Girl, Your Marginal Benefit Is Far Greater Than Your Marginal Cost

I am an avid amateur economist, as any regular reader would probably know. However, the only economics-related blog I follow on a semi-regular basis is the Freakonomics blog (authored by who else but the authors of Freaknomics, of course — Steven Levitt and Stephen Dubner). I've written on Freakonomics and my interest in economics before, so I won't dwell on the subject, but before I plunge into my main rambling, I think I ought to recommend Freakonomics to anyone interested in how we can apply economic thinking to the problems of society or daily life. For the application of economics to more economic questions, The Undercover Economist by Tim Harford also makes excellent reading. (The feed for Harford's column in The Financial Times is one of the few I subscribe to.) Both books are targeted at a lay audience, so real economists will of course not be interested in these books.

The subject of today's rambling is a bit off the beaten path. While reading the Freakonomics blog, I stumbled on this hilarious (at least to me) song, apparently written and produced by a university student. Levitt criticised the song for its economic inaccuracies, and while suffering another sleepless night yesterday, I managed to think of several possible problems with the song's economics. Before proceeding further, here's a transcription of the lyrics:

Girl, being with you has always been so tough
With each passing minute, your marginal cost goes up
But my love is inelastic and it all belongs to you
I’m the only love producer, and my good is for you to consume

Because girl your marginal benefit far outweighs your marginal cost
Without our equilibrium baby, you know I’d be lost
Trapped inside this market I need you, to buy my love
Girl without your complementing goods, I’m not enough

Now you say that I’m producing, below my ATC
But I’m optimizing quantity baby, why can’t you see?
We could share this surplus, each and every day
If you would just buy my love, I’ll make my fixed costs go away

Baby I want to keep you for the long run, Oh yeah
I think our supply and demand, will become one…

Because girl your marginal benefit far outweighs your marginal cost
Without our equilibrium baby, you know I’d be lost
Long run equilibrium is no place for me
I need the profits of our love, to grow exponentially.

The first thing that should have struck me (but was ironically the last thing that did) is that there is a glaring inconsistency that even a non-economist should notice. The problem is that the good being produced is love, and love is being demanded by the protagonist's girlfriend. Since the girlfriend is a consumer, and not a good, it makes no sense for her to have a marginal benefit or marginal cost. Only goods and services have a marginal benefit and a marginal cost. It would be more accurate to say that the marginal benefit of producing love for her exceeds the marginal cost, but this obviously makes for poor songwriting.

Now, a brief digression into the subject of elasticity. The elasticity of a good measures how much the quantity demanded or supplied responds to a change in price. Whether we are looking at supply or demand is important, as otherwise elasticity is meaningless. Since the protagonist refers to the inelasticity of his love, we can presume that we are talking about the elasticity of supply. There isn't really a problem with the economic theory here, as the singer is saying that he will produce more love even if the cost of producing it goes up (the catch is that the production increases at a rate that is less than the rate of the cost increase — that's what "inelastic" means). Producing more, but at a lesser rate, makes perfect economic sense.

The catch, of course, is that elasticity is not really relevant if the supply curve shifts. Elasticity is only relevant when the market price of the good changes, and the only way this can change besides a shift in supply is a shift in demand. In other words, elasticity of supply only comes in when the demand curve shifts. Otherwise, if there is, say, a cost increase, the supply curve will shift to the left — and supply will actually decrease. In other words, the singer's economic theory is totally wrong here. When the marginal costs of being with his girlfriend increase, he will actually produce less love, not more. (Cleverly, the singer doesn't actually say that the total quantity of love produced will increase, but that's certainly the implication one would get from the song.)

The next lines go on to establish the market structure we have. It seems that the market for love is monopolised by one producer (the protagonist) and monopsonised by one consumer (his significant other). The "equilibrium" bit doesn't tell us much, since a free market will always achieve equilibrium, and presumably the government isn't interfering in the market for love by setting minimum prices, taxes, or the like. If the market is monoposonised (i.e. there is only one consumer), it makes sense that the singer needs his girl to buy his love.

