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Topic 2 - Price discrimination - Fall 2011 Topic 2 Price...

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Fall 2011 Topic 2: Price discrimination Outline Third degree price discrimination Two-part tariffs and tying Versioning Bundling Reading ch. 5 (pp. 155-78) Lectures : 3, 4, and 5 BU620 Topic 2: Price discrimination 1 of 22
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Fall 2011 Price discrimination is the practice of charging buyers different prices for the same product for non-cost reasons feasible if the seller can ...identify different buyers ...prevent re-sale between buyers because of… …transactions costs, nature of product, legal restrictions (e.g. ROW import bans in Europe). profitable because it allows firms to …charge lower prices to some but not all buyers …extract more consumer surplus …expand output and the number of products and take advantage of economies of scale and scope legal in Canada provided …you are not selling to a competitor …your intent is not predatory .. .welfare enhancing if more markets are served ... welfare reducing if output is re-allocated BU620 Topic 2: Price discrimination 2 of 22
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Fall 2011 Monopolist can price discriminate [p i = a i 4 q i , MC = 8, a 1 = 48, a 2 = 32] Step 1 : Set MR = MC in each market to find output. FOC: p i + q i [∂ p i /∂ q i ] = ∂ C /∂ q i i = 1,2 a i – 8 q i = 8 q i = ( a i – 8)/8 q 1 = 5, q 2 = 3 Step 2 : Sub. q i into demand functions to find prices p 1 = 28, p 2 = 20 Step 3 : Find profits in both markets. FOC implies p i - c = q i [ - p i /∂ q i ] p i - c = q i which implies π i = [ - p i /∂ q i ]( q i ) 2 π i = 4( q i ) 2 π 1 = 100, π 2 = 36 Step 4 : Find consumer surplus in both markets CS i = (½)( a i p i ) q i Substitute p i = a i – 4 q i CS i = (½)4( q i ) 2 = 2( q i ) 2 CS 1 = 50, CS 2 = 18 Step 5 : Find social welfare SW = Σ i [ π i + CS i ] SW = 6 Σ i ( q i ) 2 SW = 204 BU620 Topic 2: Price discrimination 3 of 22
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Fall 2011 Monopolist cannot price discriminate [p i = a i 4 q i , MC = 8, a 1 = 48, a 2 = 32] Step 1 : Find market demand and then invert Q = q 1 + q 2 Q = (1/4)(48 – p ) + (1/4)(32 – p ) p = 40 – 2 Q Step 2 : Set MR = MC and find Q FOC: p + Q [∂ p /∂ Q ] = ∂ C /∂ Q 40 – 4 Q = 8 or Q = 8 Step 3 : Sub. Q into inverted market demand to find p p = 40 – 2(8) or p = 24 Step 4 : Sub. p into individual demand to find q i q i = (1/4)( a i p ) q 1 = 6, q 2 = 2 Step 5 : Find profits.
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