Designing Economics of the Environment – Part 3 – Assessment Strategy

~2000 words, ~10 min reading time

Part 1, Part 2
So, in Part 2, we learned that my students will have lots of ‘splaining to do, as the verb “understand” in my course learning objectives more closely align with the facet of understanding called “explanation”. So, that should play some role in my assessment strategy.

Elements of Assessment

A few elements that I’ve decided need to be part of this, for one reason or another:

(1) “Chapter Assignments” – to convince students to read, they have to, in some way, respond to that reading. So, I’m going to have my students do Chapter Summaries. Based on the course learning objectives, I’ve decided to make these written assignments where students select some combination of economic models, problems, and solutions, and explain them. The main purpose is to get students started thinking about these, and convince them to at least skim the chapter with enough attention paid to write a summary of it. Graded for completion.

(2) “Article Responses” – this is an opportunity for students to go a bit deeper into topics they find interesting. They will read papers from academic journals (or similar sources). Totally their choice. The purpose is to get students to engage with the material a little beyond what we do in class. Graded for completion.

(3) “Case Studies” – the department declares that “problem sets” are part of this course. The professor who has taught this before has provided me with the details for 5 case studies that they assign. These are reasonably advanced assignments (he noted that his students needed help with these), and require some of the more technical skills that we’ll be talking about. This hits the “Applying” aspect of “understanding”. Here, I will want to grade for quality rather than just completion.

(4) “Term Paper” – the department declares that a “research paper” is part of the course. So, here I’m doing that. I’m forcing students to go through a 4 step process – proposal, annotated bibliography, rough draft, and final draft – with a response to comments and a reflection.

(5) Reflections – every assignment has a required “From this assignment, I learned that…” section. This is to encourage reflection. Also, the form of this statement is important. “I learned that” forces a sentence to follow. “I learned…” doesn’t. Example: “From this assignment, I learned about elasticity.” That’s just a word. Only tells me that you saw the title of the chapter. Not nearly as good as “I learned that elasticity is how much quantity responds to a change in price.” In addition, I have built in “Midterm Reflections” every few weeks, to encourage students to keep track of their progress in the course. These, however, are not required.

(6) Final Exam – I’m going to follow Linda Nilson’s advice and give them the final exam early in the course – ideally, on the first day, if I can get my act together. Final exams of some variety are required by the University, and I think they are a good way to see what students actually absorbed. Because this can’t be revised, I do grade this one with partial credit.

(7) Revisions – Students are allowed to revise any unsatisfactory assignment except the final exam, as long as they submit a “Revision Form”. (This is a Word document where the student has to answer four questions: which assignment they’re revising, why they didn’t meet specs originally, what they changed to meet specs, and what they plan to do to ensure they meet all specs in the future.)

Specs Grading – The Core Concept

The core concept of specs grading is grading assignments on a pass/fail, satisfactory/unsatisfactory basis on the basis of clear “specifications”.

What these specifications look like is up to your goals for the assignment. A good rule of thumb: look at the rubric you use now. Write your specs to be somewhere around the top 2 levels of your rubric. Naturally, you don’t want to be too mechanistic about doing it this way – take the opportunity to think about WHY things are in the rubric and what is really acceptable and what would lead you to hand the paper to the student and say “do it again”.

For my purposes, I write up two sets of specs, depending on the assignment: format specs, and content specs. Format specs lay out things like length, file type, work cited pages, numbers of sources. Content specs say what should be in the paper. If I’m grading for quality, the content specs will include descriptors like “correctly” or “reasonable”. Otherwise, they won’t.

Just as a couple examples: for my chapter assignments, students must meet these specs:

A satisfactory submission will:

(1) Be at least 300 words.

(2) Be submitted as a Word document.

(3) Contain a summary that deals with at least one of these elements: (a) economic models, (b) problems in the economics of the environment, or (c) solutions to these problems, and for each of these you must include:

(a) For economic models – describe the economic model, explain its assumptions, uses, and limitations.

(b) For problems – describe the problem, and the conditions that lead to it occurring. Examples are encouraged, as appropriate.

