(* Demand Compatible and Ramsey Pricing *)



<<Pricing`

Profit[p_, d_DemandSystem, c_CostFunction] :=

    p.Demands[p, d] - Cost[Demands[p, d], c];

costfunction8 = QuadraticCostFunction[10, {1, 1, 1, 1},

    IdentityMatrix[4] + Table[.1, {4}, {4}]]



price = Array[p, 4]

KTMax[Profit[price, demandsystem2, costfunction8], price, {}, {}]



price = Array[p, 4];

startvals = Table[0, {Length[price]}];

eqn = (D[Profit[price, demandsystem2, costfunction8], #] == 0) & /@ price;

solution = Apply[FindRoot, Join[{eqn},

        Transpose[{price, Table[0, {Length[price]}]}]]];

price /. solution



price = Array[p, 4];

IndirectUtility[price, demandsystem2]



KTMax[IndirectUtility[price, demandsystem2], price, {},

  {Profit[price, demandsystem2, costfunction8]}]



price = Array[p, 4];

startvals = Append[Table[0, {Length[price]}], 1];

lagrangian = IndirectUtility[price, demandsystem2] +

      lam Profit[price, demandsystem2, costfunction8];

eqn = (D[lagrangian, #] == 0) & /@ Join[price, {lam}];

solution = Apply[FindRoot, Join[{eqn},

        Transpose[{Append[price, lam], startvals}]]];

price /. solution