Purpose of Comparative Static Analysis in Economics:
Comparative static analysis is a method used in economics to compare different equilibrium positions. It focuses on the changes in variables and their effects on the equilibrium state of the system. This analysis is essential in understanding the relationships between economic variables and determining the impact of changes in these variables on the overall equilibrium of an economic model.

Comparing Equilibrium Positions:
Comparative static analysis allows economists to compare one equilibrium position with another. It helps in understanding how changes in variables affect the equilibrium outcomes and allows for the identification of the direction and magnitude of these changes. By comparing different equilibrium positions, economists can assess the effects of various policy changes, external shocks, or other factors on the economic system.

Understanding Changes in Variables:
Comparative static analysis focuses on the changes in variables rather than analyzing the time path of these variables. It helps in understanding the impact of changes in exogenous variables on the endogenous variables and the resultant equilibrium position. By studying these changes, economists can gain insights into the behavior of the economic system and make predictions about its future performance.

Assessing Policy Implications:
Comparative static analysis is particularly useful in assessing the implications of different economic policies. By comparing the equilibrium positions before and after the implementation of a policy change, economists can evaluate the effectiveness and efficiency of the policy. This analysis helps policymakers make informed decisions by considering the potential outcomes and consequences of their policy choices.

Limitations:
While comparative static analysis provides valuable insights, it has certain limitations. It assumes that the economic system is in a state of equilibrium before and after the change in variables. It does not capture the dynamic relationships and the adjustment process that occurs over time. To fully understand the behavior of the economic system, dynamic analysis is required, which considers the time path of variables and their interdependencies.

In conclusion, comparative static analysis in economics serves the purpose of comparing different equilibrium positions to understand the effects of changes in variables on the overall equilibrium state. It helps in assessing policy implications, understanding the behavior of the economic system, and making predictions about its performance. However, it should be complemented with dynamic analysis to capture the full complexity of economic relationships over time.