"Classical" and "neoclassical" are the names for two philosophical approaches to economics. As the names suggest, classical economics was a predecessor of neoclassical economics. The differences between the two, however, aren't merely a matter of one coming before the other. Each had a distinctive approach to analyzing the economy.
Attitude of Analysis
Classical economics focuses on what makes an economy expand and contract. As such, the classical school emphasizes production of goods and services as the key focus of economic analysis. Neoclassical economics focuses on how individuals operate within an economy. As such, the neoclassical school emphasizes the exchange of goods and services as the key focus of economic analysis.
Methods of Analysis
Because the classical school aims at explaining how economic systems grow and contract, economists from this school take a holistic view of such systems. All their analyses and predictions are based on this wide perspective on the economy as a whole system. The neoclassical school, on the other hand, explains the behaviors of individual people or companies within a whole system. The neoclassical method takes a focused view of one small part of an entire system.
Importance of History
Classical economics grounds its analysis in history, specifically the history of the nation or culture of which a certain economic system is a part. History provides a notion of how this economy expanded and contracted in the past, which can then be used to try to predict how it might expand and contract in the future. Neoclassical economics, on the other hand, grounds its analysis in mathematical models that are not grounded in history. These models provide a notion of how an individual economic actor might behave in response to certain events.
Value in Analysis
Because classical economics focuses so heavily on economic systems and on the production of those systems, the school emphasizes the inherent value of goods and services. These goods and services are thought to be worth something regardless of who produces them and who uses them. Neoclassical economics, with its focus on individuals within systems, emphasizes the variable value of goods and services. These goods and services are only thought to be worth something depending upon who produces them, who uses them and how they are used.
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