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 average and freethrow average. $$ \begin{array}{l|c|c} \text { Name } & \text { Batting average } & \text { Free-throw average } \\\ \text { Kelley } & 70 \% & 60 \% \\\ \text { Jackie } & 50 \% & 50 \% \\\ \text { Curt } & 10 \% & 30 \% \\\ \text { Gerry } & 80 \% & 70 \% \end{array} $$ a. Explain how you would use the concept of comparative 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?

Step by step solution

01

Calculate Opportunity Cost for Each Player

First, we will find the opportunity cost of free throws in terms of batting average for each player. The opportunity cost is the cost of giving up one unit of good (in this case, baseball) to specialize in one unit of another good (in this case, basketball). To find the opportunity cost for each player, we will use the formula: $${\text{Opportunity Cost}} = \frac{\text{Batting Average}}{\text{Free-Throw Average}}$$

02

Find Opportunity Cost for Kelley

For Kelley, $${\text{Opportunity Cost}} = \frac{70\%}{60\%} = 1.17$$

03

Find Opportunity Cost for Jackie

For Jackie, $${\text{Opportunity Cost}} = \frac{50\%}{50\%} = 1.00$$

04

Find Opportunity Cost for Curt

For Curt, $${\text{Opportunity Cost}} = \frac{10\%}{30\%} = 0.33$$

05

Find Opportunity Cost for Gerry

For Gerry, $${\text{Opportunity Cost}} = \frac{80\%}{70\%} = 1.14$$

06

Assign Players Based on Comparative Advantage

Now, we'll assign the players to baseball or basketball teams based on their comparative advantage. Players with lower opportunity cost in terms of batting average will be better at basketball, while those with higher opportunity cost will be better at baseball. Kelley and Gerry have the highest opportunity costs (1.17 and 1.14, respectively), so they will be assigned to the baseball team. Jackie and Curt have the lowest opportunity costs (1.00 and 0.33, respectively), so they will be assigned to the basketball team.

07

Discuss Players' Satisfaction and Efficiency

Other basketball players might be unhappy because they see that Curt has a low free-throw average compared to other players, while other baseball players may be satisfied because they see Kelley and Gerry performing well in batting. Nonetheless, an economist would say that this is an efficient way to allocate players for the dormitory sports teams because it maximizes the overall performance by utilizing each player's comparative advantage in baseball or basketball. By focusing on their respective comparative advantages, each player can contribute more effectively to their team's overall success. This specialization and trade-off allow both baseball and basketball teams to make better use of limited resources (the last four players), thus demonstrating efficiency in the allocation process.

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