restart:The standard Cournot model P:=Q->(Gamma-Q);

Zio2I0kiUUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCZJJkdhbW1hR0YlIiIiOSQhIiJGJUYlRiU=

u1:=(q1,q2)->q1*P(q1+q2)-c1*q1;u2:=(q1,q2)->q2*P(q1+q2)-c2*q2;

Zio2JEkjcTFHNiJJI3EyR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiomOSQiIiItSSJQR0YlNiMsJkYsRi05JUYtRi1GLSomSSNjMUdGJUYtRixGLSEiIkYlRiVGJQ==

Zio2JEkjcTFHNiJJI3EyR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiomOSUiIiItSSJQR0YlNiMsJjkkRi1GLEYtRi1GLSomSSNjMkdGJUYtRixGLSEiIkYlRiVGJQ==

eq1:=diff(u1(q1,q2),q1)=0;eq2:=diff(u2(q1,q2),q2)=0;

LywqSSZHYW1tYUc2IiIiIkkjcTFHRiUhIiNJI3EyR0YlISIiSSNjMUdGJUYqIiIh

LywqSSZHYW1tYUc2IiIiIkkjcTFHRiUhIiJJI3EyR0YlISIjSSNjMkdGJUYoIiIh

solve({eq1,eq2},[q1,q2]);

NyM3JC9JI3ExRzYiLChJJkdhbW1hRzYiIyIiIiIiJEkjYzFHNiIjISIjIiIkSSNjMkc2IiMiIiIiIiQvSSNxMkc2IiwoSSZHYW1tYUc2IiMiIiIiIiRJI2MxRzYiIyIiIiIiJEkjYzJHNiIjISIjIiIk

assign([q1,q2],%); factor(u1(q1,q2));factor(u2(q1,q2));P(q1+q2);

LCQqJCwoSSZHYW1tYUc2IiEiIkkjYzFHRiYiIiNJI2MyR0YmRidGKSMiIiIiIio=

LCQqJCwoSSZHYW1tYUc2IiIiIkkjYzFHRiZGJ0kjYzJHRiYhIiMiIiMjRiciIio=

LChJJkdhbW1hRzYiIyIiIiIiJEkjYzFHRiRGJUkjYzJHRiRGJQ==

restart:The Cournot model with uncertain costs. P:=Q->(Gamma-Q);

Zio2I0kiUUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCZJJkdhbW1hR0YlIiIiOSQhIiJGJUYlRiU=

u1:=(q1,q2)->q1*P(q1+q2)-c1*q1;u2:=(q1,q2,c2)->q2*P(q1+q2)-c2*q2;

Zio2JEkjcTFHNiJJI3EyR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiomOSQiIiItSSJQR0YlNiMsJkYsRi05JUYtRi1GLSomSSNjMUdGJUYtRixGLSEiIkYlRiVGJQ==

Zio2JUkjcTFHNiJJI3EyR0YlSSNjMkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCYqJjklIiIiLUkiUEdGJTYjLCY5JEYuRi1GLkYuRi4qJjkmRi5GLUYuISIiRiVGJUYl

expected1:=(q1,q2d,q2u,p)->u1(q1,q2d)*(1-p)+u1(q1,q2u)*p;

Zio2JkkjcTFHNiJJJHEyZEdGJUkkcTJ1R0YlSSJwR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiomLUkjdTFHRiU2JDkkOSUiIiIsJkYzRjM5JyEiIkYzRjMqJi1GLzYkRjE5JkYzRjVGM0YzRiVGJUYl

q2plus:=solve(diff(u2(q1,q2,cplus),q2)=0,q2);

LChJJkdhbW1hRzYiIyIiIiIiI0kjcTFHRiQjISIiRidJJmNwbHVzR0YkRik=

q2minus:=solve(diff(u2(q1,q2,cminus),q2)=0,q2);

LChJJkdhbW1hRzYiIyIiIiIiI0kjcTFHRiQjISIiRidJJ2NtaW51c0dGJEYp

q1star:=solve(diff(expected1(q1,q2d,q2u,p),q1)=0,q1);