(c) For solutions – describe the problem being solved, the solution, why the solution could alleviate the problem, and any limitations to the solution.

(4) End with a paragraph starting “From reading this chapter I learned that…”

Remember, this is a “completion” grade. For these, I can use “power grading” – or what I like to think of as “grading at a glance”. Import the file to word, check the word count. Check the last paragraph. Skim the middle to make sure it’s relevant. Done. Doesn’t need to take more than a few seconds – but as a written assignment, I can get some “deep” data about what students think is worth including and what they think they are learning.

For the final draft of their term paper, my students will have this set of specs:

To be satisfactory, the final draft must be at least 1,000 words long, be “complete” in terms of its structure (with a clear introduction, body, and conclusion), have a bibliography or works cited page in MLA, APA, or a similar format, use at least 5 sources, be submitted on Blackboard in Word format, and the body must state what the problem is and evaluate two possible solutions for the problem, clearly stating the strengths and weaknesses of each approach. Finally, after the works cited page, the Final draft must have two additional sections. The first is a “response to comments” – in this section, you must respond to any suggestions that were made on the first draft, either stating how you incorporated those suggestions or stating why you decided not to. The second is a paragraph that starts “From writing this term paper I learned that…”

Here, there’s more concern about quality. “Clearly stating the strengths and weaknesses of each approach” implies that they can’t just write nonsense. If they say something is a strength that ISN’T, then the paper isn’t satisfactory. Also, notice the last parts: one of the most annoying things as a professor is when I give students comments on a rough draft telling them how to improve the paper, hand the paper back, and the student proceeds to turn EXACTLY the same paper in for the final copy. Requiring a “response to comments” section prevents that situation. Even if a student doesn’t incorporate my comments, they at least have to say why they didn’t. Both of these require that students do something they often don’t: read my comments and think about them on some level. Another thing this does: it speeds up grading of final drafts by letting me just check the revised parts.

Because pass/fail grading is somewhat high stakes, students should be given SOME chance to revise assignments. There are a number of ways to do this. Some only allow the first assignment to be revised. Some allow a fixed number of revisions for each student. Some employ a “token economy” in which students are given or awarded “tokens” (perhaps for answering questions in class, turning work in early, etc.), which can then be redeemed for various things (like a bump in the final grade, opportunity to turn an assignment in late, an additional “skip day”, etc.). Personally, I find limiting revisions to be too time consuming to track, and question the pedagogy of telling a student not to bother redoing work that wasn’t good enough. I’d rather just leave them unlimited opportunities, but force them to be a little reflective about the situation.

Putting it Together: Getting to Letter Grades

Under Specs Grading, there are two main approaches to turning a set of S&U grades into a course grade: a points-based approach and a “bundle” approach. Personally, I like the “bundle” approach, but I’ll talk a bit about each.

The points-based approach does as is typical in any other point-based system. There are X points in the course, and you need 90% of them for an A, 80% for a B, etc. (adjust as you like). The only “specs” part of it is the satisfactory/unsatisfactory grading with some revision opportunity.

The bundle-based approach ties each grade to a bundle of assignments that must be completed. For example, in my course, here are the C and A bundles:

To earn a C you must: complete 10 chapter assignments satisfactorily, complete 2 article responses satisfactorily, and complete 3 case studies satisfactorily.

To earn an A you must: complete 13 chapter assignments satisfactorily, complete 3 article responses satisfactorily, complete 4 case studies satisfactorily, and complete a term paper satisfactorily.

Notice: there is a combination of “more” and “harder” to move up the grade scale. A student who just wants a C (or a B, for that matter), can forego the term paper entirely. In my opinion, this ability to tailor the TYPES of assignments to specific grade levels is a strong reason to use the bundle-based system.

What about the final exam? I’ve decided to make the final exam determine +/- grading as follows:

>85% on the final adds a “+” to the grade.
50-69% on the final adds a “-” to the grade.
<50% on the final bumps the grade down to the “+” of the next letter down. (So, a B becomes a C+ if the final is really bad.)

