Let's analyze the given data and determine which allocation of tasks is most efficient based on the opportunity costs.
1. Opportunity Cost for Sam:
- Sam can process 7 tax returns per day.
- Alternatively, Sam can make \( \frac{30}{28} \) sales calls per day.
Opportunity Cost of 1 Tax Return for Sam:
Since Sam has the option to process 7 tax returns or make \( \frac{30}{28} \) sales calls per day, let's calculate the opportunity cost of processing one tax return in terms of sales calls:
[tex]\[ \text{Opportunity Cost per Tax Return for Sam} = \frac{\text{Sales Calls Sam can make}}{\text{Tax Returns Sam can process}} = \frac{\frac{30}{28}}{7} = 1.0714 \text{ sales calls} \][/tex]
Opportunity Cost of 1 Sales Call for Sam:
Similarly, the opportunity cost of making one sales call in terms of tax returns:
[tex]\[ \text{Opportunity Cost per Sales Call for Sam} = \frac{\text{Tax Returns Sam can process}}{\text{Sales Calls Sam can make}} = \frac{7}{\frac{30}{28}} = 6.5333 \text{ tax returns} \][/tex]
2. Opportunity Cost for KC:
- KC can make 4 sales calls per day.
- Alternatively, KC can process 1 tax return per day.
Opportunity Cost of 1 Sales Call for KC:
The opportunity cost of making one sales call in terms of tax returns for KC:
[tex]\[ \text{Opportunity Cost per Sales Call for KC} = \frac{\text{Tax Returns KC can process}}{\text{Sales Calls KC can make}} = \frac{1}{4} = 0.25 \text{ tax returns} \][/tex]
Opportunity Cost of 1 Tax Return for KC:
The opportunity cost of processing one tax return in terms of sales calls for KC:
[tex]\[ \text{Opportunity Cost per Tax Return for KC} = \frac{\text{Sales Calls KC can make}}{\text{Tax Returns KC can process}} = 4 \text{ sales calls} \][/tex]
3. Conclusions based on Opportunity Costs:
When comparing the opportunity costs, we observe the following:
- Sam’s opportunity cost of making a sales call (6.5333 tax returns) is very high compared to KC’s opportunity cost of making a sales call (0.25 tax returns). Therefore, it is inefficient for Sam to make sales calls.
- KC’s opportunity cost of processing a tax return (4 sales calls) is much higher compared to Sam’s opportunity cost of processing a tax return (1.0714 sales calls). Therefore, it is inefficient for KC to process tax returns.
Thus, the best allocation of tasks should be:
- Sam should focus on processing tax returns as this is what Sam is more productive at relative to sales calls.
- KC’s time would be best spent making sales calls as KC is more productive at this task relative to processing tax returns.
Valid economic conclusion:
- Sam's time would be best spent on tax returns.
- KC's time would be best spent on sales calls.
By following this optimal allocation, they can maximize their overall productivity and efficiency.
