1. ECON 330 Lecture 20
Tuesday, December 4

2. Please turn in your HWK#4 now
Please turn in your HWK#4 now. You can see your exams at the end of the lecture. After that you need to our course assistant Vyacheslav Arbuzov at to set up an appointment. Early final exam Friday December 21.

3. Secret price cuts
Using trigger strategies when the rival firm’s price is not observed.

4. Secret price cuts
Customer markets: each customer is sufficiently large such that price is negotiated on a case-by case basis.
Examples:
ready-mixed concrete
ocean shipping.
The prices charged by other firms are not directly observable.
There are other factors, like demand shocks, affect each firm’s profit.
Demand shocks are not observable either.

5. Secret price cuts (Cont’d)
Only firm’s own profit is observable.
To discipline firms from undercutting prices is more difficult.
Trigger strategy can only depend on its own profit.
When one firm’s profit is low, it can not distinguish two situations:
No firm undercut but demand is low;
Demand is high, but some firms undercut.

6. Secret price cuts (Cont’d)
To deter firms from deviating, firms have to carry out punishment if own profit is low.
But trigger strategy is not optimal anymore. Because a bad demand shock would break the collusion for ever.
The optimal strategy is using certain periods of price war.
Charge a high price next period if profit is high this period.
Charge a low price in the next few periods if profit is low this period, then come back to charge a high price again.

7. Secret price cuts (Cont’d)
The result is occasional price wars. (happen in equilibrium even when no firm lowers its price)
Price war doesn’t mean that collusion breaks down; it’s just a costly discipline device.

8. Now the formal analysis
We will use a most simple model

9. Inelastic demand: D units are demanded when p ≤ u demand is zero when p > u.
When demand is high, H = 1 unit can be sold at price u (or any lower price). When demand is low, only L = 0 units can be sold. In each period, demand can be high (probability 1−A) or low (probability A). Firms can’t observe the state of market demand; they can only observe their own demand. All production costs are zero. Monopoly profits are u if demand is high.

10. Modified trigger strategy
Start by setting p = u. If you receive a positive demand (namely, 1/2 ), then continue with set p = u, next period. If you receive zero demand, then set p = 0 during T = 2 periods after that After that go back to p = u again.

11. We call periods with p = u the “co-operative phase”
We call periods with p = u the “co-operative phase”. Periods with p = 0, we call “price war” Note that following a period of low demand firms enter a price war of T = 2 periods. After that they go back to p = u (the co-operative phase).

12. Suppose the other firm uses this strategy.
When is it best response for you to use this strategy? The condition is that your expected profit from using the equilibrium strategy is greater then your profit from deviating (by setting a slightly lower price and taking all of the market demand).

13. Two problems: How to write this expected profits?
How to check that no alternative strategy can bring more profits? (There are too many alternative strategies.)

14. Writing the profits for the simple case with A = 0 (demand is never 0)
Suppose the other firm follows the trigger strategy.
If your firm follows the same strategy, your firm will get half the monopoly profits in every period:
V can be written as 

15. Writing the profits for the repeated interaction; A > 0.
Let V be expected equilibrium discounted profits starting in a period during the co-operative phase. Then V = (1–A)(u/2 + δV) + Aδ3V If a firm deviates (in period 1), …

16. The One-shot deviation Principle
Given the other firm’s strategy, if a firm cannot increase profits by choosing a different action in a single period (in all other periods it follows the equilibrium strategy), then it cannot increase profits in any possible combination of periods.

17. Deviation: Lower price slightly in period 1
Deviation: Lower price slightly in period 1. In period 2 and 3 set p = 0. In period 4 return to your equilibrium strategy.

18. If a firm deviates (in period 1) its expected discounted profit is V’ = (1–A)u + δ3V Condition for equilibrium is V > V’

19. Example
A = 0.1 (prob of low demand), δ = 0.9, u = 10. Monopoly price is p = 10. With two firms, collusion profits are 5 per firm. V = (1– A)( u/2 + δV) + A δ3 V V = (1–0.1)(10/ V) + (0.1)·0.93·V V = 38.4 More general terms V =

20. Deviation profits
V’ = (1–A)u + δ3V
V’ = (1–0.1) V
V’ = 9 + (0.73)·38.4
V’ = = 37

21. Some real world example for “secret price cuts”

22. Danish Ready-mixed concrete market
Until 1993, the prices of ready-mixed concrete in Denmark were frequently subject to confidential discounts.
In 1993, Danish government required all the prices of transactions be public.
Its intention is to protect the interests of buyers.
But the result was: price dispersion decreased dramatically, while the average price increased significantly.
The data reporting requirement ceased in 1996.

