(That’s a clever title once you realize the true purpose of my exercise.)
In two previous posts (one and two), I claimed that there is something really fishy in how economists typically solve “the firm’s problem.” Namely, they have the firm maximize the absolute amount of money earnings, but don’t take into account the implicit interest cost on the financial capital invested. Specifically, I reproduced a practice exam question the Texas Tech students had been working on, which featured a corn farm vs. a wheat farm.
I’m not going to spell out the whole thing, and my attempted solution; that will be in a journal article I write up. But I had first wanted to make sure I wasn’t attributing to other economists some personal failing on my part.
Now to be sure, there’s nothing mathematically wrong with how economists have been modeling things. But Steve Landsburg says matter of factly that economists assume that workers get paid immediately out of the proceeds of sales from their output; that’s obviously not true. And I don’t think it’s a harmless assumption, I think it makes economists misunderstand what the owner(s) of a firm are actually doing, economically. (In this respect it’s analogous to my critique of the one-good model and how economists “solve” for the real interest rate by setting it equal to the marginal physical product of capital. Yes, the math works in that unrealistic model, but it gives you bad economic intuition.)
Anyway, commenter “baconbacon” claimed I was making a really basic mistake in my analysis, and challenged me to show what would happen if the workers offered to wait until harvest time to get their pay.
I have to be brief (since I have a day job) but here are the figures. Note, I am retaining the original numbers for the corn farm from the exam question, but I invented (for simplicity) the numbers that make the wheat farm have the identical “profit.” (I’m putting “profit” in quotation marks since I want to highlight that that may not be the right term, since we’re ignoring interest.)
So here you go:
Now in the original exam question version, my point was that the “correct” answer for the corn and wheat farmers’ optimization problems, has them both earning $2 in revenues-costs, where costs are taken to be the wages paid to the workers. (Landsburg and others agreed with me that that was the “correct answer” to this question.)
But I pointed out that if there is a time lag, then it implies a higher rate of return to the corn versus the wheat farmer. I just made up the fact that it’s a one-year lag, but surely with agriculture we can’t ignore the fact that there is a time lag.
So in that context, I took baconbacon to be claiming that I would see my mistake if I had the workers wait to get paid; if their wages came right out of revenue, then my (alleged) confusion would vanish because there would be no period of invested financial capital. It would not be an issue of “return on investment” but instead would be a simple matter of maximizing the total number of dollar bills in your hand, free and clear, on December 31, 2015.
OK great, I’m happy to play that game. In the second scenario above, we see that the workers defer their payment in order to earn r% interest on what would have been their original paychecks. Thus the corn farmer pockets net income from the deal of [$3 – $1(1+r)], while the wheat farmer pockets [$5 – $3(1+r)].
So, my job is to show that even in this version, it is clearly better to be Farmer A. Thus I want to show that the first expression is bigger than the second, or (equivalently) I will show that the first expression minus the second, is always positive.
Thus the advantage to the corn farmer is given by
$3 – $1(1+r) – $5 + $3(1+r),
$2(1+r) – $2.
So, can we say that this expression is positive? Yes we can, so long as r>0.
And that makes perfect sense, lining up with my initial intuition. If there is any opportunity cost of tying financial capital up for a period of time, then it is more profitable to be a corn farmer than a wheat farmer. Changing when the workers get paid doesn’t alter that fact, just like paying them in quarters instead of dollars wouldn’t alter which operation is more profitable.
THE IMPORTANT LESSON: Some may have thought Steve Landsburg was arguing that as long as workers happened to get their paychecks at the moment of final sale, then that is sufficient to rescue the traditional approach. However, as I’ve just shown, the actual requirement is that a worker’s output immediately yields the finished product. It’s not the lag between a worker’s paycheck and the final sale that’s the issue. Rather, it’s the lag between the input of worker labor and the physical yield of the output good.
In general that is clearly wrong, and in particular it’s absurd to make that assumption when you’re modeling agriculture. And I don’t think it’s a “harmless” assumption made for “mathematical tractability.” I think it teaches us the wrong intuitions and concepts of how the economy actually works.