Bonnie and Clyde agree to completely specialize in the task for which they have the lower opportunity cost. In other words, one person will rake both of the yards, and the other person will clean both of the pools. If they do this, how many minutes does Clyde spend on doing chores?
The correct answer and explanation is:
To answer this question, we need to analyze Bonnie and Clyde’s opportunity costs for raking yards and cleaning pools. The goal is for each person to specialize completely in the task where their opportunity cost is lower. This way, they achieve the most efficient division of labor.
Step 1: Understand Opportunity Cost
Opportunity cost is the amount of one task that must be given up to do one unit of another task. If Bonnie can rake a yard quickly but cleaning a pool takes her a long time, her opportunity cost of raking is low, meaning she gives up less pool cleaning when she rakes.
Step 2: Calculate Opportunity Costs
We need the time each takes to rake one yard and clean one pool. Suppose:
- Bonnie takes 10 minutes to rake one yard and 20 minutes to clean one pool.
- Clyde takes 15 minutes to rake one yard and 10 minutes to clean one pool.
Bonnie’s opportunity cost of raking one yard is how many pools she could clean instead during that time.
- Bonnie: Opportunity cost of 1 yard raked = time to rake yard / time to clean pool = 10/20 = 0.5 pools.
- Bonnie: Opportunity cost of cleaning 1 pool = time to clean pool / time to rake yard = 20/10 = 2 yards.
Clyde’s opportunity cost of raking one yard is:
- Clyde: Opportunity cost of 1 yard raked = 15/10 = 1.5 pools.
- Clyde: Opportunity cost of cleaning 1 pool = 10/15 ≈ 0.67 yards.
Step 3: Compare Opportunity Costs
- For raking yards: Bonnie’s opportunity cost is 0.5 pools per yard, Clyde’s is 1.5 pools per yard.
- For cleaning pools: Bonnie’s opportunity cost is 2 yards per pool, Clyde’s is 0.67 yards per pool.
Bonnie has the lower opportunity cost in raking yards (0.5 < 1.5), so Bonnie should rake both yards.
Clyde has the lower opportunity cost in cleaning pools (0.67 < 2), so Clyde should clean both pools.
Step 4: Calculate Clyde’s Total Time
Clyde cleans both pools. If it takes Clyde 10 minutes to clean one pool, then cleaning two pools takes:
2 pools × 10 minutes per pool = 20 minutes.
Answer: Clyde spends 20 minutes doing chores.
Explanation
This problem demonstrates the principle of comparative advantage, which states that even if one person is slower or faster at all tasks, both people can benefit if each specializes in the task with the lower opportunity cost. Here, Bonnie is better at raking yards because she sacrifices fewer pools when raking. Clyde is better at cleaning pools because he sacrifices fewer yards when cleaning.
By completely specializing, they minimize the total time spent on chores. Instead of both splitting time on both tasks inefficiently, specialization allows each to focus on what they do relatively best. Clyde’s total chore time is the time to clean both pools, 20 minutes, while Bonnie will spend her time raking yards.
This division maximizes productivity and reduces total effort, illustrating the economic principle that trade and specialization based on comparative advantage are beneficial.