(* The Relationship Between Ramsey Pricing and Optimal Nonlinear Pricing *)

<<Pricing`



E1[x_, d_DemandSystem] := Module[{price, entry, soln},

      price = Array[p, Length[x]];

      entry = Array[e, Length[x]];

      soln = 

        First[Solve[(# == 0) & /@ 

              Join[IR1[price, entry, d], DIC1[price, entry, d]], entry]];

      (entry /. soln) /. e[i_] :> x[[i]]];



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

objective = 

    Plus @@ (IndirectUtility[price, demandsystem4] - 

          price Demands[price, demandsystem4] - E1[price, demandsystem4]);

vars = price;

ineq = {};

eq = {Profit1[price, E1[price, demandsystem4], demandsystem4, 

        costfunction9]};

KTMax[objective, vars, ineq, eq]



O2[x_, d_DemandSystem] := Module[{quant, outlay, soln},

      quant = Array[q, Length[x]];

      outlay = Array[o, Length[x]];

      soln = 

        First[Solve[(# == 0) & /@ 

              Join[IR2[quant, outlay, d], DIC2[quant, outlay, d]], 

            outlay]]; (outlay /. soln) /. q[i_] :> x[[i]]];



quant = Array[q, 4]; outlay = Array[o, 4];

objective = 

    Plus @@ (Utility[quant, demandsystem4] - O2[quant, demandsystem4]);

vars = quant;

ineq = {};

eq = {Profit2[quant, O2[quant, demandsystem4], demandsystem4, 

        costfunction9]};

KTMax[objective, vars, ineq, eq]