LCxJJkdhbW1hRzYiIyIiIiIiI0kkcTJkR0YkIyEiIkYnKiZGKEYmSSJwR0YkRiZGJUkjYzFHRiRGKSomRixGJkkkcTJ1R0YkRiZGKQ==

solve({q2plus=q2u,q2minus=q2d,q1star=q1},[q1,q2d,q2u]);

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

assign([q1,q2d,q2u],%); q1;q2d;q2u;

LCxJJkdhbW1hRzYiIyIiIiIiJEknY21pbnVzR0YkRiVJI2MxR0YkIyEiI0YnKiZJInBHRiRGJkYoRiYjISIiRicqJkYtRiZJJmNwbHVzR0YkRiZGJQ==

LCxJJkdhbW1hRzYiIyIiIiIiJEkjYzFHRiRGJSomSSJwR0YkRiZJJ2NtaW51c0dGJEYmI0YmIiInKiZGKkYmSSZjcGx1c0dGJEYmIyEiIkYtRisjISIjRic=

LC5JJkdhbW1hRzYiIyIiIiIiJEknY21pbnVzR0YkIyEiIiIiJ0kjYzFHRiRGJSomSSJwR0YkRiZGKEYmI0YmRisqJkYuRiZJJmNwbHVzR0YkRiZGKUYxI0YqIiIj

expected1(q1,q2d,q2u,p);

LCYqJiwmKiYsLEkmR2FtbWFHNiIjIiIiIiIkSSdjbWludXNHRihGKUkjYzFHRigjISIjRisqJkkicEdGKEYqRixGKiMhIiJGKyomRjFGKkkmY3BsdXNHRihGKkYpRiosLEYnRilGLEYpRi1GKUYwI0YqIiInRjQjRjNGOEYqRioqJkYtRipGJkYqRjNGKiwmRipGKkYxRjNGKkYqKiYsJiomRiZGKiwuRidGKUYsRjlGLUYpRjBGN0Y0RjlGNSNGKiIiI0YqRipGOkYzRipGMUYqRio=

factor(%);

LCQqJCwsKiZJInBHNiIiIiJJJ2NtaW51c0dGJ0YoRihGKSEiIiomRiZGKEkmY3BsdXNHRidGKEYqSSNjMUdGJyIiI0kmR2FtbWFHRidGKkYuI0YoIiIq

restart:Stackelberg P:=Q->Gamma-Q;

Zio2I0kiUUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCZJJkdhbW1hR0YlIiIiOSQhIiJGJUYlRiU=

u1:=(q1,q2)->q1*P(q1+q2)-c1*q1;u2:=(q1,q2)->q2*P(q1+q2)-c2*q2;

Zio2JEkjcTFHNiJJI3EyR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiomOSQiIiItSSJQR0YlNiMsJkYsRi05JUYtRi1GLSomSSNjMUdGJUYtRixGLSEiIkYlRiVGJQ==

Zio2JEkjcTFHNiJJI3EyR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsJiomOSUiIiItSSJQR0YlNiMsJjkkRi1GLEYtRi1GLSomSSNjMkdGJUYtRixGLSEiIkYlRiVGJQ==

q2br:=q1->solve(diff(u2(q1,q2),q2)=0,q2);

Zio2I0kjcTFHNiJGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJnNvbHZlR0YlNiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JI3UyR0YlNiQ5JEkjcTJHRiVGNSIiIUY1RiVGJUYl

q2br(q1);

LChJJkdhbW1hRzYiIyIiIiIiI0kjcTFHRiQjISIiRidJI2MyR0YkRik=

u1(q1,q2br(q1));

LCYqJkkjcTFHNiIiIiIsKEkmR2FtbWFHRiUjRiYiIiNGJCMhIiJGKkkjYzJHRiVGKUYmRiYqJkkjYzFHRiVGJkYkRiZGLA==

q1star:=solve(diff(u1(q1,q2br(q1)),q1)=0,q1);

LChJJkdhbW1hRzYiIyIiIiIiI0kjYzJHRiRGJUkjYzFHRiQhIiI=

q2star:=q2br(q1star);

LChJJkdhbW1hRzYiIyIiIiIiJUkjYzJHRiQjISIkRidJI2MxR0YkI0YmIiIj

factor(u1(q1star,q2star));