For Principles of Microecon, I have the final exam as part of the bundle (so, an A in the course requires at least an 80% on the final exam, plus the other work). There are pluses and minuses to both methods. The Econ of the Environment method increases certainty for the students going into the final (“I’m going to end up with something between a B+ and a C+ in the course!”). But, it leads to interesting gaps. For example: I expect a D+ would be very rare, as would an A-, and if these DID happen under this system, I would suggest it’s a weakness of course design somewhere. (A student can do all the A work otherwise, but still end up with <50% on the final? Either your final is super-hard or your A work isn’t actually encouraging much learning – or something is poorly aligned.) On the other hand the Principles system makes the final more high-stakes, and led a few students to complain to me about how their final dragged down their course grade. (“I’m a bad test taker!”) Though, practically, the final by itself never seemed to make more than a letter grade of difference for any student. Still, high-stakes testing tends to unnecessarily increase student stress, even though I try to include a fairly significant buffer (requiring an 80% for an A, 65% for a B, 50% for a C).

So, how to figure out what I’m actually doing IN class? That’s a subject for another entry (or more!).

Designing Economics of the Environment – Part 2 – The Problem with “Understand”

~700 words, ~ 3 min reading time

Part 1 here.

So, in the previous part, I laid out my course learning objectives for Economics of the Environment, putting the verbs in bold.

1. Students will understand economic concepts, models and tools for analyzing environmental and natural resource issues and problems.

2. Students will understand problems that arise in the efficient use of depletable and renewable resources, and understand potential solutions to these problems.

3. Students will understand problems that arise from the use of environmental resources such as air and water, and understand potential solutions to these problems.

Normally, the verbs in learning objectives provide a great clue for what kinds of assessments are appropriate for the course. If a learning objective says that students should “explain” something, you better ask them to “explain” it!

The verb “understand”, though, leads to…

The Problems with Understanding

There are two main issues with the verb “understand”:

(1) It can have multiple meanings, which vary by context.

(2) “Understanding” is inherently internal, which makes it impossible to observe – let alone assess.

Good news! There is a solution! Thanks to the work of Wiggins and McTighe on “Understanding by Design”, we have a way to translate the internal, unobservable “understanding” into observable activities that we can actually assess – the trick is actually to recognize the different meanings of “understand”, and then to assess based on those.

Wiggins and McTighe suggests there are 6 “facets” of understanding:

(1) Explaining – that is, the ability to connect “cause” and “effect”.

(2) Interpreting – that is, recognizing the meaning or importance of a concept.

(3) Applying – that is, being able to take a concept and use or recognize it in a different context.

(4) Shifting Perspective – that is, the ability to approach an issue from multiple points of view.

(5) Empathy – that is, the ability to imagine being in the place of someone else.

(6) Self-knowledge – that is, being aware of one’s own mastery and limitations.

Now, not every one of these “facets” is present in every learning objective that uses the word “understand”. For example, it would be silly to think that “understand” in “Students will understand economic concepts” means “empathize with”. However, “apply” and “explain” could pretty easily fit in there.

Translating “Understand”

So, a little rewriting, then. I’m going to take out “understand” and put the relevant verbs in…

1. Students will explain and apply economic concepts, models and tools for analyzing environmental and natural resource issues and problems.

2. Students will explain problems that arise in the efficient use of depletable and renewable resources, and explain potential solutions to these problems.

3. Students will explain problems that arise from the use of environmental resources such as air and water, and explain potential solutions to these problems.

Much better! Now, when looking at it this way, it’s clear that my students will have “some ‘splainin’ to do”! Also, I should be asking students to apply the various concepts, models, and tools in a variety of relevant problems. This, naturally, should have an impact on the kinds of assessments I give – specifically, this is not a class where multiple choice questions are going to do well assessing the learning objectives, unless I spend a lot of time crafting very good multiple choice questions (which is possible!). Probably just easier to have the students write – especially since I use Satisfactory/Unsatisfactory grading with revisions, which makes grading writing MUCH easier. Given the nature of the tools we’re using “applying” will require doing some problems, as well.

