Consider the following abatement cost functions (TCAₒ) and MCAₒ) for a firm using an old abatement (Aₒ) technology:

TCAₒ = 1000 +0.25(Aₒ)² MCAₒ = 0.5(Aₒ)

where A is units of abatement undertaken by the firm, and the cost values are in thousands of dollars. Further assume that the regulatory authority has set an abatement standard (Aₛₜ) equal to
50 units for each firm and has proposed an emission charge implemented as a constant per unit tax (t) of $10 (i.e., MT = 10), where Total Tax = t(Aₛ - ₜA;), and Aᵢ; is the existing abatement level.

If the state enacts the emission charge, find the associated cost savings to the firm (because they do not have to abate all 50 units), assuming the use of the old technology.