Question

A doctor carns \(\$ 250,000\) per year, while a professor carns \(\$ 40,000\). They play tennis against cach other cach Saturday morning, cach giving up a morning of relaxing, reading the paper, and playing with their children. They could each decide to work a few extra hours on Saturday and carn more income. But they choose to play tennis or to relax around the house. Are their opportunity costs of playing tennis different?

Short answer

Explain your answer. Answer: Yes, the opportunity costs of playing tennis for the doctor and the professor are different. The doctor has a higher opportunity cost (\$250) because they earn more per hour (\$125) than the professor (\$20). If they both chose to work instead of playing tennis for two hours, the doctor would potentially lose more income (\$250) than the professor (\$40). However, personal preferences and non-financial benefits should also be considered when evaluating opportunity costs.

Step-by-step solution

Calculate hourly earnings

To calculate hourly earnings, we need to divide each person's annual salary by the number of working hours in a year. Assuming they both work 40 hours per week and 50 weeks per year (taking into account vacations and holidays), the total number of hours worked by each is 2000 hours per year. Doctor's hourly earnings: \(250,000 / 2000 = \$ 125\) per hour Professor's hourly earnings: \(40,000 / 2000 = \$ 20\) per hour

Determine time spent playing tennis

We need to know how long they play tennis on Saturday mornings to determine the opportunity cost of their choices. For example, let's assume they play tennis for 2 hours each Saturday.

Calculate Opportunity Costs

Opportunity cost is the value of the next best alternative forgone. In this case, the opportunity cost of playing tennis for each person is the income they could potentially gain if they chose to work instead of playing tennis. Doctor's opportunity cost: \(125 × 2 = \$ 250\) Professor's opportunity cost: \(20 × 2 = \$ 40\)

Comparison and Conclusion

Comparing the opportunity costs of the doctor and the professor, we find that the doctor has a higher opportunity cost (\$250) than the professor (\$40). This is because the doctor earns more per hour, and therefore has more to lose financially by choosing to play tennis instead of working. However, it is important to consider that income is not the only factor in determining the value of a leisure activity. Personal preferences and non-financial benefits, such as relaxation and spending time with family, should also be taken into consideration when evaluating opportunity cost.

Key concepts

Hourly Earnings Calculation

To understand opportunity cost, we begin with the calculation of hourly earnings, which tells us how much each individual makes for one hour of work. This calculation helps determine what they give up—in terms of potential earnings—by not working. Here, we assume both the doctor and the professor work 40 hours a week for 50 weeks a year, totaling 2000 hours annually.

The doctor earns an annual salary of \(250,000. To find the hourly rate, divide this amount by 2000:

• Doctor's hourly earnings: \( \\)250,000 / 2000 = \\(125 \) per hour

Similarly, for the professor with an annual salary of \)40,000:

• Professor's hourly earnings: \( \\(40,000 / 2000 = \\)20 \) per hour

Knowing these figures helps us understand what each person financially foregoes by choosing not to work for a given time.

Income Comparison

With hourly earnings determined, we can compare the potential income each earns during an equivalent period. This is essential for understanding who gives up more financially in not working those hours. Imagine both the doctor and professor decide to play tennis for 2 hours each Saturday.

The opportunity cost, or the income they could have earned by working instead, is calculated by multiplying their hourly earnings by the time spent on tennis. For the doctor:

• Doctor's opportunity cost: \( \\(125 \times 2 = \\)250 \)

For the professor:

• Professor's opportunity cost: \( \\(20 \times 2 = \\)40 \)

This comparison shows the doctor incurs a higher opportunity cost because they have higher hourly earnings. Therefore, the doctor sacrifices more in financial terms by playing tennis rather than working.

Leisure Activity Value

Opportunity cost isn't purely about money. While the doctor foregoes a larger amount by not working, playing tennis or spending time relaxing holds intrinsic value. For both individuals, leisure activities like tennis offer personal satisfaction and benefits that aren't measured in dollars.

Playing tennis provides:

• Physical exercise and health benefits.
• Stress relief compared to working.
• Social interaction, which might be enjoyable and fulfilling.
• Time away from demanding work environments to relax and rejuvenate.

It's crucial to remember that these aspects are integral to evaluating opportunity costs. The subjective value of leisure to the doctor and professor might be higher than the financial loss incurred, making their decision to play tennis a reasonable choice. Their enjoyment and life satisfaction can be considered invaluable, outweighing mere monetary earnings.