The Next Task

Now that I know what types of assessments I’m going to be giving (lots of writing), the next step is to figure out the content – in the learning objectives, there are three types of content mentioned:

(1) Concepts, models, and tools – I group these together, because, in this context, there is very little point in distinguishing between them.

(2) Problems

(3) Potential solutions to those problems

So, this provides a framework for me to start putting content into. Now, I have quite a bit of reading to do before I can really complete this… So, I’ll stop here for now.

Designing Economics of the Environment – Part 1 – General Principles, Backward Design, and Course Learning Objectives

~900 words, ~4 min reading time

Part 2 here.

So, next semester I’m going to be teaching Economics of the Environment for the first time. Because I think some people might find it interesting, I think I’m going to post some of my thinking process as I design this course over the break. So, I’m starting here today with some “initial thoughts”

General Principles

(1) I’m going to use Specs grading – I’ve been very happy with this so far. So, I’m going to stick with that.

(2) The Final is going to provide a “grade modifier” – where performance on the final will adjust the course grade based on other assignments by +1/3 of a letter grade to -2/3 of a letter grade. This gives the final a reasonable weight, but also ensures a clear “floor” to a student’s grade going into the final.

(3) The assignments are probably going to be a combination of reading responses, problem sets, and a research paper (for students who aim for an A). Also, need to ask metacognitive questions for all of these. (Even a simple “what did you learn while doing this assignment?” would work.)

(4) Deadlines scattered throughout the semester.

(5) I’m debating about giving the students the Final Exam on Day 1. When I heard Linda Nilson speak this year, she suggested this. For essay-based finals, I think this is pretty brilliant. As she pointed out, if you write a good final, you’re going to have students having the exact discussion that you want them to have over the course of the semester if you do this.

Planning Materials

While I believe very much that each of us needs to make a course “our own” in some fashion, I also believe that there needs to be enough commonality across instructors for a course that it can meaningfully be considered the “same course”. To that end, I have the following…

(1) Our Department has Course Learning Objectives for all courses. These have to be listed in the syllabus, and provide a good way too focus the course.

(2) Our Department also has “Basic Course Sheets”. This includes the Learning Objectives, the description in the catalog, and also a description of what in-class and out-of-class activities are used in the course.

(3) For courses that have been recently created or revised, we have “Course Information Sheets”. These add to the mix an example textbook or two, and a schedule with the amount of time spent on each topic in the course. Unfortunately, this course has not been updated recently, so getting one of these is extremely difficult.

(4) When I start teaching a course that someone else teaches or has taught, I often get whatever they’re willing to share with me – I usually just ask for a syllabus and thoughts on textbook choices, but often get more than that. The professor who teaches this course at the Kent campus was EXTREMELY generous, and provided syllabus, assignments, lecture notes, etc. I have LOADS of material here. Obviously, I’m not going to just use everything I was given – I have to adapt things to my style. But, editing a pre-existing course is much easier than reinventing the course from scratch.

Backward Design

“Backward design” is kind of the “state of the art” in course design. The idea is simple enough. While “forward design” starts with course activities/content, and then tries to figure out how to assess that, “backward design” starts with learning objectives, then moves to consider assessment, and finally designs the course activities with those assessments in mind. Now, the reality is that it’s a recursive process. Sometimes, when you’re teaching you realize that there are hidden learning objectives that you hadn’t thought about. Or, you realize that the assessments don’t *quite* assess what you wanted them to. Or that there are missing or extraneous course activities that don’t reinforce the assessed learning objectives. Alignment is a bit of a dance, and it takes a few iterations to get it right. (Example: when I taught stats this semester it was RADICALLY different than the last time I taught it.)

But, using a backward design, it turns out, works well as a first pass on the more realistic “recursive design” that actually happens. So, let’s take a look at my learning objectives.

Course Learning Objectives

Based on what I got from the Department, these are the three course learning objectives:

1. Students will understand economic concepts, models and tools for analyzing environmental and natural resource issues and problems.

2. Students will understand problems that arise in the efficient use of depletable and renewable resources, and understand potential solutions to these problems.

3. Students will understand problems that arise from the use of environmental resources such as air and water, and understand potential solutions to these problems.

