The operation of a Carnot heat pump is viewed as a production process with exergy as its output. The short-run economic optimization ol the endoreversible heat pump is performed in this paper. The profit of the heat pump is taken as the optimization objective function. Using the method of finite-time exergoeconomic analysis, which emphasizes the compromise optimization between economics (profit) and the utilization factor of energy (Coefficient of Performance, COP) for finite-time (endoreversible) thermodynamic cycles, this paper derives the relation between optimal profit and COP of an endoreversible Carnot heat pump based on a relatively general heat transfer law: q proportional to Delta(T-n). The COP bound at the maximum profit is also obtained. The results obtained involve those for three common heat transfer laws: Newton＇s Law (n = 1), the linear phenomenological law in irreversible thermodynamics (n = -1), and the radiative heat law (n = 4).