Cournot Model with Asymmetric Information

- Suppose the inverse demand function is P(Q) = 30 0.2 (Qjoe + Qsarah)

- Joe has a constant marginal cost of $10, known to both

- Joe's expectation about Sarah's constant marginal cost is:

C2=12 with probability 0.6

8 with probability 0.4

Question 1(a): Solve for the above Cournot-Nash equilibrium with asymmetric

information with Sarah as a high cost supplier (C2 = 12 ... unknown to Joe)

Question 1(b): Solve for the above Cournot-Nash equilibrium with asymmetric

information with Sarah as a low cost supplier (C2 = 8 ... unknown to Joe)

Question 1(c): Solve for the above Cournot-Nash equilibrium with complete

information with Sarah as a high cost supplier (C2 = 12 ... known to Joe)

Question 1(d): Solve for the above Cournot-Nash equilibrium with complete

information with Sarah as a low cost supplier (C2 = 8) ... known to Joe)

Question 1(e): If Sarah is a low cost supplier, what is the maximum she would be willing to spend to convince Joe of her cost ?