When moving from learning objectives to assessments, the key is to look at the verbs in the learning objectives, as they hint at the kinds of assessments you should do. “Identify” is a different kind of assessment than “explain” which is certainly different than “apply”. (“Identify” often lends itself to a matching/multiple choice assessment strategy – though you can always frame these as short answer. “Explain” often lends itself to short answer or essay – but a well-crafted multiple choice question can do the same thing.)

As you can see, there’s a strong consistency in the learning objectives for this course – students will understand. It turns out that this is a particularly difficult verb to assess – but more on that in the next installment!

Miscellaneous Thoughts on Teaching

~300 words, ~2 min reading time

  • My students need deadlines throughout the semester – too many are just not very good at organizing their work on their own.
  • Satisfactory/Unsatisfactory (with revision) grading is AWESOME.  – Highly recommend.
  • Asking students to ask “FEEDBACK PLEASE” is also a great time-saver. – Highly recommend.
  • Need to clearly label all assignments as “Engagement” or “Mastery” assignments, to make clear what I’m looking for – and to make it clear in my mind, too!
  • I’m not comfortable with late penalties – make a form for requesting late work being allowed, which asks them to explain why and to develop a prevention plan.
  • All revisions should have a reflection attached, too. “Why didn’t I meet specs” and “What I will do to meet specs in the future.”
  • All assignments should have a meta-cognitive “What I learned” component. (A “cognitive wrapper”)
  • For Specs grading, I need to “adjust” the bars in certain ways. For Analytics, I set the bar too low, on the whole – except for the A level. Need to raise it for B and C levels, and reform my project to just being an “A” requirement, but make it more demanding. The bar isn’t way off for Micro, but ends up overweighting the Final in a way that is inconsistent with the Specs grading philosophy (that is, putting grades mostly in the student’s control, so that there’s little uncertainty for them). Shifting the Final to the way I’m treating the Final in Analytics would be an improvement. Need to replace with a more predictable “Mastery” component that happens throughout the semester. Need to think more about what that looks like. (Knewton is an option – but I don’t like making my face-to-face students pay to do homework…)
  • LOVED the Learning Target Quizzes in Analytics – sadly, can’t do it for Micro, because of scheduling issues.

Did Disney Really Underestimate Day 1 Demand for Disney+?

~400 words, ~2 reading time

It’s a common refrain. Before release: “New service/game/etc. coming out!” “Lots of pre-orders!” Day 1: “Site is slow and crashing!” “Underestimated demand”, etc.

The question: is it really reasonable for us to conclude that these companies, which are SO GOOD at estimating demand most of the time suddenly suck at it – ON A REGULAR BASIS, even when they have great data about what demand is going to be?

I submit that the best answer is “no”.

A few assumptions that I’m making here: (1) Day 1 demand is unusually high. (2) Setting up temporary servers that you won’t need in the long term is costly. (3) Companies believe that very few customers are going to punish them for poor performance on Day 1.

Put these all together, and you have an obvious interpretation of the situation. Disney+ estimated how many servers they’d need on an ongoing basis, and has that much capacity ready to go. (This follows from #2 above.) Now, they know this isn’t enough for Day 1 (#1 is something they can predict), so that there will be server problems – poor performance, crashing, etc. – on Day 1. But, that’s okay. The company isn’t really going to be worse off (#3). Yeah, there’s some PR that they’ll have to deal with, but that’s okay. They can always pull an EA, and offer people some free stuff (that’s how I got SimCity 4) – maybe put some movies they “didn’t plan to” on the platform, or offer people a free download of a specific movie through Google Play/Amazon Prime/iTunes, as long as they redeem in the next week. The point is that these are manageable, fairly cheap options compared to preventing the problem in the first place.

Now, there’s another possibility as well: it might be that Disney DOESN’T know how much long-term demand they’ll have. BUT, if it is costly to set servers up and then take them down, it might make sense for them to deliberately work UNDER the needed long-term capacity for the first couple days, so that they can get a better idea of what they should do.

Traditionally, manufacturers overproduce a bit – after all, if you run out of your good, customers will often just buy from a competitor that DIDN’T. (So, assumption #3 wasn’t true.) However, in a world of strong intellectual property protections and strong brand loyalty, that concern fades.

