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First, let's define the key economic terms to better understand the exercise: - Neoclassical Economics: An economic approach that emphasizes the individual's role in the market and supports the idea of markets finding a natural equilibrium with minimal government intervention. - Keynesian Economics: An economic theory based on the premise that government intervention is needed to stabilize economic markets, and that fiscal policy can be used to achieve macroeconomic stability.

Now, let's discuss the core principles of neoclassical economics: - Individuals and firms strive to maximize their satisfaction/utility and profit respectively. - The market is the most efficient mechanism for allocating resources. - Supply and demand interact to determine prices in the market. - Prices and wages are flexible and adjust quickly to create equilibrium. - Economic equilibrium is achieved when supply equals demand, and markets clear. - Minimal government intervention is required to ensure market efficiency.

Next, let's discuss the core principles of Keynesian economics: - Government intervention is necessary to stabilize the economy. - Fiscal policy (government spending and taxation) is used to control aggregate demand. - Involuntary unemployment exists, and there's no natural mechanism to restore full employment without government intervention. - Prices and wages are sticky and don't adjust quickly to maintain equilibrium. - Economic equilibrium can exist at less than full employment. - Monetary policy has limited effectiveness in combating economic downturns compared to fiscal policy.

Lastly, we will examine whether these two economic theories can coexist or if they represent a logical contradiction: - Neoclassical economics emphasizes market efficiency, minimal government intervention, and flexible prices, whereas Keynesian economics emphasizes government intervention, fiscal policy, and sticky prices. - Keynesian economics was developed as a response to the perceived failures of neoclassical economics during the Great Depression, which questioned the self-correcting nature of markets. However, it is possible to be a neoclassical Keynesian in the sense that an economist might accept the neoclassical principles when explaining microeconomic behavior while adopting Keynesian theories when dealing with macroeconomic issues. In other words, one can combine the two theories under specific circumstances, seeing government intervention as a temporary solution during economic crises.

To conclude, it's not a logical contradiction to be a neoclassical Keynesian. Although the two theories do have some contrasting principles, an economist can adopt both approaches, applying neoclassical principles to microeconomic behavior while adopting Keynesian policies to address macroeconomic instability and involuntary unemployment during economic crises. So, they can coexist under certain conditions, and reconciling the two theories is not logically contradictory.