Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Consider a Cournot game with $2$ firms. Firm $i$ has constanct marginal cost $C_i$, where $C_1 \lt C_2$. Inverse demand is linear: $p(q)=A-q$ (where $A \gt 2C_2 - C_1$). Find the Nash Equilibrium.

share|cite|improve this question

Firstly you have to calculate the profit function (assuming no fixed cost). $$\pi(q_i,q_j)=p(q_i+q_j)\cdot q_i - c_i \cdot q_i=(A - q_i-q_j - c_i)\cdot q_i$$In order to find the Nash equilibrium, both functions $\pi(q_i,q_j)$ and $\pi(q_j,q_i)$ must be maximized. Taking the partial derivatives: $$\frac{\partial \pi(q_i,q_j)}{\partial q_i}=0 \ , i=1,2$$ you obtain the Nash equilibrium: $$q_1^{*}=\frac{A+C_2-2C_1}{3}$$ $$q_2^{*}=\frac{A+C_1-2C_2}{3}$$

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.