Read this before you teach... Production, Revenue, Costs and Profits



I recently finished a collection of 11 resources on this topic, and the experience can only be described as a labour of love. I've gone into detail about them in this post, where there's also a cheeky freebie, so it's worth checking out!


In Edexcel, this topic largely appears in Theme 3, and as a result, is part of the A-Level only. At AS, students just need to know about specialisation and productivity.


For AQA, students typically touch on this topic in their first year and come back to it in the second. For AS, students need to know average and total revenue, costs and profits. Marginal analysis of these concepts is only really needed for the full A-Level.


This can be tricky to teach, so I'm going through some general advice before looking at each sub-topic in quite a bit of detail. If you're here to look at resources from around the web, you might want to skip straight to the bottom.


I think one of the challenges of this topic is that it's easy for students to follow what's going on without properly internalising it. You might find that students have no problems in the lessons but then struggle to recall or make connections later on. That's a problem because this topic is the foundation of the Theory of the Firm.


As a result, I'd really recommend encouraging students to use their intuition and make predictions. How are we going to work this out? What is this curve going to look like? Why do these things happen at the same time? Get them to do some thinking!


Short-run Production

I like to start with teaching short-run production, and no discussion of this would be complete without the classic diminishing marginal returns activity. Every teacher has their own way of doing this, but I’ve found The Paper Chain Factory is pretty reliable in generating the desired curve (and decorating your classroom).


Here's what I do:

1) Provide students with a stapler and a pile of (coloured) paper strips. Holding an A4 sheet portrait and cutting vertically into about 8 strips usually gets them about the right size.

2) Start with just 1 student and record how long a paper chain they can make in 45 seconds.

3) This bit is crucial: choose 2 other students to do the next 45 seconds. If you just add an extra student, the ‘learning by doing’ effect might skew your results.

4) Now choose 3 different students, then 4 and so on. If you’re lucky enough to be running out of students by their point, don’t worry, you can begin to reuse students and should still start to see diminishing returns.

5) Record, plot, discuss - voila


The flatpack furniture analogy also works well, particularly at highlighting the difference between the long and short run. If I'm building IKEA wardrobes by myself, with just one drill, I might only be able to make one in a day. If I get a mate to help, but still only have one drill, he can hold bits in place whilst I screw them together. We might make 3 in a day. A third person can help by passing us screws, but isn't adding as much: perhaps we'll make 4 in a day. A fourth person might only be able to help by making cups of tea, only increasing our output by half a wardrobe to 4.5 wardrobes. Adding more labour if capital is fixed becomes less and less useful. If we contrast this to the long run, where I could buy 3 drills, we can see that the effect may well be different.


A danger point to be aware of here is that students often confuse Product, Production and Productivity, so you might want to spend a moment distinguishing between these.


Short-run Costs

If you've kept the results to The Paper Chain Factory, it's easy to extend this to a costs analogy. I usually keep it simple by ignoring the paper and staples and just focussing on labour and the stapler (capital). By assigning a wage to labour and a cost to the stapler, you can explore fixed and variable costs and produce some nice curves to compare to your product curves.


Students can struggle to understand why the marginal intersects the average at its turning point, especially those not doing Maths A-Level. I've found the biggest thing to help here is to take a minute to shift their perspectives from 'A minimum is the lowest point' to 'A minimum happens after it's stopped going down and before it starts going up'. We can then analyse what happens either side of MC=AC. If MC<AC, what we're adding is less than the average, therefore it pulls the average down. If MC>AC, what we're adding is more than the average, so it pulls the average up. MC=AC happens between where the average is going down and where it is going up, so it must be the minimum point. I make students articulate this principle for production, costs and revenues so they get used to explaining what can be quite a tricky concept.


If you've got a particularly mathsy class, you might also want to point out that the way we calculate MC in our tables isn't entirely accurate, since we use Δ instead of δ, ie we are using a unit change rather than an infinitesimal change.


Before you move on from costs, remind students that costs in Economics include opportunity costs, and so an Economist and an Accountant might have separate views.


Long-run Production

A big danger point here is that students can confuse returns to scale with economies of scale (I'm ashamed to say that I didn't fully appreciate the difference between them until I was writing my dissertation proposal...). As ever, I reckon the way around this is to be really explicit about it, and compare the two concepts side-by-side. That's why I teach Long-run production and long-run costs one after the other.


