Measuring the shortage cost through deprivation and envy in collaborating contract between the local authority and the enterprise

Collaboration between the local authority and the enterprise is important when facing more frequent disasters and pandemics, and contract design is a key step. However, most designed contracts in relevant studies fail to precisely measure the shortage cost of relief supplies as they ignore the perceptions of victims, i.e., deprivation due to lacking relief supplies and envy due to unequal allocation. To fill the research gap, in this paper, we use the sum of deprivation (measured by deprivation cost, Holguin-Veras et al. (2012)) and envy (measured by negative inequity aversion, Fehr and Schmidt (1999)) to calculate the shortage cost in contract design between the local authority and the enterprise. We then analyze three different contexts (i.e., low-risk, high-risk, mixed) based on the background of Covid-19 lock-down in China and conduct a corresponding numerical experiment. The result shows that through a Stackelberg game the local authority and the enterprise can reach an agreement. Furthermore, deprivation and envy have the same effect on the contract design, based on which the local authority will decrease the relief items shortage to mitigate the suffering of victims, thus represents a ‘people-centered’ idea.