The unit of output

If you're driving, you probably have a preferred speed in mind: so-many miles per hour. If you're working you probably earn a definite wage-per-hour or salary-per-year or take-home-per-week. The units of time are specific and well-defined. You know what an hour is, and a week, and a year.

What is cost "per unit of output" ? Output may be well-defined, but it is hardly specific; and what in god's name is a unit of output? 

Okay, let's say "a unit" is one of them. Does that help? If we talk about one unit of output, do we know what it is? I don't think so. 

Are all the units of output the same? No. Only in the imagination, if at all.

"The production of one unit"

Long ago I quoted Kaminska of FT:

unit labour costs — the labour cost attached to the production of one unit — are staying positively muted

I showed the graph, and said

Kaminska seems to think the graph shows labor cost. How does she describe it? "The labour cost attached to the production of one unit". Oh right, right: "One unit".

We're talking about the whole economy here, all the output produced in our economy. Could be a Ford. Could be a TV dinner. Could be a cup phone. Do you know what "one unit" of output is? Do we all agree on it? I don't think so.

 

My old boss used the word "unit" so much that I would listen for it and try to figure out if there was some secret meaning that I was overlooking. Nah. He just meant the assembly we were working on, in the steel shop. But since then, the word "unit" always gets my attention when someone uses it. Kaminska, for example.

"Unit labor cost" came around again recently, in another old post. At interfluidity, a clarification of the meaning of the phrase:

Unit labor costs are nominal wages per unit of output.

 And now we can no longer avoid the question: What is a "unit of output"?

I think it means what my old boss meant -- one of those things we make, when we make output. Any one of them, as if they are all equal and interchangeable. But I remember Keynes:

But it is a grave objection to this definition for such a purpose that the community’s output of goods and services is a non-homogeneous complex which cannot be measured, strictly speaking, except in certain special cases ...

Keynes was right. But that doesn't stop us from trying to tally output. It doesn't stop us from talking about "units" of output. Google Search says it finds two million links for the quoted phrase "per unit of output". The first among these -- at EconData Online -- offers this definition:

The interpretation of labor cost per unit of manufacturing output (hereafter called unit labor cost) is straightforward--it is the cost of worker compensation and benefits per unit of manufactured output.

"Labor cost per unit of output" is "worker compensation and benefits per unit of output". They define labor cost for me, but they don't define a "unit of output".

I'm not gonna check them all, but I expect all two million sites would do the same. We're supposed to just pretend we know what a unit of output is. And yes, I usually do that, too.

 

Well here's somethin. At NBER, from the out-of-print volume Capital and Output Trends in Manufacturing Industries,1880-1948:

Man-hours per unit of output — the reciprocal of "labor productivity" — are reduced whenever labor is replaced by other factor inputs ...

Labor productivity is output per hour. The reciprocal is hours per unit of output. To figure something "per unit of output", divide something by output. 

Sure. I knew that. But it still doesn't tell me what "a unit of output" is. I know what an "hour" is, and a "week", and a "year". But I don't really know what an "output" is, or a "unit of output". I know it was recently produced. I know somebody paid for it. And I know you can somehow divide by it. But I don't know what it is.

And that's all we're gonna get.

• Wikipedia: "In economics, average fixed cost (AFC) is the fixed costs of production (FC) divided by the quantity (Q) of output produced... Average fixed cost is fixed cost per unit of output." Division, again.
  
• OECD: "In broad terms, unit labour costs show how much output an economy receives relative to wages, or labour cost per unit of output. ULCs can be calculated as the ratio of labour compensation to real GDP." Division, again. So maybe a "unit of output" is a dollar's worth of real GDP? Nah, I don't think so. A dollar's worth is value, or worth. It isn't output.
  
• Google: "In order to show you the most relevant results, we have omitted some entries very similar to the 109 already displayed." 

Well that was quick.

I know about dividing by GDP. The word "per" tells me to divide, and anyway economists always divide by GDP. But if you're going to talk about "a unit of output" you need something more tangible: a widget that you can eat or drive to work or use to build a house. Something you can wear. Something you can read. Something you can relax on, while watching football on it. 

