Opportunity Cost Puzzle

John owns a retail consumer electronics business.

He sells ten 30 inch plasma TV sets per month. His wholesale price is $2000, his markup is $1000 and his selling price is $3000.

If he takes a set home for use in his den, which of these dollar amounts, if any, is his approximate sacrificed opportunity cost. Explain your reasoning.

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Unknowable. Unless we knew

Unknowable. Unless we knew all of the possible returns from an investment of the $1000 profit, we will never know exactly how much money he loses.

I was going to answer $1000,

I was going to answer $1000, since that is the lost potential profit, but Garrett has a point on a more abstract level.

I could also say zero. Why? Assuming the TV he brings home would never have been in inventory in the first place had he not bought it to use personally at his wholesale cost.

The one cost we really know is that he is out $2000, effectively his price as a consumer of televisions to buy the particular set at wholesale. that is a cost, measurable and real, not an opportunity cost.

None of the above. It's a

None of the above. It's a trick question, aren't they all.Zero was a reasonable possible answer, as above. Further, let's assume from his new home showroom he generates two sales a year.... the "unknowable" answer is also correct, if imprecise.
There's certainly an argument that his opportunity cost is ~$2000.
For fun, calculate the tax consequences. Sales tax? Income tax? Inventory tax?

This is a great question

This is a great question that is also used in first-year Contracts classes in law school to demonstrate the nature of damages.

Here the answer is $2000 assuming (1) no lost business from the sale (i.e., he has an unlimited capacity to obtain at wholesale) and (2) similarly, no change in pricing due to his action (i.e., perfectly competitive wholesale and retail markets).

The fact pattern is no different than had John walked into the TV shop of his brother-in-law, who offers him the TV at wholesale. He spends $2000, so that is his opportunity cost.

In the law school twist, the question is asked slightly differently but the analysis is similar. If A contracts with B (a retailer) to buy a TV and breaches the contract, then what are B's damages? Many students fall into the trap of saying "zero" because B "can sell the TV to someone else." But that ignores the fact that, had someone else bought a TV, then B would have sold two instead of one. B therefore does have damages (i.e., the lost $1,000 profit from the breached contract).

1) I'm totally changing law

1) I'm totally changing law schools. The notion that economics has any place in a contracts class borders on unconscionable in some professorial circles around here.

2) Why is the $1000 of lost profit not also in the opportunity cost? Didn't our hypothetical guy also forego his chance to profit off the t.v.?

Under my admittedly limited understanding of things, the opportunity cost here is $3,000 as it would include the cost of essentially "buying" the t.v. from himself and the costs of passing up the chance to sell it to somebody else for a profit.

3) If I were to distinguish the notion of "opportunity cost" from damages in contract (or in a tort action for conversion), I would say that, were somebody to steal our store owner's t.v., then all that would be needed to make him "whole" would be the $2000 wholesale price. With this, he can buy another t.v. and sell it for a profit. But where somebody foregoes the sale activity altogether, then surely he's also "costing" himself the opportunity to profit, right?

All of this sounds real good in my head right now. If I'm not making any sense, then somebody let me know. And begin your message with the words, "Tanner, you're just not making any bloody sense." That would be much more reminiscent of my contracts class.

My understanding of

My understanding of opportunity cost from my accounting days is money you could theoretically made. $2000 is the cost. Not opportunity cost. He spent an actual, real, definitive $2000 as the cost to have the TV in his home. Opportunity cost is what you give up, which can be highly theoretical. In this case you could say the $1000 markup, or $3000 total retail is the estimated opportunity cost.

A lot depends on John's intent. If he sells 10 and the one he takes home is an 11th he bought for the purpose of taking home, his cost is $2000 and his opportunity cost is zero.

If he loses a sale because he took home the 10th TV and it's not in stock when a customer wants to buy, then it's one of the figures above, in theory. If the markup is always the same. If he never discounts. If sales don't slow or expand.

But then, is this one of those questions that wants to be examined without reference to outside, unknowable facts, so we're chasing our tails if we try to pull assumptions in?

