Principles of Microeconomics In Class Question The Perils of Group Work Medium Stakes Assignment: Worth 15 points Assume Mary and Alex have been assigned a group project to do for one of their classes. Alex does not want to put much time into working on the project and while getting an A would be nice, he is perfectly fine with a C. Mary has a 4.0 and she regards anything less than an A is to be a disaster. Assume if both Mary and Alex work hard that both will receive an A. The value of the A is equal to 200 to Mary and 80 to Alex. The cost of doing the work is equal to 80 for Mary and 120 to Alex. If everyone fails to work hard everyone receives a C. The value of the C is equal to 0 for Mary and is equal to 60 for Alex. If neither Mary nor Alex works hard there is a cost to each person equal to 20. If Mary has to do all the work both she and Alex will receive an A. The value of the A for each person is the same as given above. But if Mary does all the work her cost is equal to 180 while the cost for Alex is 0. If Alex does all the work both he and Mary will receive an A. The value of the A for each person is the same as given above. But if Alex does all the work his cost is 200 and Mary's cost is 0. 1. Fill in the matrix. 2. We defined a dominant strategy as a strategy that a person will follow regardless of the strategy the other person engages in. Prove that Alex has a dominant strategy but Mary does not. 3. Prove that since Alex has a dominant strategy that we can find a unique equilibrium. What is the equilibrium? 4. How do you think this outcome explains why very few economists assign group work to their students? Alex Works Hard Alex Doesn't Work Hard Mary Works Hard Mary's Net Return Mary's Net Return Alex's Net Return Alex's Net Return Mary Doesn't Work| Mary's Net Return Mary's Net Return Hard Alex's Net Retam Alex's Net Retam