Download Simulating competition between firms using advertising

Advertising effectiveness and spillover:
simulating strategic interaction using
advertising
25th International Conference of the System
Dynamics Society
Boston, Massachusetts
29th July to 2nd August, 2007
Dr. Malcolm Brady
Dublin City University Business School
[email protected]
Profit
i  Ri  Ci
Ri  pi qi
 i  ( pi  ci )qi
Costs
C (q i )  c i q i
No fixed costs
Cost is linear in quantity
ie. no economies or diseconomies of scale
(inverse) Demand
p
a
pi  a  bqi
monopoly
q
a: reservation price
b: own price effect (market response)
Product differentiation
pi  a  bqi  dq j
duopoly
i  1,2; j  3  i
d: represents the cross price effect
d/b: represents the extent of product differentiation
Dixit, BJE, 1979
Cournot Nash equilibrium
qi 
i 
a(2b  d )  2bci  c j d
4b  d
2
2
…(3)
(ab(2b  d )  ci (2b 2  d 2 )  bc j d  ci (4b 2  d 2 ))( a(2b  d )  2bci  c j d )
(4b 2  d 2 ) 2
i  1,2; j  3  i
Game theory
Strategic interdependency
Cournot, 1838; Nash, 1951
Advertising
• Selection of amount of advertising
– Optimal amount: Dorfman Steiner
• Impact of advertising on demand
– Shifts demand function to the right
• ie. changes intercept of inverse demand function
– Tilts demand function
• ie. changes slope of inverse demand function
– Friedman
• Cumulative
• Interfirm (Spillover) effect
• Cost of advertising
– Reduces profit
Π = pq – cq - A
Ai  Ri
 Ai
 Ai
i
i  1,2
Ai  i (b  d )

. 2
qi b  d 2
pi
b
i  . 2
qi b  d 2
Δai = φiAi + ρφjAj
i =1,2, j=3 - i
Profit
Dorfman-Steiner
Advertising elasticity
of demand
Price elasticity
of demand
Friedman
…(4)
Assumptions
• Production adjusts instantaneously to
demand
• No lags or delays; no spikes or step changes
The model
•
•
•
•
five stock variables
five flow variables
ten auxiliary variables
eight parameters
Initial and Parameter Values
•
•
•
•
•
a high volume low price product
Unit variable cost c set at $8.
The initial reservation price a is set at $25.
Own-price effect b is set at 0.0001
Cross-price effect d at 0.00005.
+
advertising
elasticity
advertising
B1
+
R1
quantity
+
+
reservation price
R3
price
elasticity
+
R2
price
-
advertising
+
B2
quantity
+
+
reservation price
Two firms: Arrays
• Two sets of loops exist: one for the firm and one for its
rival.
• Additional interaction loops, generated by equation 3,
exist: they are as above but with signs reversed.
• Additional interaction loops, generated by equation 4,
exist: they are as above but all variables except reservation
price refer to the rival firm.
• When advertising is predatory all signs are reversed.
Ow n_advertising_impact_on_cross_price_effect
Cross_advertising_impact_on_cross_price_effect
cross_price_effect
Advertising_w eighting_factor
units_demanded
Revenue
advertising_effect_on_reservation_price
Advertising_w eighting_factor_1
advertising_interaction_factor
Advertising
Advertising_elasticity_of_demand
cross_price_effect
advertising_rate
Demand_reservation_price
Price_elasticity_of_demand
ow n_price_effect
Unit_price
Neither firm advertises
φ1 = φ 2 = 0
One firm advertises
Retained_earnings
φ1 = 0.000015; φ2 = 0
2
475,000
2
2
Both firms advertise
φ1 = φ2 = 0.000015
2
2
470,000
2
1
465,000
2
1
460,000
0
1
20
1
40
1
60
1
80
1
2
1
100
Time
φ1 = 0.000013; φ2 = 0
φ1 = φ2 = 0.000013
One firm advertises
with spillover
φ1 = 0.000015; φ2 = 0; ρ = 0.1
φ1 = 0.000015; φ2 = 0; ρ = 0.3
Spillover is predatory
φ1 = φ2 = 0.000013; ρ = -0.3
φ1 = 0.000013; φ2=0; ρ = -0.3
Some conclusions
• Advertising can be an effective competitive
weapon and can lead to competitive advantage
• Bifurcation in industry behavior at threshold levels
of advertising effectiveness
– Some industries advertise and some do not
• Spillover
– Where advertising is a public good firms are less likely
to advertise unless
• all firms in the industry advertise
• or firms advertise collectively
– EU: Olive Oil Ads/ Ireland: Licenced Vintners Ads
– Reduces the impact of advertising
– Predatory may be more effective than complementary
advertising