Mathematics and Economics

Don Boudreaux reminds us of a quote by great economist W.H. Hutt over at Cafe Hayek discussing mathematics and its role in the economic science (for the sake of space, I will refrain from posting the whole quote here).  What follows is my two cents on the matter.
Mathematics is a useful tool in understanding our world if, for no other reason, that to help us separate the probable from the merely possible.
But, despite the old cliche, facts do not speak for themselves. Without a good theory underneath, the data are meaningless. A theoretical framework, well-grounded and logical, is important to putting information in context and helping to determine whether an outcome is reasonable or not. Of course, if data run afoul of theory, then both must be considered. Is there a problem with the theory or with the data?
I think this is what we’re running into now in regards to minimum wage. In recent years, there have been some data to suggest that minimum wage may not have the negative consequences theory would predict (although there is also data to suggest the outcome is exactly what one would predict).
So, then, is the Law of Demand wrong? Possible, but given its consistency on many other subjects (including wages at higher-skilled positions), unlikely. Is there something unique about low-skilled labor? Also possible (and some have suggested that unique conditions like monopsony power do exist). However, given the specificity of these conditions, I think unlikely on any grand scale.
This question I think should be answered with mathematics and statistics. But I also think the evidence should be overwhelming before overturning theory. To rule simply by mathematics is to lose sight of the previous body of knowledge, which can lead to disastrous conclusions.

A Thought on the Demand Curve

A common argument we hear whenever economic competition rolls around is along the lines of “how can current participants in the market compete with lower prices offered by the newcomers?” This complaint is commonly heard in dealing with international trade or immigration; the fear is if these foreigners are allowed to have their way, they will displace domestic actors with their lower prices.

On the surface, this seems plausible.  Why pay $5 for something you can get for $3?  The sellers would have to bring down their prices.

However, the key assumption in any demand analysis is that the products compared are identical.  A different product may have a higher price than another product and there would be no substitution.  An example of this is what I discussed a few posts ago in regards to baseball.  David Price is under no threat from me by offering my cheaper pitching services because the quality simply isn’t there.

It’s a similar situation with imports (whether it be of labor or capital).  In competitive markets, a good/service’s price is equal to their marginal revenue (in other words, a good/service is priced by the benefit it provides).  If a new product comes into the market at a lower price, it may be because it is of lower quality; it provides fewer benefits.  Such an entrant would pose little risk to an already-established product of a higher quality.

So, the answer to the question posed by trade restrictionists of “how can Americans compete with low-wage workers from China (or Mexico etc), the answer is simple: remain more productive and provide more marginal benefit.  That is the nature of economic progress.

Property Rights: An Elegant Solution

Whenever two or more people get together, there is bound to be conflict (and, of course, the greater the number of people, the greater the likelihood of the occurrence).  One of the ways of heading off conflict is through the establishment of clearly-defined property rights.

Allow me to tell a story:

A few months ago, I was in New Jersey visiting my friend, her boyfriend, and their two roommates.  4 people living in a house together.  And yet, there was surprisingly little conflict between them.  That was because of the regime of property rights they established among themselves.  Some items (like the TV, furniture, Xbox, etc) were available for common use, but others (like food) were marked with initials, meaning that no one could touch that but for the owner(s).  This had the joyous consequence of heading off any potential conflicts over consumption of goods like food; no one could be accused of slacking about and consuming the goods of others (likewise, no one could feel like s/he were doing all the work and not receiving anything for it).  And what’s more, the property rights were tradeable, too.  If Roommate 1 was making a salad and ran out of mushrooms, he could ask Roommate 2 if he could use some of her’s.  She could trade (or give them away).

The end result of all this, was a peaceful house with multiple people and little conflict.  (Of course, there could be conflict arising from other things, such as the negative externality of a roommate playing their radio too loud, but that did not arise while I was there so I don’t know how they would have addressed that issue.  Knowing them as I do, I’d suspect some kind of Coasian bargaining).

