The company that you manage has invested \(\$ 5\) million in developing a new product, but the development is not quite finished. At a recent meeting, your salespeople report that the introduction of competing products has reduced the expected sales of your new product to \(\$ 3\) million. If it would cost \(\$ 1\) million to finish development and make the product, should you go ahead and do so? What is the most that you should pay to complete development?

When making economic decisions, a fundamental concept is that of opportunity cost, which refers to the value of what you have to give up in order to choose something else. In the context of the exercise you mentioned, the opportunity cost of investing an additional \( \$1 \) million into the product's development would be the value of the best alternative use of those funds.

For instance, if your company could use that \( \$1 \) million to invest in another project with expected returns of \( \$2 \) million, the opportunity cost of completing the product development would not just be the \( \$1 \) million spent, but also the \( \$2 \) million in foregone profits from the alternative investment. Therefore, when considering whether to invest in completing development, the company should weigh not only the projected net gains from this product but also what it might earn from the next best alternative investment.

The term sunk cost refers to money that has already been spent and cannot be recovered. It's a past cost that should not influence ongoing decision making since it will remain the same regardless of the outcome of current decisions. In the given exercise, the \( \$5 \) million already invested in the new product is a sunk cost.

When deciding whether to spend an additional \( \$1 \) million to complete the product, the \( \$5 \) million already spent should not be factored into the decision. Only the future costs and benefits should be considered. This is because the \( \$5 \) million cannot be recovered whether you choose to invest more and complete the product or abandon it; thus, it's irrelevant to the final decision about the additional investment.

A key tool for making rational economic decisions is the cost-benefit analysis, which involves comparing the costs and benefits of a decision to determine whether it is financially worthwhile.

In the situation described, conducting a cost-benefit analysis would require considering the expected benefits of completing the product's development, which are the expected sales of \( \$3 \) million, against the additional \( \$1 \) million cost required to finish development. The net gain (or loss) can be calculated as the Expected Sales (\( \$3 \) million) minus the Additional Development Cost (\( \$1 \) million).

If the net gain is positive, the benefit of completing the product outweighs the cost, and it would make sense to proceed. However, the analysis should also consider any opportunity costs associated with the decision. Moreover, the cost to complete development should not exceed the expected sales to avoid a loss, setting an upper limit for spending on the product's completion. This approach helps in determining the most rational financial decision based on the analysis of tangible benefits and costs.