t-conorms to Analyze Aggregate Demand and the Leader-Follower Model of Real Competition

The paper uses a new condition of consistency along with the concept of fuzzy mathematics to explain the choice problem. It gives a new method of deriving the individual and aggregate demand function of any economic object without considering any type of neoclassical utility function. Moreover, using t-conforms the paper derives the aggregate/industry demand function and the equilibrium thereof in the market considering both convex and non-convex domains. The present paper theorizes a new model of leader-follower using this newly identified method. According to Anwar, Shaikh \cite{shaikh2016capitalism}, a real competition follows that competition within an industry tends to dis-equalize profit margins and profit rates precisely because it tends to equalize selling prices. Selling prices are depicted as exactly equal, to emphasize the point that price equalization leads to profit rate disequalization. The regulating capitals are, therefore, also the price-leaders in an industry. Their price becomes the benchmark for market prices. It follows that non-regulating capitals will be price-followers, and since they must adapt their selling prices to those of the price-leaders, their profits are residuals (that is, the profit margins and profit rates of non-regulating capitals depend on their costs). Regulating capitals are the price-leaders since they are the lowest costs ones of those able to expand and create long-run supply. Individual firms had different operating costs but were forced by competition to keep their prices in line with those of the price-leader. Hence, the net margins set of price-followers were simply those which kept their selling prices in line. Competition among firms keeps these prices in line with those of the price-leaders. In the battle of competition, the price-leader becomes the one with the lowest costs. Another result of real competition is that the mobility of capital leads to the equalization of the profit rates of capitals on the best reproducible conditions of production (regulating conditions) in each industry. The present paper first derives the new methodology and thereafter explains a new leader-follower model using the new method in both convex and non-convex cases