Overshifting by a single-price monopolist

TheoryGuru applications

Load Economicreasoning package only if it is not already loaded

If[Length@Names["PLTools`*"]<10,
Get["http://economicreasoning.com"]]

Setup

profits[q,a]:=q W[q]-g[q,a]

ProfitsAreMaximized={((\[DifferentialD]((∂profits(q,a))/(∂q)))/(\[DifferentialD]a))==0,(((∂^2)profits(q,a))/(∂(q^2)))<0};

BasicAssumptions={W'(q)<0(* Demand slopes down *),
(((∂^2)g(q,a))/(∂(q^2)))≥ 0(* MC does not *),
(((∂^2)g(q,a))/(∂q ∂a))> 0(* a increases MC (a definition) *),
q>0};

ConcaveDemand=W''(q)≤0;

PassThroughRate=((\[DifferentialD]W(q))/(\[DifferentialD]a))/(((∂^2)g(q,a))/(∂q ∂a));

Result

TheoryGuru[{ConcaveDemand,ProfitsAreMaximized,BasicAssumptions},
PassThroughRate<1]

Variable interpretations