All of the above. A unit of output is the universal product: There is no such animal. And the word "widget" is used to represent it.

Calculating the Number of Units of Output

I found this old note that I left on my desktop:

net interest??
gross interest cost adds to the price of output
how much does it add, i wonder...

i can use "total labor cost"
divided by "labor cost per unit"
to get the "number of units" produced!!

and then divide business gross interest cost
by the number of units produced
to figure the interest cost per unit of output.

No shit.

I put a few graphs together at FRED. That's the trick that forces me to think about relations between data sets. And I came up with a short cut: NCB interest paid, divided by GVA NCB, equals the interest cost per dollar's worth of output.

Graph #1: NCB Interest Cost per Dollar of GVA

The interest cost was less than two cents per dollar of nominal output in the early 1950s, three cents in the early 1960s. Around five cents in 1970, and six in the mid-1970s when the economy slowed -- unless it slowed around 1966 (as Minsky and Keen describe) when interest cost went above three cents per dollar of output.

NCB interest cost reached nine or ten cents per dollar of output in 1980. Eleven before the 1991 recession, near nine for the next two recessions, and five or six cents now, per dollar's worth of output.

Since 1970, cost peaks are obvious and related by timing (and by cost, certainly) to recessions. Even in the 1950s, these recession-related peaks are visible. (And there is a pretty rapid increase around 1955-57, at the time of that pesky "creeping" inflation.)

The peaks are undoubtedly related to the rising interest rates that precede recessions. But even if we trim off the peaks and look at what remains, the line plots a mountainous path. That mountain of cost is due not so much to the rate of interest as to the mountain of debt that Nonfinancial Corporate Business accumulated over the years.  Interest rates have been trending down since 1981 and are now about as low as they were in the early 1950s. But the interest cost is still well above what it was in the 1950s.

 

Yeah, but this is all interest cost per dollar's worth of output. I want to see it per unit of output. So much for my shortcut.

FRED offers a data series named Gross value added of nonfinancial corporate business, a nominal measure of the output of NCB business.

They offer another series, named Price per unit of real gross value added of nonfinancial corporate business. How they figure that, I do not know. But price per unit is price per unit. Note that it gives the price per unit of real gross value added, but the "price per unit" price is nominal.

To divide the first series (Gross value added) by the second (Price per unit) I follow the old schoolboy's rule: Invert and Multiply. So then I'm multiplying GVA (dollars) by the number of units and dividing by Price (dollars). By the division, dollars cancel dollars and I'm left looking at the number of units produced.

That's what Graph #2 shows:

Graph #2: Number of Units of Real GVA Produced by NCB

Dollars cancel dollars, and we are left with "Billions" as our vertical axis units.

The plotted line runs from a little below 1,000 to something over 9,000. But the vertical axis units are "billions". So the plotted line shows increase, from a little below 1000 billion units produced in 1947, to something over 9000 billion units produced in 2019.

In other words, from a little less than one trillion units of output in 1947, to more than nine trillion in 2019.

As a point of information, for NCB business the nominal value of the GVA in 2019 was $10,579.340 billion (or $10.57934 trillion). The number of units of output NCB business produced that year was 9.40488 trillion units. The price per unit comes to half a penny more than $1.12 for each unit of output produced (by NCB business) in 2019. About as much as a dozen eggs.

It's simply amazing, isn't it, that such things can be calculated.

So I took the ratio from Graph #2, the number of units of output, and took the "monetary interest paid" by NCB business and divided it by the number of units, to get interest cost per unit of output:

Graph #3: NCB Interest Cost per Unit of GVA

Looks much like Graph #1, except it never goes downhill. There seems to be a floor, somewhere around 5½ cents per unit of output.

5½ cents of $1.12½. That's just about 5% of the price of every unit of output we bought from nonfinancial corporate businesses in 2019. Just for interest on their debt. And that's the floor, the low estimate.