540 CHAPTER 14 * MARKOV ANALYSIS Data for Problem 14-28 TO FROM 1 2 3 4 5 7 9 10 0.60 0.10 0.10 D.10 0.05 0.01 0.01 0.01 0.01 0.01 D.OI 0.80 0.01 0.01 0.01 D.10 0.01 0.01 0.01 0.03 3 0.01 0.01 0.70 0.01 0.10 0.01 0.05 0.05 0.05 0.01 0.0] 0.90 0.01 0.01 0.01 0.02 5 0.01 0.01 0.01 0.10 0.80 0.01 0.03 1.01 0.01 0.01 6 0.01 0.01 0.01 0.01 0.0] 0.91 0.01 0.01 0.01 0.01 7 0.01 0.0] 0.01 0.01 0.10 0.70 0.01 0.10 0.04 0.01 0.0] 0.01 0.01 0.01 0.10 0.03 0.80 0.01 0.01 0.01 0.01 0.01 0.10 0.01 0.10 0.70 0.04 D.01 0.01 0.01 D.OL 0.01 0.10 D.10 0.05 0.00 0.70 probabilities that customers will switch from one maybe I person out of 100 will try your shop after quick-lubrication shop to another. These values are visiting one of my shops. In a month, I will have shown in the table above. 99% of the market, and you will have 1% of the Initial probabilities, or market share, for shops I market. through 10 are 0.6, 0.1, 0.1, 0.1, 0.05, 0.01, 0.01, Chris: You have it completely reversed. In a month, I 0.01, 0.01, and 0.01. will have 99% of the market, and you will only have (a) Given these data, determine market shares for 1% of the market. In fact, I will treat you to a meal the next period for each of the 10 shops. at a restaurant of your choice if you are right If I am (b) What are the equilibrium market shares? right, you will treat me to one of those big steaks at (c) Sandy believes that the original estimates for David's Steak House. Do we have a deal? market shares were wrong. She believes that Sandy: Yes! Get your checkbook or your credit shop I has 40% of the market and shop 2 has card. You will have the privilege of paying for 30%. All other values are the same. If this is the two very expensive meals at Anthony's Scafood case, what is the impact on market shares for Restaurant. next-period and equilibrium shares? (a) Assume that Sandy is correct about customers (d) A marketing consultant believes that shop I has visiting one of her quick-oil-change shops. Will tremendous appeal. She believes that this shop she win the bet with Chris? will retain 99% of its current market share; 1% (b) Assume that Chris is correct about customers may switch to shop 2. If the consultant is cor- visiting one of his quick-oil-change shops. Will rect, will shop I have 90% of the market in the he win the bet? long run? (c) Describe what will happen if both Sandy and Chris are correct about customers visiting their 2:14-29 During a recent trip to her favorite restaurant, Sandy quick-oil-change operations. (owner of shop 1) met Chris Talley (owner of shop 7) 4:14-30 The first quick-oil-change store in Problem 14-28 (sec Problem 14-28). After an enjoyable lunch, relains 73% of its market share. This represents a Sandy and Chris had a heated discussion about mar- probability of 0.73 in the first row and first column kel share for the quick-oil-change operations in their of the matrix of transition probabilities. The other city. Here is their conversation: probability values in the first row are equally distrib Sandy: My operation is so superior that after some- uted across the other stores (that is, 3% cach). What one changes oil at one of my shops, they will never impact does this have on the steady-state market do business with anyone else. On second thought, shares for the quick-oil-change stores