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Keynesian economics is, strictly speaking, a macroeconomic theory or model. Such models attempt to explain economics growth and business cycles. Neoclassical economics is, strictly speaking, a set of microeconomic theories or models. Such models attempt to explain the allocation of resources in society to particular needs. Roughly speaking, all policy issues except fiscal and monetary policy fall under microeconomics and can be addressed without any reference to Keynesianism, for example, the impact of agricultural price supports or the consequences of state-run schools. The material in textbooks (including Krugman’s), therefore, is divided into micro and macro sections in order to cover the entire ground of economic theory
These waters are muddied somewhat by the so-called neoclassical synthesis which attempts to ground Keynesian macro in neoclassical micro.
Here is an accessible summary of Keynesianism: