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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