Group Of Customers Asked To Rate Five Different Brands

Group Of Customers Is Asked To Rate Five Different Brands Of Coffe

1. A group of customers is asked to rate five different brands of coffee on two characteristics; strength and body. Each brand is rated on a scale of 1 to 7 for each characteristic. Each consumer is also asked to rate an ideal coffee. The average brand ratings are as follows:

  • Brand A: Strength 3, Body 4
  • Brand B: Strength 6, Body 2
  • Brand C: Strength 6, Body 3
  • Brand D: Strength 2, Body 3
  • Brand E: Strength 1, Body 1
  • Ideal: Strength 5, Body 5

a. Represent these perceptions in Euclidean 2-dimensional space (X and Y axes), and compute the rank order of the brands according to their probable market share, assuming these product characteristics are the only factors influencing the brands’ market shares.

b. Suppose empirical analysis finds the following model to be true: where \( M_i \) = market share of brand i, \( K \) = constant, \( d_i \) = distance for brand i from ideal. Find \( K \). Also, calculate the shares \( M_A, M_B, M_C, M_D, M_E \) using the model, given that total market share sums to 1.

c. A new brand F is rated with Strength = 3 and Body = 3. Using the model from part b, estimate its market share. Analyze how brand F would draw share from other brands based on their shares before and after brand F enters the market.

Paper For Above instruction

The analysis of consumer perceptions and preferences in the coffee market provides vital insights for strategic marketing decisions. By representing brand ratings in Euclidean space and applying market share models, companies can better understand competitive positioning and potential market dynamics. In this paper, we address each component of the assignment systematically, integrating theoretical models with practical calculations to inform marketing strategies effectively.

Part a: Representation of Perceptions in Euclidean Space and Market Share Ranking

The perceptions of five coffee brands, evaluated along two characteristics, can be visualized within a Euclidean 2-dimensional coordinate system. Assigning 'strength' to the X-axis and 'body' to the Y-axis, each brand's average ratings are plotted as points in this space. The coordinates are as follows:

  • Brand A: (3, 4)
  • Brand B: (6, 2)
  • Brand C: (6, 3)
  • Brand D: (2, 3)
  • Brand E: (1, 1)

The ideal product, positioned at (5, 5), serves as a benchmark for perceived excellence. The proximity of each brand to this ideal influences consumer preference—the closer a brand is to (5, 5), the higher its presumed market share, assuming solely attribute ratings determine market share.

Calculating Euclidean distances from each brand to the ideal:

  • Brand A: \( d_A = \sqrt{(3-5)^2 + (4-5)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.236 \)
  • Brand B: \( d_B = \sqrt{(6-5)^2 + (2-5)^2} = \sqrt{1 + 9} = \sqrt{10} \approx 3.162 \)
  • Brand C: \( d_C = \sqrt{(6-5)^2 + (3-5)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.236 \)
  • Brand D: \( d_D = \sqrt{(2-5)^2 + (3-5)^2} = \sqrt{9 + 4} = \sqrt{13} \approx 3.606 \)
  • Brand E: \( d_E = \sqrt{(1-5)^2 + (1-5)^2} = \sqrt{16 + 16} = \sqrt{32} \approx 5.657 \)

Assuming that market share is inversely proportional to the distance from the ideal, the brands can be ranked accordingly. The most favorable brands are those closest to (5, 5), i.e., Brands A and C with equal distances (~2.236), followed by B (~3.162), D (~3.606), and E (~5.657). To derive a precise ranking, market share estimation can be based on a proportionality like \( M_i \propto 1/d_i \).

Calculating the inverse distances:

  • 1/d_A ≈ 0.447
  • 1/d_B ≈ 0.316
  • 1/d_C ≈ 0.447
  • 1/d_D ≈ 0.278
  • 1/d_E ≈ 0.177

Sum of these reciprocals: \( 0.447 + 0.316 + 0.447 + 0.278 + 0.177 = 1.665 \). The normalized market shares are then:

  • \( M_A = 0.447 / 1.665 \approx 0.268 \)
  • \( M_B = 0.316 / 1.665 \approx 0.189 \)
  • \( M_C = 0.447 / 1.665 \approx 0.268 \)
  • \( M_D = 0.278 / 1.665 \approx 0.167 \)
  • \( M_E = 0.177 / 1.665 \approx 0.106 \)

Part b: Market Share Model and Computation of \( K \) and Shares

Experimental analysis suggests a model where market share \( M_i \) is proportional to the exponential of the negative scaled distance from the ideal:

\( M_i = K \times e^{-d_i / \lambda} \), where \(K\) is a scaling constant ensuring the shares sum to 1, and \( \lambda \) is a parameter reflecting sensitivity to distance. Given the form in the problem, assume the model is:

\( M_i = K \times e^{-d_i} \). The sum across all brands equals 1:

\( \sum_{i} M_i = K \times \sum_{i} e^{-d_i} = 1 \).

Calculating \( e^{-d_i} \):

  • \( e^{-2.236} \approx 0.106 \) (for Brands A and C)
  • \( e^{-3.162} \approx 0.042 \) (Brand B)
  • \( e^{-3.606} \approx 0.027 \) (Brand D)
  • \( e^{-5.657} \approx 0.0035 \) (Brand E)

The sum of these is: \( 0.106 + 0.042 + 0.106 + 0.027 + 0.0035 = 0.2785 \). Therefore, the sum: \( K \times 0.2785 = 1 \Rightarrow K \approx 3.59 \).

Using this \(K\), the market shares are:

  • \( M_A = M_C \approx 3.59 \times 0.106 \approx 0.38 \) (38%)
  • \( M_B \approx 3.59 \times 0.042 \approx 0.15 \) (15%)
  • \( M_D \approx 3.59 \times 0.027 \approx 0.097 \) (9.7%)
  • \( M_E \approx 3.59 \times 0.0035 \approx 0.0125 \) (1.25%)

Note that the sum of these is approximately 1, confirming model consistency. Thus, Brands A and C dominate market share, followed by B, D, and E, mainly driven by their proximities to the ideal in the perception space.

Part c: Estimation for Brand F and Market Share Dynamics

Brand F, rated at (3, 3), has a Euclidean distance from the ideal:

\( d_F = \sqrt{(3-5)^2 + (3-5)^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.828 \).

Applying the same model with \(K \approx 3.59\):

\( M_F = 3.59 \times e^{-2.828} \approx 3.59 \times 0.059 = 0.212 \) (21.2%).

Comparing previous market shares: Brands A and C had about 38% each; now, F's share of 21.2% significantly reduces theirs. Brands B and D, with smaller shares, would be affected proportionally less.

Suppose the originally calculated shares are via explicit models, the market share of existing brands would decrease, broadly proportional to their initial shares, to accommodate the new entrant F. This indicates a shift in consumer preference towards brands closer to the ideal, now including F, and suggests that brand F could capture a substantial market segment, especially if its perceived quality aligns with consumer preferences.

Conclusion

This comprehensive analysis demonstrates how multidimensional perception data can be modeled geometrically and statistically to inform strategic market share estimates. The coordinate representation effectively visualizes consumer perceptions, while exponential decay models allow for probabilistic market share calculation based on consumer preference proximity. Similarly, introducing new competitors alters market dynamics, reinforcing the importance of perceptual positioning and strategic innovation in competitive industries like coffee branding. These analytical approaches are vital tools for marketers aiming to optimize positioning and forecast market outcomes effectively.

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