(* Optimal Nonlinear Pricing *)



<<Pricing`

demandsystem4 = NonlinearDemandSystem[{20, 25, 30, 35}, {2, 2, 2, 2}]

price = Array[p, 4]

IndirectUtility[price, demandsystem4]

Demands[price, demandsystem4]



quant = Array[q, 4];

Utility[quant, demandsystem4]



Profit1[p_, e_, d_DemandSystem, c_CostFunction] :=

  p.Demands[p, d] + Plus @@ e - Cost[Demands[p, d], c]

CS1[p_, e_, d_DemandSystem] := IndirectUtility[p, d] - p Demands[p, d] - e

IR1[p_, e_, d_DemandSystem] := Take[CS1[p, e, d], 1]

DIC1[p_, e_, d_DemandSystem] := Take[CS1[p, e, d] -

      CS1[RotateRight[p], RotateRight[e], d], -(Length[p] - 1)]

UIC1[p_, e_, d_DemandSystem] := Take[CS1[p, e, d] -

      CS1[RotateLeft[p], RotateLeft[e], d], -(Length[p] - 1)]



costfunction9 = QuadraticCostFunction[400, {1, 1, 1, 1},

    Table[0, {4}, {4}]]



price = Array[p, 4]; entry = Array[e, 4];

objective = Plus @@ CS1[price, entry, demandsystem4];

vars = Join[price, entry];

ineq = IR1[price, entry, demandsystem4];

eq = Join[DIC1[price, entry, demandsystem4],

      {Profit1[price, entry, demandsystem4, costfunction9]}];

KTMax[objective, vars, ineq, eq]



objective = Profit1[price, entry, demandsystem4, costfunction9];

vars = Join[price, entry];

ineq = {};

eq = Join[IR1[price, entry, demandsystem4], 

      DIC1[price, entry, demandsystem4]];

KTMax[objective, vars, ineq, eq]