LCQqJCwoSSNjMUc2IiIiI0kmR2FtbWFHRiYhIiJJI2MyR0YmRilGJyMiIiIiIik=

LCYqJiwoSSZHYW1tYUc2IiMiIiIiIiNJI2MyR0YmRidJI2MxR0YmISIiRigsKEYlI0YoIiIlRipGLkYrRidGKEYoKiZGK0YoRiRGKEYs

factor(u2(q1star,q2star));

LCQqJCwoSSZHYW1tYUc2IiIiIkkjYzJHRiYhIiRJI2MxR0YmIiIjRisjRiciIzs=

Entry Deterrence restart: P:=Q->Gamma-Q;

Zio2I0kiUUc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCZJJkdhbW1hR0YlIiIiOSQhIiJGJUYlRiU=

u1:=(q1,q2)->q2*P(q1+q2)-(a*q2+b);

Zio2JEkjcTFHNiJJI3EyR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUsKComOSUiIiItSSJQR0YlNiMsJjkkRi1GLEYtRi1GLSomSSJhR0YlRi1GLEYtISIiSSJiR0YlRjVGJUYlRiU=

q2m:=q1->solve(diff(u1(q1,q2),q2)=0,q2);

Zio2I0kjcTFHNiJGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJnNvbHZlR0YlNiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JI3UxR0YlNiQ5JEkjcTJHRiVGNSIiIUY1RiVGJUYl

q2m(q1);

LChJJkdhbW1hRzYiIyIiIiIiI0kjcTFHRiQjISIiRidJImFHRiRGKQ==

f:=q1->u1(q1,q2m(q1));

Zio2I0kjcTFHNiJGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JI3UxR0YlNiQ5JC1JJHEybUdGJTYjRixGJUYlRiU=

factor(f(q1));

LDAqJEkmR2FtbWFHNiIiIiMjIiIiIiIlKiZGJEYoSSNxMUdGJUYoIyEiIkYmKiRGK0YmRicqJEkiYUdGJUYmRicqJkYkRihGMEYoRiwqJkYrRihGMEYoI0YoRiZJImJHRiVGLQ==

solve(f(q1)=0,q1);

NiQsKEkmR2FtbWFHNiIiIiJJImFHRiUhIiIqJEkiYkdGJSNGJiIiI0YsLChGJEYmRidGKEYpISIj

assign(q1,%[2]); q1;

LChJJkdhbW1hRzYiIiIiSSJhR0YkISIiKiRJImJHRiQjRiUiIiMhIiM=

This value of q1 is the smallest firm 1 production quantity which makes firm 2's profit =0. The lowest quantity gives firm 1 the highest profit. P(q1)*q1-(a*q1+b);

LCgqJiwmSSJhRzYiIiIiKiRJImJHRiYjRiciIiNGK0YnLChJJkdhbW1hR0YmRidGJSEiIkYoISIjRidGJyomRixGJ0YlRidGLkYpRi4=

simplify(%);

LCgqJkkiYUc2IiIiIkkiYkdGJSNGJiIiIyEiIyomRidGKEkmR2FtbWFHRiVGJkYpRichIiY=

restart: De:=q->piecewise(q<10,100-q^2,q>=10,0); C:=q->50+q^2; plot({De(q),C(q)},q=0..15,color=[red,green]); diff(De(q),q); a:=eval( %, [q = 2*q]); qstar:=fsolve(De(2*q)+q*a-diff(C(q),q)=0,q); plot(De(2*q)+q*a-diff(C(q),q),q=0..5); De(qstar); qstar*De(2*qstar)-C(qstar); restart:with(plots): p1:=x->x^3;p2:=x->x^2; v1:=(x,y)->piecewise(x<y,2*p1(x)-1,x=y,p1(x)-p2(x),x>y,1-2*p2(x)); plot3d(v1(x,y),x=0..1,y=0..1,axes=boxed); xstar:=fsolve(p1(x)+p2(x)-1=0,x); v1(xstar,xstar); restart: f:=x->6*x*(1-x); F:=x->int(f(y),y=0..x); fsolve(1-F(x)-x*f(x)=0,x); restart:ode:=a*(y(x)-x)*diff(y(x),x)=y(x); dsolve(ode,y(x));