Vehicle Manufacture provide the insurance contract

Profitv2:=(α+r )p+e (1-α)p-(1-e)θ-k*(e*e)-cv-(1-e)l
Profits2:=-(α+r) p+e(f-(1-α)p)-cs+(1-e)l

D[Profitv2,e]

Simplify[-2 e k+l+p (1-α)+θ]

Solve[%==0,e]

e:=((l+p-p α+θ)/(2 k))

Profits2

Simplify[-cs+p (-r-α)+(((f-p (1-α)) (l+p-p α+θ))/(2 k))+l (1-((l+p-p α+θ)/(2 k)))]

D[%,p]

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

Solve[%==0,p]

p:=((f-l-2 k r-f α-2 k α+l α-θ+α θ)/(2 (((-1+α))^2)))
e

Simplify[((l+θ+((f-l-2 k r-f α-2 k α+l α-θ+α θ)/(2 (((-1+α))^2)))-((α (f-l-2 k r-f α-2 k α+l α-θ+α θ))/(2 (((-1+α))^2))))/(2 k))]

if the satellite owner ask for the panelty is f , then the optimal effort is (1/4)(((f+θ+l)/k)-((2r-2α)/(1-α)))