Assuming that your starting

Assuming that your starting point is at a time when the television has already been purcased wholesale with intent of resale, your opportunity cost is $3000 less any sales tax. Which is to say that the opportunity cost is the revenue you are foregoing by not selling the television. You don't factor in future revenues from a proposed home showroom, but they can be weighed against the opportunity cost when determining if it's a good idea.

Assuming I am reading the

Assuming I am reading the question correctly, I would say the answer is $3000. The opportunity cost of any decision consists of everything we must give up in order to carry out that decision. John sells ten TV sets per month. If he takes a set home for personal use, that is one less TV set sold; i.e., he only sells nine this month. He is giving up $3000: $2000 for the wholesale price, and $1000 in forgone profit. This assumes that demand is fixed at ten units/month, and supply is fixed at ten units/month.

Now, if we assume that demand is fixed at ten units/month but supply is not, and if John can purchase eleven units, sell ten, and keep one for himself, then the opportunity cost is only $2000.

A lot depends on John’s

A lot depends on John’s intent. If he sells 10 and the one he takes home is an 11th he bought for the purpose of taking home, his cost is $2000 and his opportunity cost is zero.

Respectfully, I think that (whether or not my above answer makes any sense) the opportunity cost will not vary according to his intent.

Opportunity cost seems to imply the question of what opportunities one foregoes by undertaking some other action. So, one's intent in undertaking that other action shouldn't affect opportunity cost.

is this one of those questions that wants to be examined without reference to outside, unknowable facts. . . ?

Yeah, I think so.

if it was after christmas

if it was after christmas the option 'delta' was against him (time) so maybe he should take it home and swallow it. rather than have it sit in inventory for months. lot of good football on in Jan. he may have reasoned.:juggle:

All, All of your answers so

All,

All of your answers so far are productive, and the combination is very educational.

I just want to interject here that I am interested in economic opportunity cost. Finding an authoritative and convincing definition has proved impossible, but my version would be something like the following :

Economic opportunity cost is inextricably tied to an act of choice. If act A is chosen over a second best choice B, then the opportunity cost of action A is the net projected beneficial result of action B that is precluded and sacrificed by the choice of A.

I would interprete this to mean that opportunity costs can include real costs as a part.

As the answers have noted, the answer must depend on assumptions about the environment in which the choice is being made. To try to restrict the range of possibilities, assume that we have an ongoing business and that the businessman is good at acting in his own self interest. Make the most likely assumptions as if the businessman is the owner of a relatively rural Circuit City franchise.

Regards, Don

As the answers have noted,

As the answers have noted, the answer must depend on assumptions about the environment in which the choice is being made. . . .

Well, then, I'm sunk. Apologies. Bowing out now.

Assuming (reasonably) that

Assuming (reasonably) that inventory is restocked regularly, and (also reasonably) that the regional demand and supply for televisions renders retail outlets and consumers as price-takers...

I would agree with Micha: $2,000, less sales tax. Perhaps $2,000 less sales tax less transaction costs if they are measurable. If he decides to purchase an extra television for the month, it will still cost $2000 dollars to his store, and none of the information given suggests that he will increase his markup. The opportunity cost must include the $2000 given up for the purchase of another television, but since that -$2000 is really +$1000 after the presumed transaction, the final opportunity cost is $2000.

Although, franchising makes this situation murky. Who is bearing the costs here? Is John stealing? Is the television damaged? If so, does the corporation write-off the cost? If John's business bears all the costs and the only transactions with the corporation are franchise fees, then my answer stays the same.

Another opportunity cost: the time and sacrifices involved with John moving this television home. Are these negligible? Does he need a company truck?

The $0 and $2000 answers are

The $0 and $2000 answers are quite amusing for their originality and convoluted reasoning :grin:, but are sadly mistaken. The accounting and legal interpretations are quite interesting, as they illustrate how these fields treat economic reasoning (that is, by largely ignoring it).

