The strategic interaction between a company and the government surrounding disasters

We analyze the tradeoff between safety and production. The government chooses safety effort and tax rate in the first stage, and then the company strikes a balance between safety effort and production in the second stage. The government, representing the general public, earns taxes on production. Both players’ safety efforts mitigate the negative impact of a disaster. The disaster probability is modeled as a contest between the disaster magnitude and the two players’ safety efforts. Seven propositions are developed. First, as the safety effort of one player approaches infinity, the marginal change in the other player’s safety effort, with respect to the first player’s safety effort, approaches zero. Second, an infinitely large safety effort by any player causes the disaster probability and the negative impact of the disaster to decrease toward a constant. Third, as one player’s safety effort approaches infinity, the other player’s safety effort approaches zero. Fourth, the two players’ safety efforts are strategic substitutes so that an increase in one player’s safety effort decreases the other player’s safety effort. This enables the players to free ride on each other’s safety efforts. Fifth, higher tax rate causes the company to exert higher safety effort. Sixth, with maximum tax rate the company focuses exclusively on safety effort and generates no profit. Seventh, the company’s safety effort is inverse $$U$$ U shaped in the disaster magnitude.