Suppose an assistant professor of economics is earning a salary of \(\$ 75,000\) per year. One day she quits her job, sells \(\$ 100,000\) worth of bonds that had been earning 3 percent per year, and uses the funds to open a bookstore. At the end of the year, she shows an accounting profit of \(\$ 80,000\) on her income tax return. What is her economic profit?

Understanding opportunity cost is pivotal for grasping the nuances of economic profit. Imagine you're standing at a crossroads where you can choose only one path; the opportunity cost is the benefit you miss out on by not taking the other path. Similarly, in the context of financial decisions, opportunity costs represent the benefits an individual, investor, or business misses out on when choosing one alternative over another.

In the given scenario, an assistant professor of economics leaves her job, which has a clear financial implication. By quitting her salary of \(75,000\) dollars a year, she forgoes this guaranteed income to venture into a new business. Additionally, she sells bonds worth \(100,000\) dollars earning 3% to finance the bookstore. The foregone interest from these bonds (\(3,000\) dollars) is also part of the opportunity cost. This means the total opportunity cost of opening the bookstore is the sum of the lost salary and the interest, amounting to \(78,000\) dollars. This cost is invisible on the accounting books but significantly impacts the actual profitability of new ventures.

Shift the lens now to accounting profit, which is a more straightforward concept often reflected in financial documents like income statements. It's calculated by subtracting the explicit costs of doing business from the total revenues. Unlike economic profit, accounting profit doesn't consider the value of the next best alternative, or opportunity cost. It's concerned only with tangible costs and revenue.

In our case, the assistant professor, now bookstore owner, calculated her accounting profit as \(80,000\) dollars. This number is what you might see on the income tax return, showing a seemingly healthy profit from the bookstore venture. However, it's a partial view of profitability since it doesn't reflect the full economic picture. Only by including the opportunity costs will we see the complete financial outcome of the professor's decision to switch careers.

Lastly, let's drill down on explicit costs, which are the direct, out-of-pocket expenses paid in the course of running a business. These are the easily identified payments made to external entities, such as rent, utilities, wages, and supplies. When you're preparing a budget or calculating the accounting profit, these explicit costs are the figures you subtract from your revenues to assess your financial health.

However, as mentioned in the problem's solution, no explicit costs have been provided for the bookstore. This lack of information implies that we're either assuming the explicit costs are zero, which is highly unlikely in the real world, or that they are somehow included in the reported accounting profit of \(80,000\) dollars. This missing piece could be confusing for a student trying to understand the concept. Clarifying that explicit costs are usually a key factor in determining profitability, even when they're not explicitly mentioned in an exercise, helps in providing a complete picture of the expenses involved in running a business.