What is opportunity cost really?

Question

It seems to me there that the most common definition of opportunity cost in economics is that opportunity cost is the net benefit of the next best alternative forgone. (See this question: What is Opportunity Cost?)

Did I interpret that correctly? Or is the definition of opportunity cost different?

So I’m going to guess that the purpose of an opportunity cost is to make a rational decision, by choosing the option with a lower opportunity cost. Is that line of reasoning correct?

Assuming that the above is indeed the most accepted definition of opportunity cost, how would one solve a problem like this which is in fact given in my textbook: I can buy a Tractor or TV a Tractor costs 5000 dollars while a TV costs 1000 dollars, assuming these are the only two options I can undertake what is the opportunity cost of buying a tractor?

Now per the above definition I would have to calculate the net benefit I would get by buying the TV, what’s this benefit? Isn’t it unanswerable?

Something similar occurs when discussing comparative advantage(perhaps I’m conflating macro and micro but why should the concept be different?). Specifically say I calculate that if I produce 1 Ton of Tea I’d have to forgo 0.2 Tons of wool. Shouldn’t may opportunity cost of producing 1 Ton of Tea be the net benefit I would have gotten by producing wool? According to Wikipedia and my textbook the answer is simply 0.2 Tons of wool. Which in my opinion makes no sense. (Imagine a fictional world where wool is completely useless shouldn’t the opportunity cost be negative?)

Either the textbook is extremely wrong or I am extremely confused.

Answer 1

Did I interpret that correctly? Or is the definition of opportunity cost different?

No you are not interpreting it correctly. Opportunity cost is the value of best alternative forgone.

So I’m going to guess that the purpose of an opportunity cost is to make a rational decision, by choosing the option with a lower opportunity cost. Is that line of reasoning correct?

No that is not the point. The point of opportunity cost is not to ignore implicit cost. For example, naive view of stroll through park is that it is costless, but that is naive because instead of that stroll you could be doing something else. Rational decision making requires that you take into account that the same time could be devoted to other activities and loss of that time is not costless as you could be studying, working etc.

Assuming that the above is indeed the most accepted definition of opportunity cost, how would one solve a problem like this which is in fact given in my textbook

It is not generally accepted definition, since you come up with that net benefit definition its up to you decide what it means. Generally accepted definition is that it is the value of best forgone alternative not net benefit.

Something similar occurs when discussing comparative advantage(perhaps I’m conflating macro and micro but why should the concept be different?). Specifically say I calculate that if I produce 1 Ton of Tea I’d have to forgo 0.2 Tons of wool. Shouldn’t may opportunity cost of producing 1 Ton of Tea be the net benefit I would have gotten by producing wool? According to Wikipedia and my textbook the answer is simply 0.2 Tons of wool. Which in my opinion makes no sense. (Imagine a fictional world where wool is completely useless shouldn’t the opportunity cost be negative?)

The Wikipedia and textbook is correct. The numerical value of opportunity cost depends on what units you use. There is no requirement to use dollars or euros. A cost (not just opportunity cost but cost of anything - ice cream etc) can be measured in goods as well. In fact dollar can be viewed as a 'numeraire good'. The Wikipedia and textbook just states the opportunity cost is 0.2tn of wool, if wool has low or no value to you it is still 0.2tn of 'low value' wool.

Answer 2

I will start with this quote:

So I’m going to guess that the purpose of an opportunity cost is to make a rational decision, by choosing the option with a lower opportunity cost. Is that line of reasoning correct?

It is not entirely correct. Opportunity cost is the cost of the best alternative option. Let's suppose you have 4 options:

$U(a) = 250$

$U(b) = 200$

$U(c) = 150$

$U(d) = 100$

If you choose a different option than the option $a$, then your opportunity cost would always be $250$. Thus the purpose of opportunity cost could not be to make a rational decision, by choosing the option with a lower opportunity cost. The purpose is to show how much the consumer would have to be compensated for changing a decision. Let's say the consumer decided to choose option $a$, then the opportunity cost is $200$, which means he has to be given at least $250 - 200 = 50$ in utility to change a decision.

What concerns the rest, it depends on your valuation of a given good. For example, you can assign a subjective value (for simplicity measured in money equivalent) such as $U(tractor) = 7000$ and $U(TV) = 2000$. Then your opportunity cost of buying a tractor would be $2000 - 1000 = 1000$. The case from your textbook is missing some important information: Does your money disappear after performing an action since you cannot choose anything else? If so, then your opportunity cost would be $1000$ dollars.

The catch is in interpretation of opportunity cost as the biggest payoff you would get by not selecting the current choice. If you can either produce 1 Ton of tea or 0.2 Tons of wool and no other valuation (price, subjective value etc.) given, then the production of wool is the opportunity cost to the production of tea, considering both cannot happen at the same time.