2. (A random utility discrete choice model). Assume that each consumer is to buy a cellphone,...
2. (A random utility discrete choice model). Assume that each consumer is to buy a cellphone, either an iphone or an android phone (not both). Let U(iphone) be the utility for owning an iphone, and U(android) be the utility for owning an android phone. A consumer buys an iphone if U(iphone) > U(android), otherwise, he buys an android phone. Let y = U(iphone) - U(android) be the difference in utilities for consumer i, and y = Bo + Bilal +...Belik tei where xi is a vector of observable individual characteristics, such as gender, age, and income; e; represents unobservable characteristics such as personal taste. Econometricians do not observe y: (only consumer i knows his yr). Econometricians do observe who buy iphones and who buy android phones. Let Yi = 1 if consumer i buys an iphone, and yi = 0 if he buys an android phone. So econometricians observe yi, Si if yt > 0 Yi = o if yi 30 Assume that e; are iid normal N(0,1). Show that P(yi = 1|x;) = Q(Bo + B1li1 + ... + Batik) This gives the motivation for the probit model. The answer to this question is simple (only contains a couple of lines). So do not overthink.