and seed demand in the production of cotton. Index Terms cotton, input demand, Maharashtra, profit function