Mathematical Economics for Theory of Social Common Capital(Chapter 5: Global Warming)
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 5: Global Warming
In the 3rd and 4th chapter, we learned about dynamic optimization problems in discrete time and continuous time. In this chapter, we will introduce a model of global warming that Uzawa discussed in his “Economic Analysis”. In today’s society, people consume many goods, but the production and distribution processes of these goods generate large amounts of greenhouse gases as a byproduct. These greenhouse gases lead to global warming, which will (and already does today) cause us suffering through extreme weather events and large-scale disasters in the future. Thus, global warming has a structure where “the more we consume and improve our quality of life today, the more greenhouse gases are emitted, making future life harder.” Uzawa described this structure as a dynamic optimization problem in ”Economic Analysis” and discussed what kind of institutional design would be necessary to achieve a sustainable society from the perspective of global warming. This session will introduce the introductory part of that discussion.
*Please see PDF file for full text and details.
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