Courtnot’s Price and Bertrand’s Price Models for Complementary Products for Deteriorating items and Incorporating Tax on Purchasing and Sales:Decisions on Demand and Green Lot Size

In this paper, Cournot’s and Bertrand’s price models for complementary products for deteriorating items and incorporating tax on purchasing and sales are considered in third order equation. Two models are developed: mode-1 is considered Cournot’s price model with Advertisement-sales return-Cournot’s price as a demand function and optimal demand and lot size are decisions variables, and in the model-2, developed Bertrand’s price model with Advertisement-sales return-Bertrand’s price as a demand function and optimal pricing and lot size are decisions variables. In both models, a comparative study has been executed between incorporating tax along with without tax. It is evident that a gradual increase in tax rate, from 1 to 10 percent, significantly impacts and reduces the total profit. In both the models, price break even point is established, and law of demand has been confirmed in two models and highest possible profit has been calculated from the three alternative variables. Transporation cost, a carbon emission cost, green technology invesment cost, are introduced to reduce carbon emissions. Finding the optimum demand, optimal pricing along lot size for maximizing overall profit is purpose of this paper. Numerical examples demonstrate this model's applicability. To evaluate stability of this suggested model, a sensitivity analysis of the optimum solutions is provided. The data are generated by using Visual Basic 6.0