5. Consider the following augmentation of the search and satisficing model discussed in class. Suppose the DM believes that the distribution of values is either uniform on [0,100] or uniform on [50, 150], and they assign a probability of 50% to each of those possibilities (and therefore a probability of 0 to any other possible distribution).

a. What is the expected marginal benefit of searching the first alternative?

b. Suppose the DM searches a first alternative and observes a value of 20. What is the DM's updated belief about the distribution of values? What is the expected marginal benefit of searching one more item?

c. Suppose now, in place of the assumption from part (b), that the DM searches a first alternative and observes a value of 120. What is the DM's updated belief about the distribution of values? What is the expected marginal benefit of searching one more item?

d. Without doing any calculation, provide an argument that compares the optimal threshold, B, that the DM should apply to the second search, from the two cases described in parts (b) and (c) above. (Note that you can't solve for B without knowing the search cost k, but you can still determine in which case the threshold should be higher.)