Conflict between plot and inequal

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Question:Conflict between plot and inequal

Posted: RezaZanjirani 40 Product: Maple 2021

October 19 2023

Dear Maple experts

I face an issue in using ‘implicit plot’ or ‘inequal’ commands in the attached file.

I use three Maple procedures to make some simple calculations and draw an output. It is Firm Profit versus ‘alpha’. This graph is correct and makes perfect sense.

Then, I use ‘inequal’ command to compare the same outputs when ‘alpha’ and ‘delta’ change. There is a conflict between these plots and the above diagram. For example, P2 plot says

FirmModelPP := proc (alpha, beta, delta) local p0, xi0, q0, Firmpf0, G01, Recpf0, Unsold0, Environ0; xi0 := 1; p0 := min(s+sqrt((v-s)*(c-s)), delta*v+sExp); q0 := u*(v-p0)/(v-s); f(N) := 1/u; F(N) := N/u; G01 := int(F(N), N = 0 .. q0); Firmpf0 := (p0-c)*q0-(p0-s)*G01; Recpf0 := (sExp-cr)*xi0*q0; Unsold0 := G01; Environ0 := q0+Unsold0; return p0, q0, Firmpf0, Recpf0, Environ0, Unsold0 end proc

$FirmModelHmax := proc (alpha, beta, delta) local q, p, pr, FirmpfSiS, F1, G1, G2, G3, RecpfSiS, sol, UnsoldSiS, EnvironSiS, p0, OldSoldPrim, xi, h, ps, qs, prs, prof1m, prof2m; option remember; xi := 1; prs := ps-delta*v; prof1m := (ps-c)*qs+((1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))-(1/2)*(1+beta*xi)^2*qs^2/u)*(ps-s)+(prs-sExp)*(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))); prof2m := (ps-c)*qs-(1/2)*(ps-s)*qs^2/(alpha*u)+(prs-sExp)*(beta*xi*qs-(1/2)*beta^2*xi^2*qs^2/(u*(1-alpha))); if alpha <= 1/(1+beta*xi) then p, q := (eval([ps, qs], solve({diff(prof1m, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps, qs < 2*u*(1-alpha)/(beta*xi)}, [ps, qs])[1]))[]; `h&Assign;`*(p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof1m, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := (sExp-cr)*xi*q; UnsoldSiS := (1/2)*(1+beta*xi)^2*q^2/u-(1/2)*beta^2*xi^2*q^2/(u*(1-alpha)); EnvironSiS := q+UnsoldSiS else p, q := (eval([ps, qs], solve({diff(prof2m, qs) = 0, qs = alpha*u*(v-ps)/(v-s), c < ps, sExp+delta*v < ps, qs < 2*u*(1-alpha)/(beta*xi)}, [ps, qs])[1]))[]; h := (p-delta*v-sExp)/(p-delta*v); FirmpfSiS := eval(prof2m, [ps = p, qs = q, prs = p-delta*v]); RecpfSiS := (sExp-cr)*xi*q; UnsoldSiS := (1/2)*q^2/(alpha*u); EnvironSiS := q+UnsoldSiS end if; return p, q, FirmpfSiS, RecpfSiS, EnvironSiS, UnsoldSiS, h, OldSoldPrim, xi end proc$

pltPP3A := plot('FirmModelPP(alpha, .35, .40)[3]', alpha = 0. .. 1.0, color = red, legend = "", style = pointline, labels = [alpha, "Firm Profit"], labeldirections = ["horizontal", "vertical"], symbolsize = 10, axes = boxed, symbol = box, numpoints = 10, adaptive = false, thickness = 1.0, view = [0 .. 1, 0 .. .18])

pltPP3B := plot([[0., eval('FirmModelPP(0., .35, .40)[3]', alpha = 0.)]], color = red, legend = ["PP"], style = point, symbol = box, symbolsize = 10, axes = boxed, view = [0 .. 1, 0 .. .18])

pltFC3A := plot('FirmModelFC(alpha, .35, .40)[3]', alpha = 0. .. 1, linestyle = [solid], color = black, legend = "FC", labels = [alpha, "Firm Profit"], labeldirections = ["horizontal", "vertical"], axes = boxed, adaptive = false, thickness = .7, view = [0 .. 1.0, 0 .. .18])

pltHmax3A := plot('FirmModelHmax(alpha, .35, .40)[3]', alpha = 0. .. 1.0, linestyle = [dashdot], color = brown, legend = [SiS(h__max)], labels = [alpha, "Firm Profit"], labeldirections = ["horizontal", "vertical"], symbolsize = 10, numpoints = 50, adaptive = false, thickness = 1.0, axes = boxed, view = [0 .. 1, 0 .. .19])