Quality, Durability, and Warranties

Transcription

1 Chapter 12. April 15, 2015

2 Product di erentiation in terms of Quality Quality has several dimensions We assume that quality can be measured by a real number Apple iphone 4S Samsung Galaxy S II Motorola Droid Bionic Carrier AT&T/Sprint/Verizon Sprint/T Mobile/AT&T Verizon Price on 2 year contract $199, $299 or $399 across carriers $199 from Sprint, $229 from T Mobile, $199 from AT&T $299 Operating system ios 5 Android Gingerbread Android Gingerbread Processor dual core (GHz unknown) 1.2 GHz dual core (1.5 GHz dual core for T Mobile) 1 GHz dual core RAM unknown 1 gigabyte 1 gigabyte Built in storage 16 gigabytes, 32 gigabytes or 64 gigabytes 16 gigabytes 16 gigabytes Expandable storage No MicroSD MicroSD Screen size 3.5 inches 4.5 inches for Sprint and T Mobile, 4.3 inches for AT&T 4.3 inches Screen resolution 960 x 640 pixels 800 x 480 pixels 960 x 540 pixels Weight 4.9 oz 4.77 oz for Sprint and T Mobile, 4.3 oz for AT&T 5.6 oz Rear camera 8 megapixel photos and 1080p video 8 megapixel photos and 1080p video 8 megapixel photos and 1080p videos Front camera VGA photo and video 2 megapixel and VGA video 2 megapixel and VGA video USB Yes Yes Yes HDMI No Yes Yes

3 Personal Income and Quality Purchase Illustration of how the level of personal income a ects the quality of brands bought by di erent-income consumers. Consider an industry with two rms producing brands with di erent qualities. Quality levels: High (H) and Low (L), where H > L > 0 High (H) Low (L)

4 Two consumers i = 1, 2 Their incomes are: I 1 > I 2 > 0 and each consumer buys one unit of the product. Consumer 1 Consumer 2 The utility level of consumer i is H(Ii p U i = H ) if he/she buys high quality L(I i p L ) if he/she buys low quality For a given price, the marginal utility of quality rises with an increase in consumer s income

5 Personal Income and Quality Purchase Proposition If the low-income consumer buys the high-quality brand, then the high-income consumer de nitely buys the high-quality brand. If the high-income consumer buys the low-quality brand, then the low-income consumer de nitely buys the low-quality brand. Proof...

6 Quality as Vertical Product Di erentiation De nition. Di erentiation is said to be horizontal if, when the level of the product s characteristic is augmented in the product s space, there exists a consumer whose utility rises and there exists another consumer whose utility falls. Di erentiation is said to be vertical if all consumers bene t when the level of the product s characteristics is augmented in the product space.

7 A modi ed Hotelling vertical-di erentiation model Now assume that all consumers would have their ideal brand located at point 1 on the [0, 1] interval. There is a continuum of consumers uniformly distributed on the interval [0, 1] There are two rms, denoted by A and B and located at points a and b from the origin (0 a b 1)

8 A modi ed Hotelling vertical-di erentiation model The utility of consumer located at point x and buying brand i is ax pa i = A U x (i) bx p B i = B Two-period game: In the rst period rms choose location and,in the second period, choose price. Let bx denote a consumer who is indi erent between buying from rm A and B U x (A) = abx p A = bbx p B = U x (B) bx = p B p A b a and 1 bx = 1 p B b p A a

9 A modi ed Hotelling vertical-di erentiation model

10 A modi ed Hotelling vertical-di erentiation model For a given location of rms (a and b), in the second period each rm takes the price of its rival as given and chooses p maxπ A (a, b, P A, P B ) = P A bx = B p A P A P A b a max P B π B (a, b, P A, P B ) = P B (1 bx) = P B 1 p B b p A a

11 A modi ed Hotelling vertical-di erentiation model We rst solve the second stage of the game PA e (a, b) = b a and PB e (a, b) = 3 2(b a) 3 Proposition The rm producing the higher quality brand charges a higher price even if the production cost for low-quality products is the same as the production cost of high-quality products.

12 A modi ed Hotelling vertical-di erentiation model Hence, rst period, p π A (a, b, P A, P B ) = B p A P A b a = b a 9 = 1 3 π B (a, b, P A, P B ) = P B (1 bx) = P B 1 b a = 2 3 2(b a) 3 2(b a) 3 p B p A b a + b a 3 b a 3 = 4 (b a) 9 Proposition In a vertical di erentiated quality model each rm chooses maximum di erentiation from its rival rm Are you confused?.