Question

You just spent \(\$ 40\) on a new movie for your collection. You would have preferred the director's cut but discovered when you got home that you bought the theatrical version. The store you bought the movie from has an "all sales final" policy, but you could resell the movie online for \(\$ 30\). The director's cut sells for \(\$ 50 .\) By how much would you need to value the director's cut over the theatrical version for it to make sense for you to sell the version you bought and buy the director's cut?

Short answer

You need to value the director's cut at \( \$20 \) more than the theatrical version.

Step-by-step solution

Understanding the Problem

You spent \( \\(40 \) on a theatrical version of a movie, but you want the director's cut which costs \( \\)50 \). You can resell the movie you bought for \( \$30 \) online. We need to find out how much more you need to value the director's cut compared to the theatrical version to justify selling the theatrical version and buying the director's cut.

Calculate the Net Cost

If you sell the theatrical version for \( \\(30 \), you are still left with a net cost of \( \\)10 \) (since \( \\(40 - \\)30 = \\(10 \)). Then you would need an additional \( \\)50 \) to buy the director's cut, which adds up to a total of \( \$60 \) spent on the director's cut after selling your current movie.

Determine the Additional Valuation Needed

You initially spent \( \\(40 \) on the theatrical version. To make it worthwhile to spend \( \\)60 \) in total for the director's cut, you must value the director's cut at least \( \\(20 \) more than the theatrical version. This is because \( \\)60 - \\(40 = \\)20 \).

Solution Conclusion

Therefore, you would need to value the director's cut at least \( \$20 \) more than what you originally paid for the theatrical version to justify selling it and purchasing the director's cut.

Key concepts

Cost-Benefit Analysis

Cost-benefit analysis is like being the math detective in decision-making. It’s about weighing the pros and cons in monetary terms. Imagine you buy a theatrical version of a movie for $40, but realize you want the director’s cut instead. The director's cut costs $50, and you can resell your current version for $30.
This scenario involves several costs and benefits:

• Initial cost: $40 spent on the theatrical version.
• Resale benefit: Selling the theatrical version gets you $30 back.
• Director's cut cost: Buying the director’s cut costs $50.

Doing the math, if you sell your movie, you will have a net remaining cost of $10 ($40 - $30 = $10). Buying the director’s cut means spending an additional $50. In total, the net cost for switching to the director’s cut after selling the original is $60 ($10 leftover cost + $50 for new purchase).
To find if this swap is worth it, your benefits (the value you place on the director’s cut) need to exceed the costs. If you value the director's cut $20 more than the theatrical version, then the switch makes sense. It's the extra benefit you need to justify the extra expense.

Decision Making

Decision making is about choosing between different options, often involving a complex puzzle of factors. In our movie example, this means deciding whether to keep the movie you bought or to sell it and get the more expensive director's cut.
Various factors influence this decision:

• Financial considerations: Total expense after reselling your movie is $60 if you choose to get the director's cut.
• Personal preference: You must consider how much more you enjoy the director’s cut versus the theatrical version.
• Market conditions: Consider the demand for the director’s cut or if it’s a rare item you cannot afford to miss.

Ultimately, decision-making in this context requires assessing whether the benefits of having the desired version of the movie outweigh the financial sacrifice and effort required to obtain it. Logical decision-making involves considering both the current situation and future benefits.

Sunk Cost Fallacy

A sunk cost is a past expense that cannot be recovered. The sunk cost fallacy happens when you let these unrecoverable costs influence your future decisions.
In our example, you spent $40 on a movie that wasn't exactly what you wanted. This money is a sunk cost because the store has a 'no returns' policy and it cannot be retrieved. It's tempting to hold onto something because you spent money on it, but doing so doesn’t change the fact that it’s spent.
The rational approach is to ignore the $40 already spent and focus on the incremental costs and benefits. You should only consider the $30 you get back from selling and the additional $50 needed for the director’s cut. This way, you avoid the sunk cost fallacy by making a decision based on your current options and potential satisfaction, not on past expenditures.
Think of it as "disposing of regret"—if future enjoyment is worth the new expense and hassle, it's better to act based on what makes you happier now, rather than dwell on money already spent.