For example, classical mechanics has good explanatory powers until you approach the speed of light or work with masses so small you are down at the molecular level. Since the 1870s the dominant paradigm in microeconomics has been marginal analysis. It is important to understand what assumptions are assumed in this paradigm. While the assumptions of the neoclassical microeconomic paradigm are very strong, the neoclassical microeconomic paradigm achieves very powerful results. Demand functions arise as the first order conditions of the calculus optimization models for production and consumption.
Today there is an increasing number of problems with the neoclassical microeconomic paradigm.
First, it is questionable that humans have the capability to instantaneously solve the optimization problems posed by the neoclassical model. Experimental research by economists and psychologists is generating an increasing number of anomalies. Finally we should be asking how producers try to maximize profits and how consumers select their market baskets in order to understand how economic agents adjust in an economic environment of constant technological change. Developing a new paradigm which is accepted as a replacement for the neoclassical microeconomic paradigm will get you a Nobel Prize. In developing such a paradigm remember that the existing paradigm must fit in the new paradigm as a special case.