Mathematical Economics for Theory of Social Common Capital(Chapter2: Kuhn-Tucker conditions)
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, 2023Fishing commons
Forest commons
Agriculture commons
Global warming
2 Chapter2:Kuhn-Tucker conditions
Introduction
This time, we will discuss the Kuhn-Tucker condition, which is an application of the Lagrangian multiplier method. The Lagrangian multiplier method, which we learned last time, is a method for solving maximization problems under equality constraints. The Kuhn-Tucker condition is an extension of this method to inequality constraints. Before we move on to the Kuhn-Tucker condition, let us first review Lagrangian method. In the previous section, we considered a two-variable maximization problem, and here we will consider a three-variable maximization problem. The problem is as follows.
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