1. ECON 330 Lecture 20
Wednesday, December 4

2. Today’s lecture
Entry and market structure
Endogenous entry costs

3. So far…
We examined how (a given number of) firms behave in a number of market structures,
Competitive markets,
Monopoly markets,
Dominant firm markets
Oligopoly markets.
We also examined the strategic interaction in oligopoly markets. (price competition versus quantity competition, Leader – Follower models, collusion versus competition)

4. The exception to “given number of firms” is…
Our analysis of competitive markets. For competitive markets we also have a theory of entry and exit that determines the number of firms in the long-run equilibrium. The so called “zero-economic-profit” condition.
Negative economic profit
Zero economic profit
Positive economic profit

5. Today we ask

6. How many firms would you expect to exist in a given industry
How many firms would you expect to exist in a given industry? and How large would you expect those firms to be?

7. A few pictures from the textbook
Remember C4 is the market share of the biggest 4 firms in an industry.

8. For today’s lecture you may want to read also
Market structure chapter

9. Industry concentration in France and Germany

10. Most points are close to the 45o line
Most points are close to the 45o line. For each industry, the value of C4 in France is very similar to the value of C4 in Germany. So what can we conclude? … that more likely there are industry-specific factors which determine number of firms and firms’ sizes.

11. Industry concentration in France and Belgium

12. The second graph shows that most points are above the 45o line
The second graph shows that most points are above the 45o line. For each industry, the value of C4 is greater in Belgium than in France. A given industry is likely to be more concentrated (has fewer firms) in Belgium than in France. - there are exceptions!

13. One important difference between the two graphs is this: The first graph has two economies of similar size (both in population and in GDP), The second graph has two countries of very different size (France is five times bigger than Belgium). Together, these graphs suggest that market size, in addition to industry-specific factors, is an important determinant of market structure.

14. In Today’s lecture:
We will focus precisely on how technology and market size influence firm size and industry concentration.

15. Now a little bit of theory
A simple model about how the market size and the (exogenous) entry costs determine industry concentration.

16. Exogenous entry costs and market structure: A simple model
All firms are identical with cost function:
TC(q) = F + cq.
F is the fixed entry cost, c is the marginal cost.
The market demand is given by Q(P) = S(a−P),
a and S are parameters.
S measures the market size.
Larger values of S indicate a larger market.

17. Demand Q(P) = S(a – P); inverse demand P(Q) = a – Q/S
Price P a Sa quantity Q

18. If you double S the market demand becomes
Now, at any given price, the quantity demanded
is two times larger than before.
Price P a
xo xo Sa 2Sa Po

19. The model explained
Stage 1 (there are many potential entrants) Firms decide whether to enter or stay out. Those who decide to enter pay the fixed cost of entry F. Stage 2 Firms that have entered compete in the style of Cournot. Note that in stage 2 (F is already paid) all firms have TC(q) = cq, (constant AC = MC = c.)

20. Solving the model
Start at Stage 2 Let N be the number of firms that have entered in stage 1. In stage 2 these N firms compete in the style of Cournot. So, we compute the Nash equilibrium of the Cournot competition with N firms.

21. Goal is…
to show that profit in the Nash equilibrium with N firms is

22. The standard procedure…
The inverse demand: P(Q) = a – Q/S, where Q = q1 + q2 +…+qN The profit function of firm #1 is: 1 = Pxq1 − cq1 1 = [ a−(q1 + q2 +… + qN)/S ]q1 − cq1 Differentiate 1 with respect to q1, set equal to zero. ∂1/∂q1 = a−(2q1 + q2 + q3 +… + qN)/S − c = 0

23. The same old trick…
All firms have the same cost function, so we “think” that in the Nash equilibrium all firms will produce the same output. a−(2q1* + q2* + q3* +… + qN*)/S − c = 0 a−(N+1)q*/S − c = 0 q* =

24. The Nash equilibrium quantity with N firms is q* =
Total output Q* is Nq* = The inverse demand is P = a – Q/S, which gives us the equilibrium price P* = P* – c = As N increases P* decreases. As N → ∞, we have P*  c, which is the competitive price.

25. A diversion: How many firms is enough?
How many rivals does it take to produce enough competition to approximate the perfect competitive outcome?
Research suggests that it doesn’t take very many.
A well-known study by Bresnahan and Reiss (1991) examined a large number of ‘local markets’ for
plumbers,
car repairs,
doctors, etc.
They found that with three rivals, competition is very intense!

26. Finally… The profit per firm (gross of entry cost F) is
∏* = q*(P* – c) =
TWO OBSERV ATIONS
As S increases ∏* increases proportionately.
(double S, and profits will double)
As N increases ∏* decreases more than proportionately.
(double N, profit per firm decreases to less than half its initial value)

27. Post entry profits (p-c)xq = ∏* decreases as N increases
Parameter values: S = 1, a = 10 and c = 1

28. Finding N*, the equilibrium number of firms
The equilibrium number of firms N* is determined by the following:
Each of the N* firms make enough profit to cover their entry cost F.
If there were N*+1 firms, post entry profit would not be enough to cover the entry cost F.

29. The equilibrium number of firms N* is defined by…
≥ F. < F. Short cut: Solve this for N*, round it down to the closest integer (whole number).

