Kayla can cook dinner in 30 minutes and wash the laundry in 20 minutes. Her roommate takes twice as long to do each task. How should the roommates allocate the work?

Question

Kayla can cook dinner in 30 minutes and wash the laundry in 20 minutes. Her roommate takes twice as long to do each task. How should the roommates allocate the work?
	a. Kayla should do more of the washing based on her absolute advantage. 	
	b. Kayla should do more of the washing based on her comparative advantage. 	
	c. There are no gains from trade in this situation. 	
	d. Kayla should do more of the cooking based on her comparative advantage

GPT-4o mini · Answer

To determine how Kayla and her roommate should allocate the work, we must first assess their absolute and comparative advantages in each task.

Kayla's times:

Cooking: 30 minutes
Washing: 20 minutes

Her roommate's times:

Cooking: 30 minutes × 2 = 60 minutes
Washing: 20 minutes × 2 = 40 minutes

Absolute Advantage:

Kayla has an absolute advantage in both tasks because she can do both cooking (30 minutes vs. 60 minutes) and washing (20 minutes vs. 40 minutes) faster than her roommate.

Comparative Advantage: To find their opportunity costs for each task:

For Kayla:
- Opportunity cost of cooking: She can either cook (30 minutes) or wash (20 minutes). The opportunity cost of cooking is 1.5 loads of laundry (30 min cooking ÷ 20 min washing).
- Opportunity cost of washing: The opportunity cost of washing is 0.67 dinners (20 min washing ÷ 30 min cooking).
For her roommate:
- Opportunity cost of cooking: 2 loads of laundry (60 min cooking ÷ 30 min washing).
- Opportunity cost of washing: 0.5 dinners (40 min washing ÷ 60 min cooking).

Comparative Advantages:

Kayla has a lower opportunity cost for washing (0.67 dinners) compared to her roommate (0.5 dinners), so her roommate has a comparative advantage in washing.
The roommate has a lower opportunity cost for cooking (2 loads of laundry) compared to Kayla (1.5 loads of laundry), so Kayla has a comparative advantage in cooking.

Based on this analysis, the answers to the options are:

a. Kayla should do more of the washing based on her absolute advantage. (Incorrect; she has the absolute advantage but we are looking for comparative advantage.)
b. Kayla should do more of the washing based on her comparative advantage. (Incorrect; her roommate has the comparative advantage in washing.)
c. There are no gains from trade in this situation. (Incorrect; there are gains from trade due to comparative advantages.)
d. Kayla should do more of the cooking based on her comparative advantage. (Correct; Kayla has a comparative advantage in cooking.)

Therefore, the correct answer is d. Kayla should do more of the cooking based on her comparative advantage.