Welfare maximization with the least subsidy: Pricing model for surface water loop heat pump PPP projects considering occupancy rate growth and coefficient of performance

The surface water loop heat pump (SWLHP) is a renewable energy technology applied to support heating, ventilation and air conditioning (HVAC) systems to address the threat of global warming. However, the operation of SWLHP-PPP projects is challenging because the demand uncertainty brought by occupancy rate growth (ORG) affects SWLHP systems' coefficient of performance (COP), leading to cost uncertainty of the SWLHP-PPP projects. In this paper, we propose an analytical framework to examine how ORG (characterized by the initial occupancy rate, IOR, and the pace of occupancy rate growth, PORG) and COP affect the private sector's and government's pricing and subsidy decisions, respectively. Our findings identify two critical coefficients, the ORG-related coefficient and the COP-related coefficient, which influence the optimal price and government subsidies. Specifically, the optimal price declines with the former but increases in the latter, while the variation patterns of the optimal unit subsidy with respect to these two coefficients are just the opposite. Furthermore, the optimal price's sensitivity to the IOR is relatively stable, whereas that to the PORG decreases in PORG; the optimal unit subsidy and the total subsidy behave similarly. These results caution the private sector and the government to not blindly improve the forecasting accuracy of the PORG as the value of accurate forecasting diminishes with the PORG. Finally, the comparative results show that the lowest total subsidy is afforded by the government when both the COP and ORG are considered.