1. ECON 330 Lecture 26
Thursday, December 27

2. Study questions (with answers) part 1 is posted on webpage
A smaller part 2 will be added later
A review session will be scheduled before the final exam, I will send you an about time and place
Today: Review/tips for the final exam

3. List of topics Perfect competition Monopoly Models of oligopoly
Cournot
Bertrand
Leader-Follower models
Repeated interaction
Entry costs/Market size and market structure
Strategic entry deterrence
Research and development

4. Sample questions solved
Repeated interaction

5. There are three firms in the industry
There are three firms in the industry. All firms have the same discount factor δ < 1. They compete in the style of Bertrand. The market demand: Q(p) = 30 if p ≤ 10, Q(p) = 0 if p > 10. Firm 1’s cost function is c(q) = 2q. Firm 2 and 3 both have the cost function c(q) = 4q.

6. Compute the Bertrand Nash equilibrium of the one- shot game
Compute the Bertrand Nash equilibrium of the one- shot game. Firm 1 (the low cost firm) sets p = … the other two firms set p = 4.

7. Describe the trigger (grim) strategy that the firms can use to support a collusive outcome in which all firms charge the monopoly price in every period in the (infinitely) repeated interaction. Firm 1: In period 1 set p =10. In period t ≥ 2 set p = 10 if all firms have set p = 10 in all past periods. Otherwise set p = … Firm 2 and 3: In period 1 set p =10. In period t ≥ 2 set p = 10 if all firms have set p = 10 in all past periods. Otherwise set p = 4.

8. Compute the range of discount factors for which there is a Nash equilibrium in the repeated game in which the firms use the trigger strategy you described above. We need to worry about the low cost firm. Following the grim strategy brings a profit of 80 in every period. Cheating in period 1 (i.e., setting p = 9.99) and then switching to p = 3.999… in all future periods brings a profit of 240 in period 1 and 60 in each period after.

9. Some more details
Profit with no cheating: 80/(1–δ) Profit with cheating: x[δ/(1–δ)] No cheating is the equilibrium if 80/(1–δ) > x[δ/(1–δ)] This gives us δ > 8/9

10. Sample questions solved
Leader-Follower models

11. There are two firms. Both firms have constant MC and AC of 2
There are two firms. Both firms have constant MC and AC of 2. The inverse demand function is P(Q) = 12 – Q. Firm 1 is the leader, Firm 2 is the follower. Firm 1 sets its quantity in stage 1. In stage 2, firm 2 observes firm 1’s quantity choice, and chooses its quantity.

12. Inverse demand is P = 12 – Q
Start with Firm 2’s profit function P(Q)q2 – 2q2 π2 = [12 − (q1 + q2]q2 − 2q2 Firm 2 wants to maximize its profits. This implies that for any q1 it must choose a best response q2: dπ2/dq2 = 12 − q1 − 2q2 − 2 = 0  q2* = 5 − q1/2

13. Firms 1’s decision problem Choose q1 to maximize π1 = [12 − (q1 + q2
Firms 1’s decision problem Choose q1 to maximize π1 = [12 − (q1 + q2*]q1 − 2q1 Write the profit function with q2* = 5 − q1/2 π1 = [12 − (q1 + 5 − q1/2)]q1 − 2q1 dπ1/dq1 = (10 – q1)q1 = 0 The solution is q1 = 5. Last step: Use q2 = 5 − q1/2 and compute q2 when q1 = 5: q2 = 2.5.

14. Sample questions solved
Entry deterrence

15. The inverse demand is P = 14 − Q
The inverse demand is P = 14 − Q. There is currently one incumbent firm, its cost function is TC(q) = 2q. The entrant has also the same cost function but it must pay an entry cost F. We observe that the incumbent has chosen qI = 6 and the entrant decided not to enter. What is the smallest value of F that is consistent with this observation?

16. Find the best response to qI = 6: πE = [14 − (qI + qE]qE − 2qE πE = [14 − (6 + qE]qE − 2qE dπE/dqE = 8 − 2qE − 2 = 0  qE = 3. Profit with qI = 6 and qE = 3 is πE = [5 − 2]3 = 9 So, F > 9.

17. Sample questions solved
R&D and market structure

18. The market demand is Q(p) = 30 – p. Firm A’s cost function is c(q) = 3q. Firm B’s cost function is c(q) = 4q.
Which of these two firms has a greater incentive to do cost reducing R&D that will bring the cost function to c(q) = 2q.

19. Note that the loser in the R&D race wil have 0 profit
Firm A: R&D brings MC down from 3 to 2 (Firm B has MC = 4) A’s profit if A innovates: (4 – 2)x26 = 52 A’s profit if B innovates: 0 Firm B: R&D brings MC down from 4 to 2 (FirmA has MC = 3) B’s profit if B innovates: (3 – 2)x27 = 27 B’s profit if A innovates: 0

20. On the graph
Firm A has MC = 3. The winner of the R&D race will price at slightly lower than the loser’s cost. Firm A has a greater incentive to win the R&D race. This leads to “persistence”.
MC = 4
MC = 3
MC = 2

21. Cournot competition: Leapfrogging or Persistence?
Inverse demand: p = 20 – Q cH = 3, co = 2, cL = 1. Profits in the Nash equilibrium (Cournot competition) Firm A has MC = cA, Firm B has MC = cB πA = (20–2cA+cB)2/9 πB = (20–2cB+cA)2/9

22. cA 3 2 1 cB
profit A 32 40 49
profit B 28 25 44
Suppose A wins the R&D race in round 1. Which firm will win the R&D race in round 2? Do we have persistence of leapfrogging in this industry? Please explain.

23. NOW:
Course evaluations

24. Course evaluations 019837 019838 Murat Usman ECON 330 Lec1 Fall 2012
MGEC 330 Lec1
Fall 2012
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