<p>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. Finding the optimum demand, optimal pricing along with lot size for maximizing overall profit is the objective of this paper. 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 decision variables, and in 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 decision variables. In both models, a comparative study has been executed between incorporating tax along with without tax. In both models, price break-even point is established, and the law of demand has been confirmed in two models and the highest possible profit has been calculated from the three alternative variables. Transportation cost, carbon emission cost, and green technology investment cost are introduced to reduce carbon emissions. Numerical examples demonstrate this model’s applicability. To evaluate the stability of this suggested model, a sensitivity analysis of the optimum solutions is provided. The data are generated by using Visual Basic 6.0. It is evident that a gradual increase in the tax rate, from 1 to 10 percent, significantly impacts and reduces the total profit.</p>