Question

Use the following data to work. Four methods of completing a tax return and the time taken by each method are with a \(\mathrm{PC}, 1\) hour; with a pocket calculator, 12 hours; with a pocket calculator and paper and pencil, 12 hours; and with a pencil and paper, 16 hours. The \(\mathrm{PC}\) and its software \(\cos t \$ 1,000,\) the pocket calculator costs \(\$ 10,\) and the pencil and paper cost \(\$ 1\). Which method is economically efficient if the wage rate is (i) \(\$ 5\) an hour, (ii) \(\$ 50\) an hour, and (iii) \(\$ 500\) an hour?

Short answer

At \(\text{\$5}\) and \(\text{\$50}\) per hour, use the Pocket Calculator. At \(\text{\$500}\) per hour, use the PC.

Step-by-step solution

Identify the Costs

List the costs for each method, both the time taken and the product costs: - PC: 1 hour and \(\text{\$1,000}\) - Pocket Calculator: 12 hours and \(\text{\$10}\) - Pocket Calculator and Paper and Pencil: 12 hours and \(\text{\$11}\) - Pencil and Paper: 16 hours and \(\text{\$1}\).

Calculate Total Cost for Each Method

Determine the total cost (time cost + product cost) for each method at various wage rates.i. For wage rate of \(\text{\$5}\) per hour: - PC: \(1 \text{ hour} \times \text{\$5} + \text{\$1,000} = \text{\$1,005}\) - Pocket Calculator: \(12 \text{ hours} \times \text{\$5} + \text{\$10} = \text{\$70}\) - Pocket Calculator and Paper and Pencil: \(12 \text{ hours} \times \text{\$5} + \text{\$11} = \text{\$71}\) - Pencil and Paper: \(16 \text{ hours} \times \text{\$5} + \text{\$1} = \text{\$81}\).ii. For wage rate of \(\text{\$50}\) per hour: - PC: \(1 \text{ hour} \times \text{\$50} + \text{\$1,000} = \text{\$1,050}\) - Pocket Calculator: \(12 \text{ hours} \times \text{\$50} + \text{\$10} = \text{\$610}\) - Pocket Calculator and Paper and Pencil: \(12 \text{ hours} \times \text{\$50} + \text{\$11} = \text{\$611}\) - Pencil and Paper: \(16 \text{ hours} \times \text{\$50} + \text{\$1} = \text{\$801}\).iii. For wage rate of \(\text{\$500}\) per hour: - PC: \(1 \text{ hour} \times \text{\$500} + \text{\$1,000} = \text{\$1,500}\) - Pocket Calculator: \(12 \text{ hours} \times \text{\$500} + \text{\$10} = \text{\$6,010}\) - Pocket Calculator and Paper and Pencil: \(12 \text{ hours} \times \text{\$500} + \text{\$11} = \text{\$6,011}\) - Pencil and Paper: \(16 \text{ hours} \times \text{\$500} + \text{\$1} = \text{\$8,001}\).

Compare the Total Costs

Identify the method with the lowest total cost for each wage rate:i. At \(\text{\$5}\) per hour, the Pocket Calculator (total cost: \(\text{\$70}\)) is the most economical.ii. At \(\text{\$50}\) per hour, the Pocket Calculator (total cost: \(\text{\$610}\)) is the most economical.iii. At \(\text{\$500}\) per hour, the PC (total cost: \(\text{\$1,500}\)) is the most economical.

Key concepts

time management

Time management is about using your available time efficiently. In this example, different tax preparation methods take different times: using a PC takes 1 hour, whereas using a pencil and paper takes 16 hours. To effectively manage your time, it's crucial to consider how long each task will take and choose the methods that will save you the most time without compromising on quality. For instance, if you have a busy schedule, dedicating 1 hour to using a PC might be far more practical than spending 16 hours with paper and pencil. This understanding ultimately helps allocate your time to more productive activities in life.

cost analysis

Cost analysis is the process of determining the overall expenses involved in an activity. It includes both the direct costs (like the price of tools/materials) and indirect costs (such as time spent). In the tax preparation example, we look at:

• PC: Costs \(1,000 and 1 hour
• Pocket Calculator: Costs \)10 and 12 hours
• Pocket Calculator with Paper and Pencil: Costs \(11 and 12 hours
• Pencil and Paper: Costs \)1 and 16 hours

The idea is to weigh the financial and time costs to find the most economical method. This can change depending on your hourly wage. A higher wage means your time is more valuable, shifting the balance towards quicker but more expensive methods.

wage rates

Wage rates indicate how much your time is worth in financial terms. In our calculations:

• At a \(5/hr wage, your time isn't highly valued, making cheaper but time-consuming methods attractive
• At \)50/hr, time starts to become more valuable
• At \(500/hr, spending less time becomes crucial due to the high opportunity cost of your time being spent elsewhere

This can significantly affect your decision about which tax preparation method to use. For example, at \)500/hr, the quickest method, using the PC, becomes the most cost-effective despite its high product cost because your time is saved.

opportunity cost

Opportunity cost is the value of what you give up when you choose one option over another. In this tax preparation example, choosing a slower method like using a pencil and paper (16 hours) means foregone earnings from other potential activities you could have done in that 16-hour window. For example, if your wage is \(500/hr, that's \)8,000 you could have earned doing something else. Therefore, understanding opportunity cost helps us make better economic decisions by considering not just the direct costs, but the value of the alternatives we're giving up.