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3 limit points you are considering developing a new produet...

Question: 3 limit points you are considering developing a new produet...

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3) Limit points You are considering developing a new produet in a niche financial market. There are very many (basically infinitely many) potential customers in the market, who have significantly heterogeneous tastes Specifically, the product market can be classified along two dimensions, which we may think of as taste for nsk and duration of each product. A customer will only consider purchasing a pioduct that fits hisher tastes for risk and duration fairly well. We formalize the market in a mathematical model by representing each potential customer by the point a -(s tn) E [0,1] x [0,1 R2. The total pool of customers can thus be viewed as a sequence Defining the Euclidian metric, d(x, y)- V(x,-)(x y2)2, the assumption that people will only buy products that are close to their tastes can be modeled as associating the point p E [0,1 x 10,1] with a given product, and making the assumption that a customer, a will only buy the product if d(a, p) ε for some small ε > 0. You are in a business development meeting to discuss whether your compan y should target the market or not Since there are significant fixed costs associated with developing a new product, your company will only consider introducing one such product. Moreover for the product to be profitable, a very large number of customers is needed. Your company does not know cus tome rs tastes at this point, but you are con fident that this information could be obtained through market research. The cument discussion in the meeting concerns whe ther there is a business case for introducing the product A product manager for a completely different product in the companys product portfolio is arguing that this is not the case. Specifically, his argument is that although there is bas ically infinitely many potential customers, the ir tastes are so heterogeneous that it will never be possible to capture more than a marginal part of the market, whatever product is chosen. Whatever product we choose there will only be a limited number of cus tomers who wl buy it, the product manager argues. You are heavily in favor of entering this new exciting market and have, as well, ves ted much effort on analyzing the business case. Can you formulate a - strictly mathematically based - counter argument for why it makes sense to enter the market? MFE Mathematical Foundations, Spring 2019, Assignment I

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