Riditna Paper withdraws river water for use in its paper mill, and returns it, along with waste effluent, back into the river. (Effluent is a co-product of Riditna's paper, such that production of each ream of paper generates a specific amount of waste.)
Two kilometers downstream from the paper mill, Maissahger Brewery produces beer using water from the river.
Riditna Paper receives $336 for each reem of paper produced, and its production cost rises non-linearly with output. Riditna Paper's (weekly) profit function is πR(R)=336R-6R2 where "R" represents output of paper in reams.
The effluent discharged by Riditna's paper mill increases the costs borne by Maissahger Brewery, as the water must be purified before it can be used in the brewing process. The cost of purification can be represented as a quadratic function of the "filth" of the river water: CPurify = 2R2 (this is a function of Riditna's output, since the greater the amount of paper produced, the greater the amount of effluent in the river).
Maissahger receives $192 for each cubic meter "keg" of beer it produces, and its own production cost, net of purification cost, is a quadradic function of the amount of beer produced.
The (weekly) profit function of Maissahger Brewery is πM(K||R)=192K-4K2-2R2 where "K" represents beer output in cubic-meter kegs, and "R" represents quantity of paper produced upstream by Riditna Paper.
As Riditna Paper was located on the river before the brewery, it is judged by the Board of Directors of Maissahger Brewery to have prior claim on the river. Norm Christensen, one of the younger directors, proposes paying Riditna Paper a specific sum each period in exchange for reducing its output to the socially-optimal amount. Another director, Otto Postinger, agrees, but is adamant that the payment to Riditna not be "overly generous, we pay enough to encourage them to make the change..but we're not paying a king's ransom."
Assume Riditna Paper is amenable to negotiation. Of the following five amounts, what is the SMALLEST payment the paper firm would accept as compensation for altering its output to the sociallly-optimal quantity?