Cournot Model:<?xml:namespace prefix = o ns = \"urn:schemas-microsoft-com:office
ID: 1187996 • Letter: C
Question
Cournot Model:<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
P= 1,100 - 2Q
TC = 20qi
Note: Q = q1 + q2
1. Construct the Cournot profit function. Differentiate this function and solve for the reaction functions of firm one and firm two.
2. Consider the following general reaction function: qi = Ri (qj)
a. What is the Nash equilibrium level of output for firm i?
b. What is the Nash equilibrium level of output for firm j?
c. What is the Nash equilibrium level of output for the industry?
d. Suppose that firm one were attempting to prevent firm two from entering the market.
Howmuch output must firm one threaten to produce in order to cause firm two to stay
out of the market?
e. Consider your answer to part d, is this threat credible? Explain the rational for your
answer.
3. Is the Cournot equilibrium preferable to the monopoly equilibrium? How do we know this?
Explanation / Answer
Profit function = P*Q-TC = (100-2Q)Q-20Q= 80Q-2Q^2 Differentiating it, we get= 80-4Q Reference: This is easy to understand numerical example. http://old.econ.ucdavis.edu/faculty/bonanno/teaching/121/Cournot.pdf