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My university is using this textbook. The text clearly states, “Economists use the term opportunity cost to indicate what must be given up to obtain something that is desired.”

This leads me to believe that if you are a salaried worker who makes 50 dollars per hour and works a standard five-day workweek, the opportunity cost of you mowing your lawn during the weekend is 0 dollars. You are giving up your unpaid free time to mow the lawn. When I brought this up in the online discussion I was told by the instructor, "the cost of your free time is estimated using your wage rate."

Is free time = wage rate just the standard convention? This hardly seems appropriate since you aren't giving anything up other than your free time. The situation would be different if you were giving up weekend work to mow your lawn.

Will
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    You are right that’s not completely appropriate. Maybe the worker cant work during the weekend at his job because of labor laws that restrict working during weekend (in some countries grocery store clerks can’t work on Sunday). Also, wage may vary on the margin. But, it would not be zero but the value of the next best alternative. Furthermore, even though the answer your teacher gave is not totally accurate it’s common approximation to assume that opportunity cost is just given by your wage (even often used in serious research), so within the class context such answer is not necessary bad – 1muflon1 May 25 '20 at 02:20
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    Also you are making mistake when you equate free time with no value. In fact maybe the second best alternative for the worker is to go see a movie which the worker values at 10$ then the opportunity cost of mowing lawn would be 10$ and so on. Free time can be actually quite valuable especially if you don’t have a lot of it. – 1muflon1 May 25 '20 at 02:24

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There is a crucial detail missing in the scenario you describe. Is the worker working a five day week (and no more) because that is what their terms of employment require? Or do they have the option of doing additional paid work (at the same rate, and for as many hours as they wish) at weekends, but on this occasion have opted to work only five days in the week? If the latter, then it is clear that the opportunity cost of mowing the lawn is the value of the time taken at the wage rate.

If however, the worker's paid work is limited to five days in the week, then it is not paid work that is being given up in order to mow the lawn at the weekend. Although the concept of opportunity cost seems clear enough, its application in this situation can be quite difficult, because it may be hard to identify what exactly has been given up. Suppose (as suggested in the comment by 1muflon1) that an alternative use of the time was to watch a movie. Fleshing out this scenario, suppose that late on Sunday afternoon, the worker was just about to watch the movie, but suddenly noticed that the grass was getting long, and decided that it couldn't be left for another week, so instead went to mow it. So far, it seems that what has been given up is watching the movie. But suppose that, having mowed the grass, they decide to watch the movie in the evening, displacing some other activity. Rather than a clearly identifiable alternative that has been given up to mow the lawn, there may be a whole series of activities, each of which has merely been slightly postponed to give priority to another.

A context in which economists make use of the opportunity cost of leisure time is the travel cost method for estimating the value of non-market environmental goods such as parks. In this context the value of leisure time has often been taken to be a fraction of the wage, an influential source explaining the basis for such an assumption being Cesario (1976). Use of a fraction of the (average) wage can be a pragmatic way to avoid the complexity of identifying what an individual has given up, and for aggregation over individuals in different circumstances.

Reference

Cesario, F J (1976) Value of Time in Recreation Benefit Studies Land Economics 52(1) Feb 1976 pp 32-41

Adam Bailey
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Since you are presumably not working 24 hours a day, your free time clearly has an economic value > 0 to you (otherwise driving an Uber or solving tasks on Amazon's MTurk would be preferable to having any free time at all). So working on the weekend most definitely still has an opportunity cost.

The only question remains how to price this opportunity cost for your weekend. Using your base hourly salary rate makes sense as a proxy. If you are a salaried employee, you are in fact already trading in 40 hours a week every week for this price, so it stands to reason that your price for 5 more hours of work should not be that far off.

Of course, as is true for all economic models (and especially the ones you find in introductory texts), this is somewhat of an oversimplification. Local regulations may prevent you from working more than 40 yours in a salaried position, you may have trouble finding a salaried position with an acceptable price for the weekend, or your free time may be a good with diminishing returns (i.e., while your salary rate is an acceptable price to you for the first 40 hours of work per week, you expect a higher price to work overtime or on the weekend since you by then have less free time to give away). However, as I said, your base salary rate is still a reasonable starting point to value your time.

xLeitix
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If you mow the lawn, you give up time on the couch, not time at work. So the opportunity cost is zero.

Or, you could pay the neighbor boy to mow your lawn. So the opportunity gain is his salary, which makes opportunity cost the negative the gain.

If you pay him 10 Dollars to mow the lawn, your opportunity cost ist -10 Dollars.

And, now lets calculate the cost of going to the gym you avoid paying by mowing your lawn .. ;-)

weberjn
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