Equilibrium Structure in Successive Oligopoly with Multiproduct Firms

1
Equilibrium Structure in Successive Oligopoly
with Multiproduct Firms

• Chrysovalantou Milliou,
• Emmanuel Petrakis,
• Igor Sloev
• Dept. of International European Economic
  Studies, Athens University of Economics and
  Business
• Department of Economics, University of Crete,
• Department of Management, NRU Higher School of
  Economics
• July 2012, Nignij Novgorod

2
?. Motivation

• A number of industries are characterized by
• A small number of Upstream Firms/ Manufacturers
  ? oligopolistic structure in the upstream sector
• Each Upstream Firm produces a spectrum of
  horizontally differentiated goods
• A small number of Downstream Firms/Retailers,
  each selling most (or even all) of the
  manufacturers products ? oligopolistic structure
  in retailing
• Intensive Product Creation Activities at the
  upstream sector ? enhancement of product variety

3
?. Motivation (contd)

• We develop a successive oligopoly model that
  captures some of the characteristics of the above
  industries in order to address the following
  issues
• The manufacturers incentives to enter in the
  upstream market and invest in new product
  creation processes
• The impact of the downstream tier concentration
  on product variety offered in the market,
  upstream market concentration, wholesale prices
  and output quantities sold in the market.
• The impact of the intensity of the economies of
  scope on product variety offered in the market,
  upstream market concentration, wholesale prices
  and output quantities sold in the market.
• The welfare implications of economies of scope
  i.e. their impact on consumer surplus, upstream
  and downstream profits and total welfare

4
I. Related Literature

• Literature on Multi-product Firms
• Helpman (1985), Nocke and Yeaple (2006), Anderson
  and de Palma (1992, 2006), Ottoviano and Thisse
  (1999)
• (They consider one-tier industries)
• Literature on Vertically Related Industries
• Reisinger and Schnitzer (2008), Smith and
  Thanassoulis (2008), Dobson and Waterson (2007),
  
• (They consider single-product upstream firms)

5
II. Market Structure

• Upstream manufacturer m 1,,M produces nm
  different goods. Total number of goods is N n1
  n2 nM
• Downstream retailer r 1,,R resell all N
  goods.
• Representative consumer has the linear-quadratic
  quasilinear utility function.

6
II. The Model (market structure)
M1
MM
R1
RR
Final Consumers
7
II. The Model (1)
Utility function of the representative consumer
(1)

• a reflects the size of the market.
• 1 gt ί gt ? gt 0 represents the degree of
  product substitutability
• L represents the income spent on the rest of
  goods.

Hence, the system of the demand functions is
(2)
8
II. The Model (2)

• Retailers
• R downstream firms/retailers, r 1,,R, each
  selling all the manufacturers goods.
• Each retailer r chooses the quantity of each
  good that he buys from each manufacturer and
  resells it to the final consumers, qi.
• The total quantity of good i sold in the market
  by all retailers is
• Qi? r qi r, i 1,,N.
• There are no reselling costs, thus the retailing
  marginal cost for each good is equal to the
  manufacturers wholesale price
• w (w1,,wN).

9
II. The Model (3)
The retailer r maximizes its profit function
given wholesale prices w
(3)
(4)
where
The solution of retailer problems is
It determines the demand system for upstream
manufacturers goods for all possible wholesale
prices w
(5)
10
II. The Model (4)

• Manufactures
• Each manufacturer m 1,,M decides how many
  differentiated goods to produce, nm. The total
  number of goods produced is
• N n1 nm.
• Each manufacturer m sets the quantity of each
  good he produces correctly anticipating the price
  system determined by (5)
• The cost function of each m is TC F n G. The
  lower F or/and the higher G, the stronger
  economies of scope in the new product creation
  process. Manufacturer m maximizes its profit
  function

(6)
(7)
11
?II. Equilibrium
Strategies and timing. (1) Each Manufacturer ms
sets its product variety and outputs nm, Qm
(2) For given manufacturers outputs, market
generates prices w (3) Retailers choose their
outputs qr, r 1,,R, given prices w. We solve
by backward induction, SPNE (at equilibrium
path) a) Given w and N, we obtain the solution
of retailers problem qi(w) b) This provides
the demand for manufacturers goods wi (q) c)
Finally manufacturer ms maximization problem
provides nm, Qm, with
12
?II. Solution
FOCs symmetry (qir qi) Now, for given
nm each m solves The FOCs Gives Finally,
provides nm n .
13
IV. Equilibrium Analysis

• Case 1 Number of manufacturers (M) is given
• In the symmetric equilibrium individual variety,
  output of each good and wholesale price are

14
IV. Equilibrium Analysis
Case 1 Number of manufacturers (M) is given
In the symmetric equilibrium prices, profits of
manufacturers and retailers are
15
IV. Results

• The lower upstream market concentration (the
  higher M),
• the lower product variety of each manufacturer
  (n)
• the lower manufacturers profits
• the higher the total number of goods produced (M
  n)
• the higher retailers profits
• the lower wholesale prices (w) and final price
  (P)
• the higher consumer surplus.

16
IV. Results

• The lower concentration of the downstream market
  (the higher R),
• the higher the product variety of each
  manufacturer (n)
• the higher manufacturers profits
• the higher the total number of goods produced (M
  n)
• the lower retailers profits
• the lower wholesale prices (w)
• the lower final price (P).

17
V. Equilibrium Analysis Free Entry
Case 2 Free-entry in the upstream sector
In the symmetric equilibrium the number of
manufacturers, wholesale prices, individual
varieties are
18
V. Equilibrium Analysis Free Entry
Case 2 Free-entry in the upstream sector
In the symmetric equilibrium the total variety,
and quantity of each good are
19
V. Results

• The lower concentration of the downstream market
  (the higher R),
• the higher the number of manufacturers (M)
• The higher product variety of each manufacturer
  (n)
• the higher the output of each good (Q)
• the higher the total number of goods produced (M
  n)
• the lower retailers profits
• the lower wholesale prices (w)
• the lower final price (P)
• the higher consumer surplus (CS).

20
V. Results

• The lower the per-variety fixed cost F,
• the higher the number of manufacturers (M)
• the higher product variety of each manufacturer
  (n)
• the lower the output of each good (Q)
• the higher the total number of goods produced (M
  n)
• the higher retailers profits
• the lower wholesale prices (w)
• the lower final prices (P).

21
V. Results

• The higher the firm-level fixed cost G,
• the lower the number of manufacturers (M)
• the higher product variety of each manufacturer
  (n)
• the lower the total number of goods produced (M
  n)
• the lower retailers profits
• the higher wholesale prices (w)
• the higher final prices (P).

22
V. Results

• The higher the market size a,
• the higher the number of manufacturers (M)
• the higher the total number of goods produced (M
  n)
• the higher retailers profits
• the lower final prices (P)
• the higher consumer surplus.
• However,
• product variety of each manufacturer (n),
• wholesale prices (w),
• the output of each good (Q)
• do not depend on a

23
XII. Conclusions

• We have developed a successive oligopoly model
  where multi-product manufacturers sell their
  differentiated goods to a given number of
  retailers, which in turn resell them to final
  consumers.
• Both the cases of fixed number of firms upstream
  and free-entry upstream are analyzed.
• Particular emphasis is given on the role of the
  economies of scope in the product creation
  process.
• The effect of various market features (i.e.
  number of retailers, size of the market) on
  equilibrium market outcomes (i.e. wholesale
  prices, product variety, number of manufacturers
  etc.) and on welfare is investigated.

24
THANK YOU