Sustainability of profit and corporate social responsibility: Mathematical modelingwith phase diagram

Business in modern world targets both profit and social responsibility. In the trading-off between making profits and spending for social responsibility, a firm needs to balance these two goals and maintain them in the long-run. Sustainable profit will prevent the firm to fall into the decaying stage of the product life cycle. Sustainable social responsibility will ensure that the business consistently contributes social benefits. This study develops a mathematical model using phase diagram to find a steady state and stable path for a firm to achieve the sustainability of both profit and social responsibility at the same time. It indicates four areas that are crucial to the operation and performance of the firm. They consist of warm glow area, frozen area, charitable area and decayed area. Major results indicate that a firm cannot automatically achieve both sustainable profit and social responsibility at the same time. It needs policy manipulation and well-planned adjustment to move the business to the twin sustainability. Without manipulation, a firm located in warm glow area is expected to achieve only sustainable profit but it cannot easily stop spending for social responsibility. A firm located in frozen area can achieve only sustainable profit too but it has to shrink its social responsibility. The society will enjoy a firm located in charitable area when it spends too much for social responsibility and face the risk of bankruptcy. When the firm is located in the decayed area, it will face the downfalls of both the profit and expenditure for social responsibility.