Long-run Costs

There are lots of nice examples of factory videos showing large scale production, such as this one about a cake factory (I recommend the first 3 minutes). I particularly like this one because most students have some kind of concept of what baking on a small scale looks like for comparison. This means you can ask them how the production would differ if they just set up a small cake business from home, and to identify the economies of scale we see: At the start, we see huge quantities in packets you wouldn't see in the shops. They probably bulk purchase to get purchasing economies. Next, we see a giant whisk, and later a slicey machine; these are technical economies of scale. Everyone appears to have a different job (specialisation), this is also a technical economy. We see fancy boxes that a home-baker probably wouldn't have access to, this is a marketing economy. You can also talk about what might be harder in a big cake factory compared it home, and begin a discussion on diseconomies of scale.


Revenue

This tends to be the easiest topic in the lesson sequence, as students are usually starting to get the idea of total, average and marginal calculations. You might want to take a moment to discuss the relationship between AR, Price and Demand to prevent misconceptions later down the line.


This is a nice topic if you want to extend students, especially those applying for Economics courses at University. You can give them a flavour for modelling revenue with this Extension Booklet. It guides them through how to use their AS-Level Maths to make sense of total, average and marginal revenue graphs, so can be given to students to do independently, outside of class time. If you want to give students more examples of how maths is used in Economics degrees, I recommend showing them Mathematics for Economics and Business by Ian Jacques, which is a staple on the first-year reading list at many universities.


Profit

Students really struggle to understand economic profit. You might want to start by recapping factor payments opportunity cost, especially the opportunity cost of an entrepreneur starting a business. Once you've established that he gives up what he could be earning elsewhere, you can postulate that he would need to pay himself at least this much. And what do we call the payment to the entrepreneur? Profit.


Economic Profit, on the other hand, = revenue - economic costs. Since these economic costs include opportunity costs, they also include the opportunity cost of enterprise: profit. (It's not hard to see why they get confused!)


Lesson Resources

This area of study is made up of a LOT of building blocks, some made of prior knowledge and some new. Sequencing matters here, and remembering to refresh all the crucial prior knowledge as well as drawing out the new ideas is a tricky task for teachers.


I think the solution is to drip-feed students bite-size concepts and give them a chance to predict and process each step. I'd be wary of using a PowerPoint without requiring students to do something alongside it: it's too easy to just whizz through the slides and for students to 'follow' without internalising. Try switching to a visualiser or giving students a handout version with some bits blanked out so they are forced to engage without mindless copying.


I've used these Guided Note Taking sheets for a few years now (with a few tweaks each year) to get around this and they have worked better than I could have imagined. As well as ensuring students have notes on all the important stuff, I also rely on them to keep me on track and make sure I don't forget anything. They require students to rationalise each step and fill in tables and plot graphs along the way and feature lots of repetition of the new concepts to embed them.




I've found the best way to use them is with a visualiser, but I have made accompanying PowerPoints if you don't have one or if you aren't yet confident enough to go slide-less. These are in a 'Click to Reveal' style, so you have a chance to discuss questions with students before showing the answer.


I've put all 11 of my resources on this topic into a MegaBundle which is on a sale price of £10 for 10 days from today. After that, it'll be £14, which is still pretty good considering there's over £20 worth of stuff in it.


Once students have learned the concepts, they will likely need lots of practice. There some great resources out there to help you with this.


Lucy Temple has shared lots of activities for this area:

This booklet of exercises on costs, revenues and profits including lots of tables and graphs plus the answers

This quick cost calculation task in case you need an extra activity

This worksheet of 17 MCQs plus answers

A cheat sheet of formulae


If it's MCQs you're after, you could do worse than this bank of 140 questions on production and costs posted by the University of Dayton.


This booklet, which I *think* is from Peter Davis, combines textbook-style information with tables to fill in, and is great for revision.


ReviewEcon has some questions which come with explanations for students to practice with at home.


GBOxford on TES has come up trumps again with a 2 page Knowledge Organiser, also great for revision. There's also a version for AS-Level if you're on AQA.


There's a nice article from FT4Schools and accompanying worksheet (not sure of the author- let me know if it's you!) on profit at Fevertree which incorporates lots of earlier topics.


Once you're ready to assess students, you might want to use these Exam-Style Questions (Edexcel) for practice. There's a topic assessment by CF split into different sections on Costs, Revenue and Profits, as well as Tutor2U's exam-style topic assessments for AQA and Edexcel.