1. ECON 330 Lecture 21
Thursday, December 6

2. Today’s lecture Next week Entry and market structure
Market size and minimum efficient scale
Endogenous Entry costs
Next week
Free entry and social welfare
Strategic entry deterrence

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

4. Today we ask
What determines the number of firms in a given industry? Common sense: There will be more firms if the market is large, and if entry costs are small. The two main factors we focus on are (i) the size of the market, and (ii) the (fixed) entry costs. Therefore in our first attempt to answer this question… We will look at how technology and market size influence the firm size and industry concentration in a given industry.

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

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

9. Entry costs and market structure
A very simple model :
All firms are identical with cost function: TC(q) = F + cq. The market demand is given by Q(p) = S(A−P), where S measures the market size. Larger values of S indicate a larger market.

10. Demand Q = S(A – P); inverse demand P = A – Q/S
Price P A
SA quantity Q

11. If you double S the market demand becomes
Price P A
SA 2SA

12. The model explained
Stage 1 Firms simultaneously and independently 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. In stage 2 all firms have constant AC = MC = c.

13. Solving the model
Start at Stage 2 Suppose N is the number of firms that have decided to enter in stage 1. In stage 2 these N firms compete in the style of Cournot. We must find the Nash equilibrium of the Cournot competition with N firms.

14. The standard procedure…
The inverse demand: P = A – Q/S The profit function of firm #1 is: 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

15. 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* = S(A−c)/(N+1).

16. The Nash equilibrium quantity with N firms is q* = S(A−c)/(N+1)
Total output Q* is Nq* = NS(A−c)/(N+1) = [N/(N+1)]S(A−c).
The inverse demand is P = A – Q/S, which gives us the equilibrium price P* = (A+Nc)/(N+1).
TWO OBSERVATIONS
P* doesn’t depend on S.
As N increases P* decreases. As N gets larger and larger we have P*  c, which is the competitive price.

17. A diversion: How many firms is enough?
How many rivals it takes 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 (non cooperating) rivals competition is about intense as it gets. You don’t need large numbers!

18. Finally… The profit per firm (gross of entry cost F) is
∏* = q* (P* – c) = S[(A–c)/(N+1)]2.
TWO OBSERV ATIONS
∏* increases proportionately as S increases (double S profits will double)
∏* decreases more than proportionately as N increases.

19. ∏* decreases more than proportionately as N increases Profit ∏*

20. Finding N*, The equilibrium number of firms
The equilibrium number of firms N* is determined by the following:
Firms that have entered make enough profit to cover their entry cost F.
If one more firm would have entered profit would not be enough to cover the entry cost

21. The equilibrium number of firms N* is defined by…
S[(A–c)/(N*+1)]2 ≥ F. S[(A–c)/(N*+1+1)]2 < F. Short cut: Solve S[(A–c)/(N*+1)]2 – F = 0 for N*, round it down to the closest integer (whole number). N* = (A–c) – 1.

22. N* = (A–c) – 1.
If we double the market size, (by multiplying S by 2) the equilibrium number of firms will not double, it will increase by a factor of 1.41.
To double N* we need to quadruple S!
What is the intuition?
As the number of firms increases, the competition between firms gets more intense. More competition reduces the profit margin P*–c, and this limits the number of firms which might enter.

23. SUMMARY The 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.

24. Extensions
We have assumed that – all firms have the same technology – firms have perfect information
Entry is well coordinated (sequential) In practice, – Learning curve (aircrafts, titanium dioxide)
First-mover advantage (network effects, consumer awareness) – Sustainable competitive advantage (patents)

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

26. A few pictures…

28. What is this “MES”
The Minimum Efficient Scale (MES), is the output level at which the average cost is within 5% (or 10%) of minimum AC, minAC = c
Define MES as min q where AC ≤ (1 + X)c c
Here X could be 0.05 or 0.1, meaning that AC is at most 5% (or 10%) higher than minAC.

30. Example: Computing MES for TC(q)=F+cq
AC(q) = F/q + c, so as q increases AC decreases to c. To find MES use c’ = F/q + c, where c’ = (1+X)c, X = 0.05 or 0.1 Solve this for q: q = F/(c’ − c) = 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.

31. Back to the graphs

34. 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.

35. Advertising Costs
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

36. 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 DK 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.

37. Advertising and R & D are both:
– Sunk costs
– Incurred to increase consumers’ willingness to pay for the good: shift demand up
– Endogenous variables

38. When firms compete by “one-upping” each other (advertising, R & D, product quality) this creates endogenous sunk 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 sunk costs, which deters entry.

39. Empirics & Testable Predictions
John Sutton (1991) collects industry data for a number of countries
– Non-advertising, non-R&D intensive industries:
We expect inverse relationship between concentration and market size
– Advertising and R&D intensive industries:
We expect no relationship between concentration and market size

40. Sutton’s Data
• 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

41. Variables
Market size (S): Total output volumes or value of total sales
Concentration: Four firm concentration ratio: CR4
Exogenous sunk entry costs (F): ratio of output level of industry’s median plant to total industry output (this is a proxy for MES)

42. Industries are divided 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

43. 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

44. End of lecture