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Unformatted text preview: Fall 2011 Topic 7: Vertical pricing Outline • Monopoly manufacturer Linear pricing and Twopart tariffs with n dealers Twopart tariffs and screening Twoparttariffs and signaling • Manufacturer competition, Twopart 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 .
 Fall '11
 Ziss
 Microeconomics, Monopoly

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