Topic 7 - Vertical pricing

# Topic 7 - Vertical pricing - Fall 2011 Topic 7: Vertical...

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Unformatted text preview: Fall 2011 Topic 7: Vertical pricing Outline • Monopoly manufacturer Linear pricing and Two-part tariffs with n dealers Two-part tariffs and screening Two-part-tariffs and signaling • Manufacturer competition, Two-part tariffs • Contracts as a barrier to entry Lectures : 21, 22, 23, 24, 25 and 26 EC620 Topic 7 : Vertical pricing Fall 2011 Linear pricing Retail demand: P ( Q ) = 120 – Q, Q = q i + Q- i Dealer cost: MC = w + d , d = 20, FC = , n dealers Manufacturer cost: MC m = m = 40, 1 manufacturer Stage 2: Dealer’s output (q i ) . Pay- off and FOC are D i = ( P ( Q ) - w- d ) q i- i = 1 ,…,n FOC P + q i- w- d = 0 a- 2 q i- Q- i- w- 20 = 0 Apply symmetry q i = q , Q- i = ( n- 1) q to get q ( w ) = , Q ( w ) = FOC imply P ( Q ) - w- d = q and dealer profits equal to D ( w ) = - Stage 1: Manufacturer offer (w) . Pay- off and FOC are M = ( w- m ) Q ( w ) FOC: Q + ( w- m ) = 0 Sub. Q ( w ), a = 120 + ( w- 40) = 0 w = 70 Equilibrium profits (let a = 120) M = , D = - , M + nD = - n Two- part tariffs Retail demand: P ( Q ) = 120 – Q, Q = q i + Q- i EC620 Topic 7 : Vertical pricing Fall 2011 Dealer cost: MC = w + d , d = 20, FC = F + , n dealers Manufacturer cost: MC = m = 40, 1 manufacturer Stage 3: Dealer output (q i ) . Pay- off and Q ( w ) are D i = ( P ( Q ) - w- d ) q i- i = 1 ,…,n Q ( w ) = (Same as linear tariff case) Stage 2: Dealer contract choice . Dealer accepts contract if D i ≥ F ≤ ( P ( Q ) - w- d ) q i- Stage 1: Manufacturer offer (w, F). Man. pay- off & FOC M = ( w- m ) Q ( w ) + nF = ( P ( Q ) - m- d ) Q ( w )- n FOC or Q = 30 which implies P = 90, q = 30/ n Set Q ( w ) = Q to solve for w or Set D i = 0 to solve for F F = ( P- w- d ) q = (30/ n ) 2 Equilibrium profits M = 900 - , D i = 0, M + nD = 900 - Two- part tariffs and screening EC620 Topic 7 : Vertical pricing Fall 2011 A monopoly manufacturer has n L + n H markets in which they wish to hire a dealer to sell its product. Each dealer is given an exclusive territory and is therefore the monopoly dealer in the territory. A dealer is either high quality or low quality. The dealer knows their quality. The manufacturer knows that there are n L low quality dealers and n H high quality dealers in the population but cannot distinguish between them prior to contracting. Case 1: Continuous LQ dealers: P L = a L – q L , HQ dealers: P H = a H – q H Dealer cost: MC i = w j + d , FC = F j + , i = L,H Manufacturer cost: MC m = m Stage 3: Dealer output choice ( q i ). Dealer’s maximized profit & wholesale demand q i ( w j ) D i ( w j , F j ) = - i, j = L, H q i ( w j ) = , (see linear tariff case for n = 1) EC620 Topic 7 : Vertical pricing Fall 2011 Stage 2: Dealer’s contract choice....
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## This note was uploaded on 10/16/2011 for the course ECONOMICS 620 taught by Professor Ziss during the Fall '11 term at Wilfred Laurier University .

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Topic 7 - Vertical pricing - Fall 2011 Topic 7: Vertical...

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