Strategies in Mixed Budget: A Bitopological Approach

The forecasting graphs of World Bank, Reserve Bank of India, etc. are mostly line graphs or time series graphs. Any forecasting contains “standard error” as an error with complicated statistical formulae. A keen observation shows that mathematical patterns are available in nature, but in most of the cases, it is difficult for us to recognize these patterns. Similarly, it is most important for us to know the least upper bounds of these line graphs or time series graphs so that peaks of the prices with respect to time will not exceed these least upper bounds. It is hard to find any statistical or mathematical tool to determine these least upper bounds. Thus we give methodology to obtain these least upper bounds. We show existence of an equilibrium between the expected price and the original price of a commodity with the help of local functions and expansion operators of a bitopological space. These methods are based on choice of a consumer. Examples are provided to show that price of a commodity cannot exceed the interval of expected price. Moreover, we try to provide possible answers to the problem of “Control of Economic Variable” of Morgenstern [O. Morgenstern, Thirteen critical points in contemporary economic theory: An interpretation, Journal of Economic Literature 10(4) 1972 1163–1189] by determining least upper bounds.