Marx’s Capital Volume III – Chapter 7 – Supplementary Remarks

~300 words, ~2 min reading time

Summary

This short chapter summarizes some of what came before, and also makes clearer the main purpose: Marx was trying to show that the rate of profit is typically not independent of the size of the capital involved. This view (which Marx attributes to the German socialist Rodbertus) claims that capital and profit levels move in lock-step – so a 20% increase in capital and 20% increase in profit would go together, so that the rate of profit would be unaffected. Marx claims that this is true in only two cases: First, if there’s a change in the value of the monetary commodity. In that case, it’s not really that capital and profit are both increasing by 20%, it’s that gold (or the dollar or whatever) is decreasing in value by 20%. So, here, there is actually no “real” (inflation adjusted) change in either capital or profit – only in its nominal (money) value. Second, if variable and constant capital move in lock-step, so that the ratio between the two does not change. (In modern terms, economists would say that the enterprise is changing by “replication”, a simple repeating of the same process an extra time, half a time or whatever.)

Why It Matters

Marx’s view of distribution and cycles are closely tied with the fact that there is a connection between capital accumulation and the rate of profit, I suspect. So, this is going to play a bigger role when we reach that point.

Where Marx Goes Wrong

Here, Marx’s comments are few enough, and mostly in the form of a recap and application against Rodbertus that I don’t have any specific objections that wouldn’t show up elsewhere.

Marx’s Capital Volume III – Chapter 6 – Effect of Price Fluctuations

~420 words, ~3 min reading time

Summary

In this chapter, Marx considers the effects of variations in various prices on the rate of profit. First, raw materials. As one might expect, there is an inverse relationship between raw material prices and the rate of profit. Thus, low material prices are important to capitalists maintaining profit levels. Marx explains that this is true, even though changes in the prices of raw materials tend to be reflected in the price of the product. Because of competition, the change in cost is typically not fully reflected in the price of the final good. In the case of wages, higher wages tend to decrease both the rate of surplus value (which decreases the rate of profit), and also tend to decrease the capitalist’s scope of production – further decreasing profit. One of the more interesting observations Marx makes in this chapter is that there is a tendency in capitalism for the growth of the stock of machinery to run ahead of the ability of nature to produce nature-given factors (like agricultural goods, for example), and this creates imbalances that lead to cyclical fluctuations. Marx specifically considers cotton markets, showing how there was a repeated boom and bust in that industry in England through the mid-1800s.

Why It Matters

In this chapter, Marx hints that a good part of the instability of the capitalist system that he will explain later rests on the relationship between the prices of the factors of production and the rate of profit.

Where Marx Goes Wrong

From a modern mainstream or Austrian perspective, Marx’s analysis here isn’t “wrong” in one sense – but is wrong in another. On the one hand, from an individual firm’s perspective, Marx’s analysis of the effect of prices of factors on the rate of profit is fairly sound. But, from the perspective of the economy as a whole, we have the problem that the prices of factors of production are not exogenous. They depend on the (expected) price of the product. Value is then imputed back from the product to the factors that produce it. In mainstream terms, the demand for the factors of production is “derived” from the demand for the product. So, the causal analysis, if we’re trying to analyze the system as a whole, is backwards – UNLESS we’re considering cases where the price is changing because of a change in availability of the goods under consideration, but Marx isn’t very clear about that (though there are certainly places where he considers these cases).

Marx’s Capital Volume III – Chapter 5 – Economy in Employment of Constant Capital

~700 words, ~ 4 min reading time

Summary

Since workers create surplus value, it makes sense for capitalists to minimize how much they spend, relatively, on non-labor. (That is “constant capital” in Marx’s terminology.) In general, they can do this by increasing working hours. Since the same building can operate for 8 hours or 24 hours, a greater profit margin will be attained if work happens for more hours. In addition, capitalists look for ways to use the “excretions of production” – that is, by-products or “waste”.