30. If we double the market size, (multiply S by 2), N
If we double the market size, (multiply S by 2), N* the equilibrium number of firms will not double! N* will increase by a factor of To double N* we need to quadruple S! What is the intuition? As the number of firms increases, the competition gets more intense. More competition reduces the profit margin P*–c, and this limits the number of firms which might enter.

31. Parameter values: a = 100, c = 30, F = 100

32. N* the equilibrium number of firms in a market
SUMMARY
N* the equilibrium number of firms in a market
Increases as the size of the market (measured by S) increases.
Decreases as the fixed cost of entry F increases.

33. Now something slightly different
The co-called endogenous entry costs

34. In-class exercise

35. The inverse market demand is p(Q) = 21 − Q
The inverse market demand is p(Q) = 21 − Q. All potential entrants have constant marginal and average cost of c = 1. The entry cost is F = 10. Entering firms compete in the style of Cournot.
 What is the equilibrium number of firms?
 What is the post entry profit per firm in equilibrium?
 Compute the Consumers’ surplus.

36. A few pictures…

38. What is this “MES”
The Minimum Efficient Scale (MES), is the output level at which the average cost is “close” to the minimum AC. Say the q level at which AC = c’, where c’ is 5% (or 10%) higher than the minimum AC.

39. The AC function (parameter values F = 10, c = 2)
MES = 50

40. The AC function (parameter values F = 15, c = 2)
MES = 75

41. Example: Computing MES for TC(q) = F+cq
AC(q) = F/q + c, so as q increases AC → c. To find MES, use c’ = F/q + c, where c’ = (1+λ)c, λ = 0.05 or 0.1 Solve c’ = F/q + c for q: qM = F/(c’ − c) = qM is the MES. Note that MES is proportional to F. We can use MES as a proxy substitute for F, the fixed entry cost. A measure of MES/market size is used in most empirical studies.

42. Back to the graphs

45. The beer industry
The U.S. Beer Industry is dominated by three firms: Anheuser- Busch, Miller, and Coors The Portuguese Beer Industry is dominated by two firms: Centralcer, and Unicer The U.S. economy is 30 – 50 times bigger than the Portuguese economy. Our simple theory predicts that the number of firms to be 5 – 7 times greater in the US.

46. Advertising as entry cost!
Advertising is a significant sunk entry cost for the beer industry. Advertising to sales ratios are similar in U.S. and Portugal. Total sales are much higher in U.S, so the total advertising is much higher in U.S.; which implies larger sunk entry costs for U.S. market New firm must keep up with huge advertising budgets of Anheuser Busch, Miller, and Coors

47. Some entry costs may be rising in market size Advertising: The absolute amount of advertising to enter the US market to obtain a given amount of sales is probably larger than in Portugal and Denmark Advertising decisions are part of firms' strategic decisions - entry costs are partly endogenous Endogenous entry costs increasing in market size implies that number of firms may increase very slowly as market size grows.

48. Much of the entry cost into (national brand) beer is advertising
Much of the entry cost into (national brand) beer is advertising. Advertising expenditures are roughly proportional to sales (when comparing various countries). Hence, as S increases, so does F! In the exteme case where F is proportional to S, (for example: F = kS fo some k < 1) then N*remains flat w.r.t. S. N*= Prediction: C4 decreasing (N* increasing) in S. However, relation is flatter in advertising-intensive industries.

49. Number of firms may not change with increases in market size.
When firms compete by “one-upping*” each other (advertising, or R&D) this creates endogenous entry costs.
Increases in the value of the market (market size) tend to be competed away.
Number of firms may not change with increases in market size.
Increased market size causes increased endogenous entry costs, which deters entry.
* one-upping: to be one step ahead of the rivals

50. Famous study: Sunk Costs and Market Structure: Price Competition, Advertising, and the Evolution of Concentration, by John Sutton (1991)
Sutton (1991) collects industry data for six countries:
U.S., Japan, Germany, France, U.K., and Italy
Twenty industries in year 1986:
Salt, sugar, flour, bread, processed meat, canned vegetables, frozen food, soup, soft drinks, margarine, RTE cereals, mineral water, roast and ground coffee, instant coffee, sugar confectionery, chocolate confectionary, biscuits, pet foods, baby foods, beer
Some are non-advertising, non-R&D intensive industries:
We expect inverse relationship between concentration and market size
Some are advertising and R&D intensive industries:
We expect no or weak relationship between concentration and market size

51. Advertising/Retail Sales ratios for a selection of industries and countries (France, Germany, Italy, Japan, U.K., U.S

52. Sutton divides industries into two groups based on advertising to sales ratio: The cut-off is advertising to sales ratio of 1% – Low advertising (commodities): salt, sugar, bread, flour, canned vegetables, and processed meat. These have Exogenous sunk costs only. – Advertising intensive: remaining 14 industries, these have both exogenous and endogenous sunk costs

53. Non-advertising industries Advertising-heavy industries
ln(size/MES)
ln(size/MES)

54. S is the market size measure,  is the MES variable, which is used as a measure or the fixed entry cost F Sutton’s Estimation Results

55. End of lecture