The "complementing goods" part suggests that demand for the protagonist's love is derived demand — in other words, his love is being bought so it can be processed and combined with the consumer's own complementary goods, which are then sold on to someone else (either an end consumer or another producer). This is clearly a very odd relationship, perhaps one reminiscent of a Cyrano de Bergerac situation.

ATC stands for average total cost. I may be misunderstanding something, but if the producer wants to maximise productive efficiency (i.e. make the most of his resources), he should be producing on the average total cost curve, not below it. He definitely could produce more by producing at a point below the average total cost curve, but it would probably not be worth it — there's a good chance he would be making losses at this point.

On the other hand, he might aim for allocative efficiency instead — producing all the love his girlfriend wants. Perhaps the diagrams I am used to seeing don't represent the full range of possibilities, but I think this would be at a point above the average total cost curve — to be more precise, the point where marginal cost is equal to average revenue. Here's a photo of the diagrams from my notes; unfortunately I'm a bit of a lazy arse and thus can't be bothered to explain them, so this'll just be something for the economically-informed. (Note: AC, or average cost, is the same as average total cost.)

The singer says he is optimising quantity, but this is not the behaviour a monopolist would naturally take. (And in the first place, by achieving either productive or allocative efficiency and thus optimising quantity, he would be producing on or above the average total cost curve.) A monopolist typically behaves by producing a non-optimal quantity, and selling it at a very high price. (In the diagrams, the mark-up is represented by the vertical difference between the point where the marginal revenue and marginal cost curves intersect and the corresponding point on the average revenue curve.) The singer has to be rather altruistic, which either implies government intervention, or a monopolist who doesn't think of his own self-interest. Clearly, the latter is desirable.

Surplus, in microeconomical terms, refers to either the difference between the cost of producing a good and the price received (producer surplus) or the difference between the price that would be willingly paid for the good, and the price actually paid (consumer surplus). There's nothing particularly wrong with this terminology, as far as I can see.

The singer says his fixed costs will go away (at least, that's the implicit conclusion one would draw). Obviously, the girl is not waving a magic wand and making his fixed costs vanish by buying his love, so the revenue the singer earns covers his fixed costs. This implies he is either making a profit, or breaking even. (Total cost consists of fixed costs and variable costs; the latter cost varies with the quantity produced, while the former is fixed.) A producer making losses would be able to only partially cover fixed costs. This isn't especially surprising, since a monopoly always makes a profit.

"Long run" has a special meaning in economics, especially because the shapes and positions of curves can vary depending on whether we are looking at the short or long run. In competitive markets, for example, the freedom of entry and exit prevents producers from making a profit in the long run. In the long run, new producers will enter any market with potential profits, while others will exit markets where they make losses, and as a result, any potential profits are ground away by the competition. (If you're wondering why reality differs from theory so much, bear in mind the infamous John Maynard Keynes quote: "In the long run, we are all dead.") The monopolistic market structure, however, does not differ all that much between the short and long run. There's no reason to think the protagonist's partner will leave him (i.e. exit the market) in the long run.

The reference to supply and demand becoming one is a subtle reference to market equilibrium, where the quantity demanded and quantity supplied are equal. This is the different from the "long run equilibrium" mentioned at the end of the song, which is about the natural equilibrium position of the monopoly. At this point, there would be a non-optimal quantity, and non-optimal price.

The suggestion that the singer wants his profits to grow exponentially is a bit out of whack, however. The only way to grow profits would be to either raise prices, which would shrink his girlfriend's consumer surplus (not good), or to restrict quantity. Somehow, I'm not sure telling your girl you will increase your profits by reducing your supply of love to her is a very good idea. Furthermore, if the singer is truly intent on producing at an optimum quantity, he would actually be reducing his profits. Neither the point of productive or allocative efficiency would yield a greater profit than the long run equilibrium.

I know I've terribly overanalysed a simple and hilarious song, but I can't help it — I have nothing better to do with my life. I hope I've done something besides bored you out of your skull. Maybe you've even learnt a bit about economic theory. Or perhaps you've just learnt that I'm a nutcase. Whatever makes you happy, then. As The Beatles would say, all you need is love.