Mathematical Economics for Theory of Social Common Capital(Chapter 7: Structural Estimation on Natural Capital)

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

1. Lagrange multiplier method and imputed price
   • Apr 30, 2023

2. Kuhn-Tucker conditions
   • May 20, 2023

3. Dynamic programming
   • June 17, 2023

4. Optimal investment and Penrose function
   • Sep 17, 2023

5. Global Warming
   • March 17, 2024

6. Saddle Point Solution
   • May 19, 2024

7. Structural Estimation on Natural Capital
   • December 1, 2024

2 Chapter 7: Structural Estimation on Natural Capital

1 Overview of Modern Economics

Economics is broadly classified into two approaches: theoretical economics and empirical economics.
Theoretical economics seeks to analytically understand economic mechanisms using mathematical models, while empirical economics aims to validate theories and estimate causal relationships using data.

1.1 Classification of Economics

Modern economics can be categorized as follows:

• Theoretical Economics

  • Fundamental Theory

    • Game Theory

  • Applied Theory

    • Spatial Economics, International Trade, Industrial Organization, . . .

• Empirical Economics

  • Reduced-form Approach

    • Conducts Randomized Controlled Trials (RCT).

    • Utilizes natural experiments, where exogenous shocks or policy changes create treatment and control groups in a near-random manner.

      • Example: Analyzing the effect of minimum wage increases using the difference between New Jersey and Pennsylvania.

      • Example: Using the distance from the former East-West German border to study trade costs and economic growth.

  • Structural Estimation

    • Constructs economic models and derives equilibrium analytically.

    • Estimates model parameters to ensure consistency with observed data.

    • Conducts counterfactual simulations to evaluate policy interventions.

      • Example: Simulating the impact of subsidies for environmentally friendly production equipment.

*Please see PDF file for full text and details.