His wholesale cost is irrelevant (sunk cost), and therefore the markup is also irrelevant, so $2000 and $1000 are clearly wrong. I don't know where folks are getting $0, which would mean he didn't give up anything in taking the set home, or equivalently that it had no alternative uses whatsoever.

David Rossie hit on the right answer: $3000 less sales tax. Why is this correct? Simple: it's the highest valued alternative he gives up by taking a set home.

Noah, David Rossie hit on

Noah,

David Rossie hit on the right answer: $3000 less sales tax. Why is this correct? Simple: it’s the highest valued alternative he gives up by taking a set home.

You've inadvertently agreed with David's first comment, not his second.

I may be missing something, but I can't see how a sales tax gets involved in this problem. A sales tax flows undiminished from the retail customer to the government. Maybe the retailer can benefit from the float between the time he collects the tax and the time he pays the government, but that's in the noise for this problem.

Now that I've previewed my comment, I can't go back and quote the part of your comment on sunk costs as I intended.

However, the $2000 wholesale cost is a marginal cost, not a sunk cost for an ongoing business. More specifically it is a replacement cost, but it acts like a marginal cost. It is only after the last order (ever) has been placed that the wholesale cost effectively becomes a sunk cost.

Regards, Don

Noah, I agree with you about

Noah, I agree with you about the $0 figure but I think the $2000 figure makes sense, so long as he cannot sell an eleventh unit for profit, and so long as he can purchase an additional eleventh unit without this purchase effecting his other sales. Assuming these two factors hold true, he would not be forgoing any profit, and he would be forgoing the uses to which he could put the $2000 he spends on wholesale product.

Accounting definitions are different than economic definitions (e.g., two different definitions of the term "profit"), but one is not more valid than the other. Both have their uses. Although I'm not sure that issue is related to Don's initial question.

Sorry, I assumed that sales

Sorry, I assumed that sales tax was included in the markup.

The way I see opportunity

The way I see opportunity cost is as the most preferable alternative given up by making a choice. The TV taken home has already been paid for with $2,000. There is no way to change this.

The alternative to taking the TV home is selling it for $3,000. $3,000 is the direct opportunity cost.

I don't see how taxes are a factor.

..Perhaps unreasonably. So

..Perhaps unreasonably. So therefore it's $2000. Same reasoning. Don's question is about opportunity cost, which is purely economic reasoning. And I think the assumption about rolling inventory still holds, correct?

All, WARNING, ANSWER FOLLOWS

All,

WARNING, ANSWER FOLLOWS --

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The initial answer is $2000. Under the reasonable assumptions that the retailer may order at least 11 units, and that the market will buy 10 units per month at at price of $3000, also a profit-maximizing price for the retailer in his eyes, the taking of a unit home doesn't affect the retailer's sales and no sale is precluded and cannot produce an opportunity cost. Taking the unit home DOES result in a cash balance reduction of $2000, the wholesale price, so this is both a real cost and an opportunity cost. Until the retailer actually decides in the future what he will spend the $2000 for, it is proper to say the opportunity cost is simply $2000.

However, separately, this is the INITIAL opportunity cost. How can the final opportunity cost differ?

Regards, Don

OK, Don, forgive me for this

OK, Don, forgive me for this but I went to the chalk-board during a tutoring session and re-thought this out.

Assumption 1: Inventory is replinished (10 TV's/Month quota)

Opportunity Cost-

1.) - $3000 ->Forgone Retail Revenue
2.) - $2000 ->Forgone money, required to meet the 10 TV's/Month quota
3.) + $3000 ->Retail Revenue from the final television sold

Ok, and I apologize once more, but I see the answer for Assumption 1 as being $2000, or $5000. "1.)" is certainly a direct opportunity cost. And since 10 TV's must be sold, the $2000 wholesale price is a direct cost of bringing the said TV home. Under assumption one, that $2000 cost is inextricably linked to John's act of bringing the TV home. So I'm left thinking that $5000 is the opportunity cost. That's what John gives up at the moment he brings the TV home. Now, costs are costs, and revenue is revenue, so we shouldn't include the Retail Revenue of the final TV. Or do we? Here I am thinking as an accountant. Perhaps the $3000 is an opportunity benefit and the net opportunity loss is $2000.

