Two manufacturing firms are located on the banks of the Crimea River.
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.
Consider the profit of Maissahger Brewery when both Riditna Paper and the brewery choose their optimal outputs PRIVATELY (Riditna ignores the effect of its effluent-generation and disposal on the brewery). Call this Profit-Private. Now, consider the profit of the brewery if both Riditna Paper and Maissahger Brewery produced the socially optimal (surplus-maximizing) outputs of paper and beer. Call this Profit-Social
What is the difference between Maissahger's Profit-Social and Maissahger's Profit-Private?