Question

1. (25 pts) Assume that three types of smart phones are dominating the market. For the sake of this question, assume that these phones are Galaxy, iPhone, and Pixel. The consumer surveys indicate that the customers update their phone every two-years based on their satisfaction and the deals available to them. We are assuming that everybody who had a phone two years ago will continue to own a phone. The data illustrate that every two-years 20% of the Galaxy users switch to an iPhone and another 20% to a Pixel On the other hand, 10% of the iPhone users become Galaxy users. Moreover, every two- years 10% of the Pixel users switch to a Galaxy and another 10% to an iPhone. Let x(t) e R be the state vector representing the percentages of users for Galaxy, iPhone, and Pixel. Assume that initially 40% of the customers are Galaxy users, 45% are iPhone users, and 15% are Pixel users. Construct the dynamical system x(t + 1) = Ax(t), x(0) = Xo, t = 0.1, 2, which models the customer preference dynainics where A is a 3 × 3 matrix and x0 is the initial distribution. What s the unit of time t in yor model?

Answer 1