Government Reserve of Rare Earths under Total Quota Management: An Interactive Game between Government and Rare-Earth Firms

The total quota control and reserve of rare earths are important means for the sustainable development and utilization of rare-earth resources. Focusing on the government reserve of rare-earth products under stochastic demand, this paper analyses the interactive decisions of the government and the rare-earth firms from a game-theoretic perspective. The government determines the total quantity, reserve quantity and reserve–release quantity of the rare-earth products to maximize social warfare, while the firm decides the price of rare-earth products to maximize its own profit. The results show that the production cost and the expected net present value (NPV) of the reserve are important factors affecting the government’s decisions. When the expected NPV of the reserve is below a threshold, the government adopts the no-reserve strategy: it determines only a total quota index that maximizes the current-period social welfare but keeps no reserve. When the expected NPV of a reserve is higher than the above threshold but lower than the production cost, the government adopts the low-reserve strategy: it determines a total quota index and a low reserve that are both in increasing in the expected NPV of reserve, and will release the reserve as many as possible if there is a supply shortage. When the expected NPV of a reserve is higher than both the above threshold and the production cost, the government adopts the high-reserve strategy: it sets a total quota index which is sufficiently large to cover the entire market demand, reserves a large amount, and releases part of the reserve to completely fill the demand gap (if any).