Consider a standard random utility model of the form uj = vj + &j, where u; is the utility of product j, v; is the deterministic observable component of utility, and j is the random unobserved error term. a) Fill in the following table for the case of two products j = {A,B}. [4 points] MODEL Assumed PDF distribution of j LOGIT PROBIT Formula to calculate PA = Pr[UA > UB] Advantages Disadvantages b) What is the IIA property? Show that the logit model has the IIA property, and give an example where the logit model would be an inappropriate model because of this property. [6 points] c) Show that (in the context of discrete choice models) utility is a relative concept (rather than an absolute concept) by demonstrating mathematically that adding the same constant c to the observable utility v; of each alternative j does not change choice probabilities with the logit model. Given this result, what does it mean when a product has negative utility? [4 points] d) Write the maximum likelihood solution for a logit model with two product alternatives and one attribute. Specifically, if v; = xj, vk = xk and P; = ej ej+ek' what is *? [4 points]