Final answer: $5000

Assumption 2: Inventory is not replinished (9 TV's sold this month)

Opportunity Cost-

1.) -$3000 ->Forgone Retail Revenue

Final Answer: $3000

conceptual aids: is the tv

conceptual aids:
is the tv he takes home one of his 10 sales?
is the tv he takes home part of his inventory?
what is his rate of return? is it in tbills or kilos?
how much is he charging people to watch his tv at home?

The answer is obviously zero

The answer is obviously zero and remember you can't divide by that. After watching the plasma tv for a while, she doesn't like the picture quality very much and takes it back to her store and sells it to someone else. Naturally, she made her husband do the heavy lifting. Even if she decides to keep the tv, she has traded one asset (cash) for another (tv). Did you all flunk Econ. 101? (I really don't expect much from male Libertarians in the 20-30 range.) Not only that, she paid wholesale for it. Ha, ha, ha! How did this wholesale, retail crap develop in the first place? Who needs used car sales people? People who can, do & people who can't end up selling cars,homes, tvs or toilet paper. What a way to spend your life, selling crap. Or, blogging on Cata-Malarkey!! Btw, how do guys explain wasting your time here? Do you all have rich parents or trust funds?

What opportunity cost? He

What opportunity cost? He has a $1000 profit:stupid: He wanted a $3000 TV, and he paid $2000 for it. Clearly he is the gainer by the $1000 difference. The TV qualifies as a need as much as any other need.

There is a story about a local car dealer who was stranded on the east coast by 9/11, and he had to get back here to Oregon quickly, and it looked like no one was going to fly for a long time. So he bought a car in DC and drove it to Oregon. And then so sold it off his lot. As far as he is concered, the price he got for the car in Oregon is pure profit, and the price of the car in DC is not a cost of goods sold, but the price of transportaton between DC and Portland.

Just in case you turkeys

Just in case you turkeys don't know it, she has to pay sales (use) tax on the tv if she keeps it for herself. You wouldn't want to gyp the state out of any tax receipts or spend time in jail with Martha would you?

Detailed answer -- If no

Detailed answer --

If no unit is taken home, 10 units are ordered each month and all 10 are sold for $3000 each. In order to sell 11 units in a month, the price would have to have been lowered so far below $3000 that the total profit would have been reduced. At least the owner believes this, or he would have ordered more than 10 each month, and his supplier would have supplied them.

If he orders 11, the same 10 units are sold for the same $3000 and he takes the unit home. His sales revenue and profit on sold units is the same, but he has spent an extra $2000 at wholesale. At this point his opportunity cost is $2000.

After a month or two, he resells the unit, either as a 'demo' or an 'open-box' unit. Whether he sells it directly from home or takes it back to the store doesn't really matter. It would be reasonable to expect that he could command $2000 for the unit, a 33% discount to new.

If he successfully does this, his final opportunity cost is about zero, as lulu says. The customer pays the sales tax on the $2000 discounted price, so taxes don't affect the opportunity cost.

The only requirement is the ability to price discriminate to the minimal degree of one discounted set so that it is not sold to a customer willing to pay $3000 for a new set.

There should be a number of ways to accomplish this, including selling to a relative or friend, or by distributing lottery tickets for the right to buy the discounted set. Charity sales or donations are also possible.

Regards, Don

The whole thing has me

The whole thing has me confused... There are two choices with different opportunity costs which need to be distinguished. And opportunity costs have to do with foregone utility, not money. First choice: whether to spend $2000 on a TV or not. (Which is the same choice that applies to all the other TVs he buys. Most of the set-up is just pointless. John could just as well walk away from the TV business, having decided that for every $2000 he has, there is something he'd rather do with it than buy a TV.) So John buys the TV. The opportunity cost of that choice is the foregone utility of the next most valued use of the $2000. Suppose it was a trip to Cancun. So the opportunity cost is the utility he would have gained from a trip to Cancun. Next choice: sell the TV or put it in the den. Selling the TV gets him $1000 in profit. But he puts it in his den. So, we know having the TV in the den is better utility-wise to him than anything else he could do with $1000. But we can't say that $1000 is the opportunity cost of the second choice. The opportunity cost of putting the TV in the den is the foregone utility from the next most favored use of the TV whether that is selling it, smashing it, or using it as a canvas for a conceptual art project.