Marx goes a bit deeper on a couple of examples. He discusses savings on labor conditions – pointing out that capitalists can decrease their expenses by tolerating unsafe or uncomfortable working conditions, and presents data showing that disease and mortality are more common among workers in industries where conditions are particularly bad. Marx also observes that large-scale production is encouraged, in part, by the way that power works in industrial machinery. It is often more economical to operate one large plant than multiple smaller ones. These economies of scale (to use the modern phrase) allow capitalists to economize on constant capital. Marx goes a bit deeper into the “excretions of production”. Strangely, he criticizes capitalism for not putting human feces on fields to use as manure. Finally, Marx observes that new inventions are often not economical – so that the first to buy a new product end up paying far more than when the product gets more developed.

Why It Matters

Here we’re getting much more to the practical criticism of the capitalist system that Marx provides. The most important part here is the criticism regarding requiring long working hours and the one about unsafe and unhealthy working conditions. These are the two activities that look the most like “exploitation”, and, I would suggest, are often at the heart of criticisms of a market system.

Where Marx Goes Wrong

Here, Marx’s wage theory is what creates the biggest problems. Since Marx buys into the classicals’ iron law of wages – that is that wages will stay at the level of subsistence – Marx misses the actual dynamics of what is happening. For example, people will trade off wages against other features of a job. So, for example, people may be willing to accept worse conditions – but they only do so if they are compensated for it financially. Conversely, it can sometimes be cost-saving for a company to offer more benefits but pay less – in fact, Marx himself points out a case where a business ended up saving money by installing safety equipment. Marx’s argument then, in this section, relies on the existence of two “irrationalities” – one of which Marx is explicit about, the other of which is missing from the explicit argument, as it is ruled out by Marx’s wage theory. The first irrationality: that capitalists habitually seek to avoid certain kinds of costs – specifically for safety devices. Marx reported one case where a group of manufacturers spent more paying lawyers to fight the imposition of safety regulations than it would have cost to simply implement the regulations themselves. A second is that workers care only about wages and pay no attention to the conditions of production. But these are unlikely to be true. There are systematic differences in certain wages which are explained by differences in job characteristics – sometimes explicitly. This makes perfect sense – people would be willing to be paid less for safe, comfortable jobs, other things equal – but doesn’t fit the iron law of wages which suggests that wages will fall to subsistence levels. In addition, employers take this fact into account when making decisions about safety procedures and the like. Do they get things wrong sometimes? Of course. But, it hardly seems accurate to suggest that employers regularly, irrationally avoid measures that are actually cost-saving – in a competitive world, such decisions put you at a disadvantage compared to your competitors. Which brings us back to a central issue with Marx – for Marx, competition between competitors seems to exist sometimes, but is not worked into the logic consistently. So, competition keeps prices of products in check – but doesn’t let wages rise above subsistence. Competition leads to capitalists being cost-minimizers – but they do so very poorly.

Marx’s Capital Volume III – Chapter 4 – The Effect of the Turnover on the Rate of Profit

~300 words, ~2 min reading time

Summary

The previous chapters were considering the rate of profit for a single “turnover” of capital – effectively a single productive period. In this chapter, Marx broadens the analysis to examine the annual rate of profit if there are multiple turnovers of capital in one year. For example, if I advance $100 in wages at the beginning of the year for wages, and workers make a product I can sell for $110 at the end of the week, then I can “turnover” the $100 from my revenue to pay for wages in the next week. As a result, the same $100 can be spent on wages 52 times over the course of the year, resulting in a profit of $520, while I only had to advance $100 – a 520% return. Marx shows that the annual rate of profit is simply the rate of profit for a single turnover multiplied by the number of turnovers in a year.

Why It Matters

If you’ve read his previous volumes, you’ll know that Marx is a bit obsessed with the idea of “turnover” with capital. The reason is simple: it is what makes capital self-replicating in the Marxian system. So, it makes sense that, as Marx is turning to questions of profit, that he would consider how profit is affected by turnover.

