Solutions: Problem Set 5 ECON 290, Models of Choice in Competitive MarketsSol-PS5-290 ECON 290|all you need

Solutions: Problem Set 5 ECON 290, Models of Choice in Competitive Markets Jean Guillaume Forand∗ Winter 2017, Waterloo 1. An unemployed worker has a job offer with wage w. She has also applied to another job, which would offer a wage of w w. However, the worker must accept or decline the first firm’s offer before she hears back from the second firm. The worker is also entitled to an unemployment benefit u as long as she stays unemployed. (a) Describe the set of consequences that should be used to model this situation of decisionmaking under uncertainty. Solution. The simplest way to specify consequences in this case is to focus on the worker’s final income. Thus we can set C = (w, w, u). (b) Describe the lottery ΠY ES that corresponds to the worker accepting the first firm’s job offer. Solution. If we suppose that the worker, when accepting the first offer, communicates this to the second firm, we have that Π Y ES = (0, 1, 0). If we suppose instead that the worker quits the first job whenever she subsequently receives an offer from the second job, and that the probability of receiving an offer from the second firm is 0 ≤ π ≤ 1, we have that Π Y ES = (π, 1 − π, 0). (c) Describe the lottery ΠNO that corresponds to the worker turning down the first firm’s offer. ∗Room 131, Department of Economics, University of Waterloo, Hagey Hall of Humanities, Waterloo, Ontario, Canada N2L 3G1. Office phone: x. 33635. Email: . Website: http://arts. 1 This study source was downloaded by from CourseH on :09:41 GMT -06:00 Solution. In this case, because the worker turns down the first offer, it does not matter what we assume about her behaviour after she accepts the first offer. We have that Π NO = (π, 0, 1 − π). 2. Suppose that Blackberry is deciding whether or not to develop a new smartphone. If the firm develops the phone and it is a success with customers, then its current profits will increase by 50%. However, if the phone is not a success, the firm will suffer losses, but these losses depend on whether or not the phone’s design can be of value to other firms: if some other firm is willing to buy the phone’s design from Blackberry, then Blackberry suffers a 25% drop in its profits, while if no other firm is interested in the design, Blackberry suffers a 100% drop in its profits. Blackberry believes that there is a 70% chance that the new phone will be a success with customers. (a) Describe the list of consequences for this decision problem. Solution. Let W be Blackberry’s current profits. We can describe the list of consequences as the firm’s final profits, that is, C = (W, 3/2W, 3/4W, 0). (b) Describe the following lotteries: • ΠN is the lottery corresponding to Blackberry not developing the new phone. • ΠY Y is the lottery corresponding to Blackberry developing the new phone and being certain that other firms will buy th