Decision-Making Under Opportunity Cost for Entertainment Choices if one option is free but the other incurs some cost

Question

You have a free ticket to attend a classical music concert. If you had to pay for the ticket, you would have to pay Rs. 500/- to attend the concert. On the same evening, you have an alternative entertainment option, namely to enjoy a film music and dance event for which tickets are priced at Rs. 300/- each. Suppose your maximum willingness to pay for the event is Rs. X to attend the film music and dance event. What will you do, i.e., will you attend the classical music concert, or the film music and dance show, or does he do neither? Justify your answer.

I have encountered this question while going through my Economics Assignment. I tried to solve this in the following way.

The classical music concert is free, but its usual cost is Rs. 500. The film music and dance event costs Rs. 300.

So, I formulated the following decision criteria

If $𝑋<300$, your willingness to pay for the film music and dance event is less than its cost, so you won't attend it.

If $𝑋\geq 300$, you are willing to pay at least the ticket price for the film music and dance event.

Now we compare the alternatives.

If $𝑋<300$, the best choice is to attend the classical music concert since it is free. If $𝑋\geq 300$, we need to consider the utility or enjoyment from both events. If the utility from the classical music concert is greater or equal to the film music event, attend the concert. Otherwise, attend the film music and dance event.

However, I am unable to rigorously write it down using well established economic concepts and problem solving techniques. It would be a great help if someone could help me out here.

Answer 1

The question cannot be answered based on the information provided and assuming only knowledge of $X$.

First, note that the price of the classical music concert ticket is irrelevant, since you already have a free ticket (and it is tacitly assumed that you cannot sell it).

Let $X>0$ be the WTP for the film music and dance event, and let $Y>0$ be the WTP for the classical music concert concert. Set the utility of staying at home to $0$. Then your utilities (measured in Rs.) for the two events are $X-300$ and $Y-0=Y$, respectively. This implies that (i) you will not stay at home, and that (ii) you will go to the classical music concert if $X\le 300$. But for $X>300$ the answer also depends on $Y$.

Also, I would advise not to try thinking through this in terms of opportunity costs. This is likely to increase confusion.