Market entry with Cournot/Stackelberg: Demand function

Question

Hello,

I have to create an own problem set concerning Market entry with Cournot / Stackelberg.

I should not use a linear inverse demand function (i.e. P(Q) = a - bQ) and was wondering what other type of functions would work out with the said models.

I would highly appreciate your help.

Answer 1

Try using a constant elasticity of demand P=AY^(1/ε) With ε <-1. This Has Total Revenue forevever increasing at a decreasing rate.. You can Incorporate non linear cost functions. . Take second order Taylor expansion about A/ε about You will get a quadratic prof function and quadratic reaction functions. That should be mathematical enough for your professor