The question of formulation of a social planner criterion for an imperfect economy is examined using an example of a polluting economy negatively affected by growing temperature. Imperfection of the economy is expressed here in deviations from the optimal initial state. It is shown that a criterion not linked to a specific initial state almost always implies either unsustainable or inefficient paths in the economy. In this paper, I link the constant-utility criterion to the initial amount of the resource reserve. This criterion implies efficient resource use and the paths of utility asymptotically approaching some constants, which depend on the parameters of the temperature function. The criterion can be formulated for the cases when the reserve estimate changes over time and when the high level of temperature can cause extinction.