Question

16.You are in charge of allocating residents to your dormitory's baseball and basketball teams. You are down to the last four people, two of whom must be allocated to baseball and two to basketball. The accompanying table gives each person's batting aver- age and free-throw average. Name Batting average Free-throw average Kelley Nina Curt Yul 70% 50% 1090 80% 60% 5090 30% 70% a. Explain how you would use the concept of com parative advantage to allocate the players. Begin by establishing each player's opportunity cost of free throws in terms of batting average. b. Why is it likely that the other basketball players will be unhappy about this arrangement but the other baseball players will be satisfied? Nonetheless, why would an economist say that this is an efficient way to allocate players for your dormitory's sports teams?

Answer 1

a) Comparative advantage refers to having an advantage to produce a good more efficiently than another good. In the context of the above question , this is the advantage of batting average over free throw.

Here we began by finding the opportunity cost of each player for free throws in terms of batting average.

If we allocate Kelley to basketball ( ie free throws ), then the team gains 60% free throw average whereas the baseball team is losing a player with a batting average of 70%. So opportunity cost or comparative advantage of allocating Kelley to basketball (free thropw) is   70/60 or 7/6  

Similarly if we look at the second player Nina , the opportunity cost of allocating Nina to basketball (free throw) is 50/50 or 1

Curt's opportunity cost is 10/30= 1/3 of playing free throw (basketball )

Yul's opportunity cost is 80/70= 8/7 of playing free throw (basketball )

Nina and Curt have lowest opportunity cost and hence comparative advantage in free throw . So both of them should be in the basketball team.

Yul and kelley should be baseball team (batting average )

b) The basketball players would likely be unhappy because they would be losing team players with free throw average of 60 and 70% which is more than the ones allocated to them ( we can see that Nina and Curt are worse off at playing basketball than Yul and Kelley . So basketball team is worse off.

on the other hand , the baseball team is in a good position, because they have Yul and Kelley who have better batting average than the other two players and hence would be good for the team . Overall Nina and Curt have absolute disadvantage in both the sports while Yul and Kelley have absolute advantage in both.

But in view of economist , this is an efficient outcome because the overall chances of the team to win increases for both. (maximisation )

(You can comment for doubts )