(* Surplus Maximizing Nonlinear Tariffs *)

<<Pricing`



Profit2[q_, r_, d_DemandSystem, c_CostFunction] := Plus @@ r - Cost[q, c]

CS2[q_, r_, d_DemandSystem] := Utility[q, d] - r

IR2[q_, r_, d_DemandSystem] := Take[CS2[q, r, d], 1]

DIC2[q_, r_, d_DemandSystem] := 

  Take[CS2[q, r, d] - 

      CS2[RotateRight[q], RotateRight[r], d], -(Length[q] - 1)]

UIC2[q_, r_, d_DemandSystem] := 

  Take[CS2[q, r, d] - CS2[RotateLeft[q], RotateLeft[r], d], (Length[q] - 1)]



In[48]:=

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

objective = Plus @@ CS2[quant, outlay, demandsystem4];

vars = Join[quant, outlay];

ineq = IR2[quant, outlay, demandsystem4];

eq = Join[

      DIC2[quant, outlay, 

        demandsystem4], {Profit2[quant, outlay, demandsystem4, 

          costfunction9]}];

KTMax[objective, vars, ineq, eq]



In[54]:=

objective = Profit2[quant, outlay, demandsystem4, costfunction9];

vars = Join[quant, outlay];

ineq = {};

eq = Join[IR2[quant, outlay, demandsystem4], 

      DIC2[quant, outlay, demandsystem4]];

KTMax[objective, vars, ineq, eq]



In[59]:=

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

demandsystem5 = NonlinearDemandSystem[{20, 40, 60, 80}, {2, 2, 2, 2}];

Demands[price, demandsystem5]



In[62]:=

objective = Profit1[price, entry, demandsystem5, costfunction9];

vars = Join[price, entry];

ineq = {};

eq = Join[IR1[price, entry, demandsystem5], 

      DIC1[price, entry, demandsystem5]];

soln = KTMax[objective, vars, ineq, eq]



In[67]:=

Demands[price, demandsystem5] /. Last[Last[soln]]



In[68]:=

price = Drop[price, 2]; entry = Drop[entry, 2];

demandsystem6 = NonlinearDemandSystem[{60, 80}, {2, 2}];

costfunction10 = QuadraticCostFunction[400, {1, 1}, Table[0, {2}, {2}]];

objective = Profit1[price, entry, demandsystem6, costfunction10];

vars = Join[price, entry];

ineq = {}; eq = 

  Join[IR1[price, entry, demandsystem6], DIC1[price, entry, demandsystem6]];

KTMax[objective, vars, ineq, eq]



In[75]:=

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

objective = Profit2[quant, outlay, demandsystem5, costfunction9];

vars = Join[quant, outlay];

ineq = Take[quant, 2];

eq = Join[IR2[quant, outlay, demandsystem5], 

      DIC2[quant, outlay, demandsystem5]];

KTMax[objective, vars, ineq, eq]