# unit three (1).pptx - Product Variety and Quality under...

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1 Product Variety and Quality under Monopoly

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2 Introduction Most firms sell more than one product Products are differentiated in different ways horizontally goods of similar quality targeted at consumers of different types how is variety determined? is there too much variety vertically consumers agree on quality differ on willingness to pay for quality how is quality of goods being offered determined?
3 Vertical differentiation Indirect utility to a consumer of type i from consuming a product of quality z at price p is V i = i ( z – z i ) – p where i measures willingness to pay for quality; z i is the lower bound on quality below which consumer type i will not buy assume 1 > 2 : type 1 consumers value quality more than type 2 assume z 1 > z 2 = 0: type 1 consumers only buy if quality is greater than z 1 : never fly in coach never shop in Wal-Mart only eat in “good” restaurants type 2 consumers will buy any quality so long as consumer surplus is nonnegative

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4 Vertical differentiation 2 Firm cannot distinguish consumer types Must implement a strategy that causes consumers to self- select persuade type 1 consumers to buy a high quality product z 1 at a high price and type 2 consumers to buy a low quality product z 2 at a lower price, which equals their maximum willingness to pay Firm can produce any product in the range MC = 0 for either quality type z, z
5 Vertical differentiation 3 For type 2 consumers charge maximum willingness to pay for the low quality product: p 2 = 2 z 2 Suppose that the firm offers two products with qualities z 1 > z 2 Now consider type 1 consumers: firm faces an incentive compatibility constraint 1 ( z 1 z 1 ) – p 1 > 1 ( z 2 z 1 ) – p 2 Type 1 consumers prefer the high quality to the low quality good 1 ( z 1 z 1 ) – p 1 > Type 1 consumers have nonnegative consumer surplus from the high quality good These imply that p 1 < 1 z 1 – ( - 2 ) z 2 There is an upper limit on the price that can be charged for the high quality good

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6 Vertical differentiation 4 Take the equation p 1 = 1 z 1  1  2 ) z 2 this is increasing in quality valuations increasing in the difference between z 1 and z 2 quality can be prices highly when it is valued highly firm has an incentive to differentiate the two products’ qualities to soften competition between them monopolist is competing with itself What about quality choice? prices p 1 = 1 z 1 – ( 1 2 ) z 2 ; p 2 = 2 z 2 check the incentive compatibility constraints suppose that there are N 1 type 1 and N 2 type 2 consumers
7 Vertical differentiation 5 Profit is  N 1 p 1 + N 2 p 2 = N 1 1 z 1 – ( N 1 1 – ( N 1 + N 2 ) 2 ) z 2 This is increasing in z 1 so set z 1 as high as possible: z 1 = For z 2 the decision is more complex ( N 1 1 – ( N 1 + N 2 ) 2 ) may be positive or negative z

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