Opportunity Costs Don Lloyd

Opportunity Costs
Don Lloyd at Catallarchy posts what he calls an "Opportunity Cost Puzzle." What I find puzzling is that so many of the other commenters find it puzzling. I always thought that the opportunity cost of an action is the utility...

Will, I don't understand

Will,

I don't understand your objection. How is everyone else confused?

Don't most people in this thread assume that when someone says, "The opportunity cost is $2,000", what they mean is, "The opportunity cost is the marginal utility of $2,000"?

I'm with Jonathan. Isn't the

I'm with Jonathan. Isn't the utility of money inherent in its definition? Will attempts to make a distinction between money and utility, but that distinction is false. Money represents pure utility, pure opportunity. With the exception of rare currency collectors, I don't see too many people associating a $20 bill with the "utility" of paper and green ink.

Wait, how is the wholesale

Wait, how is the wholesale price of the television brought home not a sunk cost? If John brings the television home from the store and not from the wholesaler, the wholesale cost is irrelevant. It has already been paid. I thought that was the assumption.

David, He could always save

David,

He could always save the unit and sell it next month; instead of purchasing ten units, he purchases nine. Hence, the cost is not sunk.

Actually, I deliberately

Actually, I deliberately agreed with David's first answer :)

If he takes a TV home, his opportunity cost is the $3000 he could have sold it for.

If he orders a TV to take home his opportunity cost is the $2000 he could have spent elsewhere (assuming, reasonably, that TV could not also have been sold for $3000).

I gave the first answer since that's how the puzzle was phrased.

There's no such thing as "immediate" or "final" opportunity costs, and reasoning that extends to subsequent actions is flawed. Opportunity costs are always associated with a single choice, and exist irrespective of chains of choices and actions that may or may not follow.

Noah, There’s no such

Noah,

There’s no such thing as “immediate” or “final” opportunity costs, and reasoning that extends to subsequent actions is flawed. Opportunity costs are always associated with a single choice, and exist irrespective of chains of choices and actions that may or may not follow.

Be that as it may, all we need to do in this case is to flesh out the description of the original choice so as to say that the set is taken home with the intent of reselling the unit as a 'demo' or 'open-box' after a month or two.

Regards, Don

That doesn't change a thing.

That doesn't change a thing. X now != X later.

Even ignoring time preference, it doesn't matter because regardless of his initial intent, bringing the TV back to the store and selling it as "open box" is a seperate choice with a seperate set of alternatives. If in a week he can sell the used set for $2500, or keep it, whichever he doesn't choose is the opportunity cost of that decision, wholly unrelated to the decision he faces today.

I am in agreement with Noah

I am in agreement with Noah who agreed with my first intuition. I should have stayed with that one. All this talk of assumptions and the variety of answers shows how non-concrete even our fundamental assumptions in economics are.

All that matters here is the precise time when John determined he would bring the television home. Was it as he was purchasing it from the wholesaler, or after that transaction was "sunk"? By sunk I don't mean that the costs are unrecoverable, but that the intitial transaction is irrelevant to his future actions. No matter what he does with that television, the $2000 has been spent. The $2000 was the opportunity cost of purchasing the television in the first place. Simple, right?

At the time of action, opportunity costs are possible future benefits that are sacrificed. How any of these actions affect future inventorying is a matter of seperate choices. That is why my $5000 figure was flawed. It's just as mistaken as $2000, unless and only if John purchased the television with the express intent of bringing it home.

If he resells it, that's a whole seperate action as well. Now, tell me where I'm wrong.