Property rights, when clearly-defined and enforceable, are key to a peaceful civilization.  If we look at the places with the most violence in the world, the key factor among them is a lack of property rights, either for all or for some marginalized group.

A Quick Update

Hello everyone-

Sorry for the long delay since my last post.  I am in the process of moving from NH to VA and preparing for grad school.  I will have some post forthcoming in the coming days


The Goal of Economic Activity is to Maximize Net Benefits

Mark Perry points to an article at PBS Newshour written by Professor John Komlos, professor emeritus of economics at University of Munich.

Mark’s post does an excellent job discussing one of the many economic flaws, mistakes, and outright contradictions Mr Komlos’ column contains.  I won’t rehash his arguments here but I strongly recommend the read and some of the commentors are good, too.  Rather, I want to discuss a rather glaring Econ 101 mistake he makes.

Mr Komlos writes:

Or consider orange juice. I paid $2.35 for a quart the other day, but it was worth $4.00 to me. So in a sense I made a “profit” of $1.65. Thus, if the price were to increase to $3, I would still buy that orange juice, and I would still make $1 “profit.” See what I mean?

Any first semester Econ 101 student could point out why this is incorrect reasoning for his case of increasing minimum wage.  The reason is economics focuses on what occurs at the margin and that the goal of economic actors is to maximize their economic profit, not just to make profit.

Let’s examine Mr Komlos’ statement quoted above:

Mr Komlos writes that he values a quart of orange juice at $4, but only had to pay $2.35 for it, thus giving him an economic profit of $1.65.  However, if the cost were to rise to $3, he still gets an economic profit of $1.00, but he is made worse off because of the price rise.  His economic profit fell from $1.65 to $1.00.  That $0.65 is now gone.  Lost forever.  It is the unseen cost of the price rise.

Additionally, he fails to recognize that the marginal analysis has changed.  In economics, we demonstrate that benefit-maximization occurs when your marginal benefit (MB, or what you gain from the consumption of one extra item) is equal to the marginal cost (MC, or what you have to give up to consume one extra item).  In the example above, the MC rises but the MB doesn’t.  Therefore, the same amount of orange juice no longer maximizes benefits.  In order to have his net benefits maximized, he’d have to adjust his consumption.  And this is true whether it is with orange juice or labor.

Do people always act in a net benefit-maximizing fashion?  Of course not, but to imply, as Mr Komlos does, that people behavior do not change because their profit (that is, benefit) changes is categorically incorrect.

And Now Pitching for the Boston Red Sox…

Below is a slightly – edited comment I posted on this post at Cafe Hayek:

Another way to think about it:

Why are the Boston Red Sox paying David Price $20 million a year when they could have me do the same job for 1/1000 the price?

The Red Sox would be crazy to hire me to be their ace starting pitcher, even given they could pay me so much less than what Price makes because I simply don’t have the productive value he does.  My fastball tops out at 65 MPH; his is regularly in the mid-90’s.  My walk-to-strike ratio and WHIP (walks/hits per Innings Pitched) would be through the roof.  His are closer/below league average.  In short, the Sox would be getting a poor deal if they signed me.

This is a key matter to keep in mind when discussing trade and low-wage workers competition in competition with high-wage workers. The argument that economic individuals will substitute lower-cost inputs for higher-cost inputs holds only if the two are comparable.  The price of an input (in this particular case, labor) reflects the marginal value added and thus a lower-cost option (such as myself) is not necessarily a good, or even preferable, substitute to higher cost options (such as David Price).

It is for this reason that we’ve seen some manufacturing jobs go to China or Mexico over the years, but not many others.  The jobs that have gone are mostly labor-intensive assembly-line work.  In other words, something the foreign worker could do a comparable job for less cost.  Conversely, the manufacturing jobs that have stayed are more capital-intensive precision work.  In other words, something that the foreign workers could not do a comparable job for less cost. In fact, this is why (despite the ruinous predictions by anti-progress politicians like Sanders or Trump) globalization has made the world (including the developed world) far wealthier.