Professor Vigdor leads a Girl Scout troop that sells cookies in front of local grocery stores each year. The way it works is that the local Council procures 2-hour slots at particular stores, and then they are allocated to the troops. Professor Vigdor’s Girl Scouts have decided that credit for the cookies sold this way will be allocated by dividing the total number of cookies sold in a particular day by the number of shifts each girl works. So for example, suppose the troop has 2 time slots one Saturday. The first one is staffed by Girl A and Girl B, and the second one is staffed by Girl B and Girl C. Girls A and C would each get credit for ¼ of the total cookies sold at both booths, and Girl B would get credit for ½ the total (because she worked half the available shifts).
a) Why might they choose to do it this way instead of dividing the sales in each particular shift among the girls who worked that shift?
b) Based on what you’ve learned this quarter, will this allocation system maximize the girls’ effort?