Mgt 87540 - Quantitative Research Methods

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Using historical data, we can determine the where the market shares are going to be for the next period. We need to know what the current states are and what the anticipated states are going to be in order to calculate an accurate depiction of the business statistics. To figure out the market shares for the next period use the following matrix:

(.25, .25, .25, .25) 0.6 0.2 0.1 0.1

0 0.7 0.2 0.1

- 0.1 0.8 0

0.05 0.05 0.1 0.8

Now that we have the matrix aligned, we can begin to solve the equation, by taking our matrix information and multiplying it out with the equal market shares as follows:

= .25(.6) + .25(0) + .25(.1) + .25(.05) + .25(.2) + .25(.7) + .25(.1) + .25(.2) + .25(.8) + .25(.1) + .25(.1) +.25(0) + .25(.8)

Solve the equation:

= .15 + 0 +.025 + .05 + .175 +.025 + .0125 + .025 + .05 + .20 + .025 + .025 + .025 + 0 + .20

= .1875, .2625. .30, .25

University: 18.75%

Bill’s: 25.25%

College: 30%

Battles: 25%

University loses shares of the market, while College and Bill’s gains market shares. Battles remains the same. The problem lies in that University is not retaining as many of their customers as the competition is. For long-term, College will continue to dominate the market. Bills’ will continue to grow slowly, while University will continue to decline and lose customers to the competition. Battles will likely remain where they are and continue to remain consistent.

Problem 14-29 During a recent trip to her favorite restaurant, Sandy (owner of shop 1) meet Chris Talley (owner of shop 7) (see problem 14-28). After an enjoyable lunch, Sandy and Chris had a heated discussion about market share for the quick-oil-change operations in their city. Here is their conversation:

Sandy: My operation is so superior that after someone changes oil at one of my shops, they will never do business with anyone else. One second thought, maybe 1 person out of 100 will try your shop after visiting one of my shops. In a month, I will have 99% of the market, and you will have 1% of the market.

Chris: You have it completely reversed. In a month, I will have 99% of the market, and you will only have 1% of the market. In fact, I will treat you to a meal at a restaurant of your choice if you are right. If I am right, you will treat to one of those big steaks at David’s Steak House. Do we have a deal?

Sandy: Yes! Get your checkbook or your credit card. You will have the privilege of paying for two very expensive meals at Anthony’s Seafood Restaurant.

- Assume that Sandy is correct about customers visiting one of her quick-oil-change shops. Will she win the bet with Chris?

Using historical data, we can determine what percentage of customers are going to stay in Sandy’s shop. We need to know what the current states are and what the anticipated states are going to be in order to calculate an accurate depiction of the business statistics. Based on the data provided, Sandy would have 98.01% of the customers calculated as follows:

Shop 1= .99(.60) + .99(.09) + .99(.10) + .99(.05) + .99(.01) + .99(.01) + .99(.01) + .99(.01)

= .594, .0891, .099, .099, .0495, .0099, .0099, .0099, .0099, .0099

Adding the numbers together results in Shop 1 at 98.01%

- Assume that Chris is correct about customers visiting one of his quick-oil-change shops. Will he win the best?

We mirror this process for Chris’s shop determination.

Shop 2 = .99(.01) + .99(0) + .99(.01) + .99(.01) + .99(.01) + .99(.70) + .99(.01) + .99(.10) + .99(.04)

= .0099 + 0 + .0099 + .0099 + .0099 + .0099 + .693 + .0099 + .099 + .0396

Therefore, Shop 2 = 89.1%

- Describe what would happen if both Sandy and Chris are correct about customers visiting their quick-oil-change operations.

Even if Sandy and Chris are both correct about their predictions, Sandy will still hold the majority of the market shares of the stores. Since she had 98% of the shares compared to 89% for Chris, she will garner more of the customers overall. She will win the bet.

References

Render, B., Stair, R. M., Jr., Hanna, M. E., & Hale, T. S. (2015). Quantitative analysis for management (12th ed.). Boston: Pearson Education.