23. General Electric
In 1963, GE announced a new pricing policy for turbine generator.
Set price according to a public price book
If GE offers a discount to a customer, all the customers who bought from GE within 6 months are entitled to the same discount.
Soon, GE’s rival Westinghouse followed the same policy.
Until 1975, the prices charged by both companies were stable and identical.

24. A slightly different story

25. Demand fluctuations In each period demand can be either high or low.
At the beginning of each period, firms observe the demand of that period.
With collusion, profits are higher when demand is high.
Firms will have more incentive to undercut each other’s price when demand is high.

26. Demand fluctuations (Cont’d)
When demand is high, undercutting doubles the profit in high demand state. When demand is low, undercut can only double the profit in low demand state. Monopoly profit may not be supported in high demand states. Firms can voluntarily reduce the collusive price in the high demand states, to reduce the incentive to cheat when demand is high.

27. Demand fluctuations (Cont’d)
Result: counter-cyclical pricing
Collusive price is high demand state maybe lower than the collusive price in low demand state.
Example: The price of cement from
A 1% increase in GDP is associated with a decrease in the relative price of cement between .5-1%

28. Monopoly price is u. Demand is d = l or h with h > l
Profit to p = u in every period.
Profit to deviation is ul in low demand period and uh in high demand period. No deviation can raise profits if

29. Solve these equations for δ
This is intuitive: the temptation to cheat on the agreement and set a slightly lower price is especially strong in periods of high demand. The condition for stability of the full-collusion is the first condition

30. Summary and a few general remarks

31. Market structure and Collusion
Number of firms.
Two firms
undercutting results in double of profits in current period.
Three firms
Undercutting leads to triple of profits in current period.
More firms means higher incentive for individual firms to undercut.
Collusion is less likely as the number of firms increases in an industry.

32. Market structure and Collusion (cont’d)
Asymmetry between firms.
2 firms. Firm 1 has cost advantage.
A high collusive price is more difficult to sustain.
Firm 1 has a strong incentive to undercut
it has a cost advantage, firm 2’s retaliation is less harmful to him.
Collusion is more likely to be sustained among symmetric firms.

33. Asymmetric shocks
Firms that are in financial trouble (or weaker) firms usually have a low discount factor.
Collusion is more difficult to sustain among this “impatient” firms.
Airline industry.
The main cause of price wars is the financial trouble of individual carriers.
CEO of the Alaska Airlines: “Fares are dictated not by the strongest, but by the financial troubled.”

34. Multi-market contact
Use punishments in both markets to deter cheating.
Two firms compete in two(same) market. They contact more often in market 1 than in market 2.
Some firms compete in more than two markets.
Airline industry.
In 1988, American and Delta appeared jointly in 527 of the top 1000 routes;
American and Northwest were present in 357 routes.
Delta and Northwest were present in 323 routes.

35. Multi-market contact (cont’d)
The discount factor in market 1 is δ = 2/3, while the discount factor in market 2 is δ =2/5.
Individually, Collusion is sustainable only in market 1, but not in market 2.
Consider the following strategy: if one firm cheats in market 2, then collusion in both markets is broken.
Payoff from cheating: 2πM.

36. Multi-market contact (cont’d)
Payoff from following equilibrium strategy:
(πM /2)/(1-2/3)+(πM /2)(1-2/5)= (3/2+5/6) πM =7πM/3
Collusion can be sustained in both markets.
Econometric evidence showed that the number of overlapping routes, has a positive impact on airfares.
Retaliation in other markets can effectively discipline firms in one market.

37. Most-favored-customer clauses
This clause forbid firms from offering a discount to a particular customer without offering the same discount to every other customer within a specified time.
It seems that this clause protects the interests of buyers.
But it indeed facilitate collusion.
Price cut becomes less attractive
Price becomes somewhat public.