(Note that second page has some partial answers so that you can check yourself. I think these are correct, but I did it quickly. So I will offer one bonus point per mistake for the first person who finds the mistake in my answers with a maximum of 3 points per student.):
1) Demand is given by P=100-Q/2. Two firms compete according to the Cournot model and each has TC=10q. What profit does each firm earn? How would your answer change if the second firm observed the first firm’s decision (this is the Stackleberg problem)?
2) Demand is given by P=80-2Q. There are three identical firms each with TC=10. Find the profit of a firm if they each pick quantity simultaneously (Cournot). Find the Profit of a firm if the each pick price simultaneously (Bertrand).
3) Suppose there are n firms that compete according to the Cournot model and that each has MC = C. If demand is given by P=A-BQ, what profits will a firm earn? What would a cartel do?
4) Factory 1 has TC=20q +10 and Factory 2 has TC=10q. If both factories are operated by rivals who compete according to the Cournot model, what profits would each earn assuming that demand is given by P=180-Q? If this was one firm (a cartel) what would it do (hint: if the one firm decided to operate both factories it would want MC to be the same at both locations or else it could increase profits my shifting where it produced)?
5) Firm 1’s demand is given by P=49-q1+0.25q2 and Firm 2’s demand is given by P=49-q2+0.25q1. If TC=q2 +5 for each, what profit will each firm earn? What kinds of goods are the two firm’s selling?
1) q1=60 and q2=60 for Cournot while q1=90 and q2 = 45 for Stackleberg. 2) Under Cournot, q1= q2 = q3 =10. Under Bertrand, the firms will push price down to 0. 3) Each firm will produce q = (A-C)/[B(n+1)] under the Cournot solution. 4) In the competitive situation, q1=50 and q2= 60.
5) Each firm would make q=13.07.