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Neoclassical economics is a school of economic thought that emerged in the late 19th century. It is characterized by its emphasis on rationality, utility maximization, and market efficiency. In this school of thought, individuals and firms are seen as rational actors maximizing their utility or profits. Additionally, the neoclassicals believe that markets are efficient in allocating resources and that government intervention should be limited.

Keynesian economics is another school of economic thought, which was developed by the British economist John Maynard Keynes in the 1930s. The Keynesian approach focuses on the role of aggregate demand in determining economic activity, and it stresses the importance of fiscal and monetary policies in stabilizing the economy. Keynesians argue that government intervention is necessary, especially during periods of economic downturns, to stimulate demand and restore economic growth.

There are several key differences between neoclassical and Keynesian economics: 1. Neoclassical economists believe in the efficient market hypothesis, meaning that markets can self-correct and achieve equilibrium. In contrast, Keynesians believe that markets may not always self-correct and may require government intervention to achieve full employment and economic stability. 2. Neoclassical economics focuses on the supply side of the economy, while Keynesian economics emphasizes the importance of the demand side. 3. Neoclassicals advocate for minimal government intervention in the economy, as they believe that markets can effectively allocate resources. In contrast, Keynesians argue for more active government involvement in the economy, especially during economic downturns, to promote stability and growth.

The term "neoclassical Keynesian" might sound contradictory, as neoclassical and Keynesian economics have contrasting views on the role of government intervention and market efficiency. However, it is not necessarily a logical contradiction to be both. Some economists may appreciate the insights from both schools of thought and choose to adopt a more eclectic approach. For example, they may believe in the importance of market efficiency and utility maximization while also acknowledging that markets can fail and that government intervention can play a crucial role in stabilizing the economy. The neoclassical Keynesian perspective may thus reflect a more pragmatic and balanced view rather than rigidly adhering to either neoclassical or Keynesian doctrines. In summary, while neoclassical and Keynesian economics have opposing views on various economic topics, it is possible for an economist to draw insights from both schools of thought and be considered a neoclassical Keynesian. It is up to the individual to weigh the evidence and arguments of both schools and determine which aspects they find most convincing and applicable to their understanding of the economy.