Where Marx Goes Wrong

Marx’s devotion to the labor theory of value muddies his analysis because his price theory is a bit goofy. Sensibly, if a particular set of labor and materials allows for twice as high a turnover, and therefore twice the rate of profit, it seems obvious that entrepreneurs would bid up the wages and material prices, which, in turn, lowers the per-turnover rate of profit. Marx’s system doesn’t seem to allow for this, because it is bound by the labor theory of value.

Marx’s Capital Volume III – Chapter 3 – The Relation of the Rate of Profit and the Rate of Surplus Value

~ 800 words, ~ 4 min reading time

Summary

If we define the rate of profit as the profit divided by the expenditure (not too far from profit margin by standard accounting, though also not quite the same), and the rate of surplus value as the amount of surplus value (that is, profit) divided by the wage bill (that is, the amount of variable capital), then we’ll find this relationship:

Rate of profit = rate of surplus value x (variable capital/total capital)

“Capital” here being the term that Marx uses for “costs” – including wages (that is variable capital), depreciation, materials, etc.

This chapter mostly focuses on different ways in which the rate of profit can change/differ. He considers a number of cases, but comes to this conclusion in the end:

(1) The rate of profit moves in the same proportion as the rate of surplus value if the share of variable capital stays constant.

(2) The rate of profit moves more than the rate of surplus value, but in the same direction, if the share of variable capital moves in the same direction as everything else.

(3) The rate of profit moves less than the rate of surplus value, but in the same direction, if the share of variable capital moves in the opposite direction, but less than, the rate of surplus value.

(4) The rate of profit moves opposite the rate of surplus value if the share of variable capital moves in the opposite direction and more than the rate of surplus value.

(5) The rate of profit stays constant if changes in the rate of surplus value are offset exactly by changes in the variable capital share.

Marx feels a need to explain #5. So, let’s look at Marx’s example (but I’ll use $ instead of pounds). Let’s say that, originally, the capital is divided as: $80 constant capital + $20 variable capital + $20 surplus value. In this case, the rate of profit is 20% ($20/$100), while the rate of surplus value is 100% ($20/$20). Then, let’s say that wages fall, so that you can produce the same stuff with just $16 paid in wages. Then, we’d have $80 constant + $16 variable + $24 surplus value. The problem is that this would mean that the rate of profit has increased 25%. For that not to happen, the constant capital has to have increased, for example, like so: $104 constant + $16 variable + $24 surplus value. Now, the rate of profit is $24/$120 = 20%. The change from $80 to $104 constant capital means that either labor productivity has dropped – that is, that workers need more materials to produce the same quantity of product, or that the cost of materials has increased.

Why It Matters

Marx’s big point from this chapter was to establish that it is possible for two capitalists to have the same rate of profit, but different rates of surplus value. The above examples shows how that can happen. Similarly, it is trivial now to show that two capitalists can have the same rate of surplus value, but different rates of profit. I’m still not 100% sure where Marx is going with this – but I suspect part of the point is to show that, since there is a tendency toward rates of profit to equalize, we’ll have capital-intensive firms (for whom the wage share is low) with relatively higher rates of surplus value. That is: an increase in capital intensity across the economy leads to greater labor exploitation. But, I’m just speculating about that at this point.

Where Marx Goes Wrong

This chapter was mostly mathematical identities. But, I do want to point out two oddities in Marx in this regard:

(1) Marx’s use of the rate of surplus value is really strange. Why “profit divided by wage bill” is meaningful at all is unclear to me. Even if we accept that constant capital should basically be discounted, and only consider a “value added basis”, it seems that the rate of surplus value should be “profit divided by value added by labor (that is profit + wage bill)”. No idea why Marx does what he does on this.

(2) Marx’s use of “labor productivity” is also a bit non-standard to the modern reader. Where we typically think of labor productivity as the ability of labor to make a product in a period of time, Marx is thinking in terms of relative value added (compared to the value already “embodied” in the means of production) – so a lack of productivity is seen more as a worker needing more tools/materials to produce the same thing, as opposed to the modern notion where a lack of productivity is seen more as a worker needing more TIME to produce the same thing.

As is always the case, a definition can’t be “wrong” per se. It’s just more or less useful. These are similar – but could cause confusion because of the difference between modern usage and Marxian usage.