Mathematical Economics for Theory of Social Common Capital(Chapter 6: Saddle Point Solution)
1 Introduction
1.1 Summary
In constructing his theory of social common capital, Hirofumi Uzawa modeled it through mathematical economics as well as he discussed in a institutional-school analysis through natural language. The basic concept of his model is “how to make evaluate something that cannot be priced, such as the natural environment, in a price manner.” Uzawa approached this problem using the idea of “shadow pricing” in dynamic optimization.
Shadow pricing is an application of the Lagrange multiplier method which we often use real analysis. In this lecture, starting from the Lagrange multiplier method with high school mathematics as a prerequisite, we will discuss the theory of dynamic optimization and then read Uzawa’s mathematical paper on the theory of social common capital.
1.2 Schedule
Lagrange multiplier method and imputed price
• Apr 30, 2023Kuhn-Tucker conditions
• May 20, 2023Dynamic programming
• June 17, 2023Optimal investment and Penrose function
• Sep 17, 2023Global Warming
• March 17, 2024Saddle Point Solution
• May 19, 2024Fishing commons
Forest commons
Agriculture commons
2 Chapter 6: Saddle Point Solution
We have been solving dynamic optimization problems and plotting their solution paths on phase diagrams.
The solutions to the problems we have seen so far in this series are all of a type called saddle point solutions.
In this session, we will explore the properties of these saddle point solutions.
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