We directly observed a Cobb–Douglas symmetric plane using the index of surface openness, which is used in geography, and successfully identified it. Based on this observation, we measured the capital shares (capital elasticity) and labor shares (labor elasticity) and compared them with the results of multiple regression analysis used in economics. We confirmed consistent agreement in seven countries: Japan, Germany, France, Spain, Italy, the UK, and the Netherlands. Thus, we show that the Cobb–Douglas production function can be clearly captured in empirical data as a geometric entity with a quasi-inverse symmetry of variables. Based on the above discussion, we theoretically clarified why the Cobb–Douglas production function is better fitted to empirical data in economics, because it uniquely derives the fact that its variable follows a power-law distribution.

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为什么生产函数采用Cobb–Douglas形式？

我们使用在地理学中使用的表面开放指数直接观察了Cobb–Douglas对称平面，并成功地对其进行了识别。基于此观察，我们测量了资本份额（资本弹性）和劳动力份额（劳动弹性），并将它们与经济学中使用的多元回归分析的结果进行了比较。我们确认了七个国家/地区的一致同意：日本，德国，法国，西班牙，意大利，英国和荷兰。因此，我们证明了Cobb–Douglas生产函数可以在经验数据中清晰地捕获为具有准逆对称变量的几何实体。基于以上讨论，我们从理论上阐明了为何Cobb–Douglas生产函数更适合经济学的经验数据，