Profits:=v-( α p-e (1-α)p+cs)

Profitv:=α p-e (1-α)p-(1-e)θ-k*(e*e)-cv

Profitv

Profitv

D[Profitv,e]

Factor[-2 e k-p (1-α)+θ]

Solve[-2 e k-p (1-α)+θ==0,e]

e:=((-p+p α+θ)/(2 k))

e

Profitv

D[Profitv,p]

Simplify[-((p (1-α) (-1+α))/(2 k))+α+(((-1+α) θ)/(2 k))-(((1-α) (-p+p α+θ))/(2 k))-(((-1+α) (-p+p α+θ))/(2 k))]

((p (((-1+α))^2)+2 k α+(-1+α) θ)/(2 k))

Solve[((p (((-1+α))^2)+2 k α+(-1+α) θ)/(2 k))==0,p]

{{p->((-2 k α+θ-α θ)/(((-1+α))^2))}}
p:=((-2 k α+θ-α θ)/(((-1+α))^2))

e:=((-p+p α+θ)/(2 k))

e

p

((-2 k α+θ-α θ)/(((-1+α))^2))
Profits:=v-( α p-e (1-α)p+cs)

Profits

Simplify[-cs+v-((α (-2 k α+θ-α θ))/(((-1+α))^2))+(((1-α) (-2 k α+θ-α θ) (θ-((-2 k α+θ-α θ)/(((-1+α))^2))+((α (-2 k α+θ-α θ))/(((-1+α))^2))))/(2 k (((-1+α))^2)))]

Profits:=v-( α p-e (1-α)p+cs)

e:=((-p+p α+θ)/(2 k))

Profits

Simplify[-cs+v-p α+((p (1-α) (-p+p α+θ))/(2 k))]

D[-cs+v-p α-((p (-1+α) (p (-1+α)+θ))/(2 k)),p]

Simplify[-((p (((-1+α))^2))/(2 k))-α-(((-1+α) (p (-1+α)+θ))/(2 k))]

Solve[((-2 p (((-1+α))^2)-2 k α+θ-α θ)/(2 k))==0,p]

D[-cs+v-p α-((p (-1+α) (p (-1+α)+θ))/(2 k)),α]

Simplify[-p-(((p^2) (-1+α))/(2 k))-((p (p (-1+α)+θ))/(2 k))]

Solve[-((p (2 k+2 p (-1+α)+θ))/(2 k))==0,α]

Solve[{-((p (2 k+2 p (-1+α)+θ))/(2 k))==0,((-2 p (((-1+α))^2)-2 k α+θ-α θ)/(2 k))==0},{p,α}]

Profitc=v-cs-cv-(1-e)θ-k*e*e

Profitc

D[Profitc,e]

Solve[-2 e k+θ==0,e]

e:=(θ/(2 k))

Profitc=v-cs-cv-(1-e)θ-k*e*e

Simplify[Profitc]

Solve[-cs-cv+v-θ+((θ^2)/(4 k))==0,v]

e:=((-p+p α+θ)/(2 k))

e

Profits:=v-( α p-e (1-α)p+cs)

Profits

D[-cs+v-p α+((p (1-α) (-p+p α+θ))/(2 k)),α]