Noah and David, I'm taking

Noah and David,

I'm taking your viewpoints seriously and trying to make all the pieces fit together, but I'm not there yet.

In the meantime, we certainly have to allow for complex, compound actions that may occur over extended time. If I choose to cross the room, that inherently will mean that I must choose to place one foot in front of the other multiple times. The overall action of crossing the room can certainly have its own opportunity cost, can't it?

Also, the opportunity cost may well not be able to reduced to a single thing. If I offer you a choice of a basket of 4 apples and 7 oranges OR a basket of 5 apples and 6 oranges, you will choose the one that you expect will leave you in a preferred state of satisfaction. If you choose the first basket, then the opportunity cost will be the basket of 5 apples and 6 oranges, without any possibility of further reduction or objective comparison with the first basket.

In the case at hand, we may have to identify more than two alternatives and rank each of them on an individual's subjective scale of values.

#1 -- Buy 11 sets, sell 10 sets, sell the 11th set at cost after 2 months at home, repeat all.

#2 -- Buy 11 sets, sell 10 sets, keep the 11th set at home forever.

#3 -- Buy 10 sets, sell 10 sets.

It would seem reasonable that #1 would be preferred to #3 as the finances are the same and the owner has the use of a set at home continuously.

Also #1 would likely be preferred to #2 since both provide the owner with the continuous use of a set, but #2 involves an additional outlay of a wholesale price for 1 set.

But choosing between #2 and #3 is entirely subjective. If #2 is the preferred second best, then it is the opportunity cost for #1. Else, the opportunity cost for #1 is #3.

Opportunity cost, as defined, is a state, not a difference from the preferred choice, since differences between subjectively ranked states are not possible to compute. We may be able to compare the second best state with the state that existed before any choice was made, but even then it can't be reduced to a single thing in general.

That's as far as it makes sense to push without some reaction.

Regards, Don

The correct short answer

The correct short answer would be $2000. Taking a TV home is unlikely to affect his opportunities to sell them in any normal business conditions.

If you're quibbling, you'd give an answer dependent on the outcome of a programming problem. If he is maxed out with his credit at the wholesaler, or if the TV is a popular model where outlets have been supply-rationed, then there is a genuine lost opportunity to sell a TV and the opcost is $3000.

On the other hand, if the televisions were already bought and paid for and held on inventory, but simply weren't selling, then his markup is irrelevant (because he wouldn't get it) and the $2000 wholesale price is a sunk cost, so the opportunity cost could be zero.

In certain bizarre cases, like maybe if taking the TV home clears up a space in his warehouse and allows him to sell more valuable stuff, the opportunity cost of the TV could be much lower and (I'm guessing) even negative.

Will is correct. The

Will is correct. The opportunity cost of the decision to keep the TV for himself is the foregone expected utility from his next most preferred choice. True opportunity cost cannot be measured - it is subjective. Read Buchanan's *Cost and Choice* for the full argument.

And money and utility are NOT the same thing. We can make the assumption that money/income are what we're measuring as opportunity cost, but *true* opportunity cost is as Will and I have said.

If you want to work with money, you need to, as many folks have said, precisely define the moment of choice. If the TV has already been bought for inventory and he decides to take it home, he forgoes $3000 for that choice. It's either "keep it" and enjoy the utility stream from it or "sell it" and have $3000 more in hand than otherwise.

If he chooses to buy one at wholesale and keep it, then the moment of choice is the purchase at wholesale price, in which case the opportunity cost of keeping the TV is his next best use of the $2000.

Cost is always at the moment of choice. (It's also always subjective and about expectations, but here we're staying with money.)

Note to Will - you were paying attention at Marymount that summer, eh? ;)

I owe everything to you,

I owe everything to you, Steve.

Horwitz on Opportunity

Horwitz on Opportunity Costs
I'm pleased to see that Steven Horwitz, a real live top-notch economist and master of catallactics, has endorsed my interpretation of the opportunity cost puzzle in the comments over at Catallarchy. Steve, who taught at an IHS seminar I ran...