How can we explain quantity competition and price taking?

Question

Note: This is a question on the didactics of microeconomics, directed to those of you who have some experience teaching this subject.

When I studied the basic principles of microeconomics, a price-setting monopoly made perfect sense to me, but price-taking firms under perfect competition never did. No single firm can influence the market price individually, but collectively they do? Nobody sets a price for their product, but magically some "market price" falls from heaven? That seemed like a clear contradiction to me.

Then I learned about Cournot competition. Again, firms competed in quantities and the market price fell from heaven via the indirect demand function. Again that didn't make any sense to me. Real firms don't just produce some quantity and then "throw it on the market", whatever that means, to watch the market price magically materialize out of nowhere. Demand is a causal consequence of price, not the other way round. For me, in the real world, all firms were always competing in prices. So why study Cournot at all?

Now that I am teaching microeconomics to undergraduates myself, I still struggle with the question of how to motivate and explain these basic models. Should I keep things simple and insist on just assuming quantity competition under Cournot, and additionally price-taking behavior under perfect competition, thereby risking to lose the connection to the real world and establishing a kind of shut-up-and-calculate culture (which might actually make sense for quantum physics, where it comes from, but hardly for introductory economics)?

Or should I start with a more realistic approach of price competition, talk about capacity constraints and capacity-then-price competition a la Kreps and Scheinkman (1983) to justify Cournot? And then explain that the limit case of Cournot with the number of firms going to infinity approaches a perfectly competitive market under some mild assumptions, thereby having to reverse the usual order of introduction of these models and also risking to overtax my students?

I have variously tried both approaches, and mixtures thereof, but I have never been fully satisfied in the end. What is your approach and/or recommendation?

I'm not so much interested in comparing model outcomes with the real economy, but more with capturing the behavior of agents within the models, in a sense with the "microfoundations of introductory microeconomics".

Answer 1

When I studied the basic principles of microeconomics, a price-setting monopoly made perfect sense to me, but price-taking firms under perfect competition never did. No single firm can influence the market price individually, but collectively they do?

Although non-intuitive it is well established that some properties are emerging (i.e. they hold only for collection, not individual parts).

I think you can explain it by analogy. For example:

• A single molecule of water is not wet, but collectively thousands of molecules of water are wet.
• A single brain cell is not conscious. If you put a lot of them together consciousness emerges.

Nobody sets a price for their product, but magically some "market price" falls from heaven?

Instead of this you can explain that each firm individually faces perfectly elastic demand. Hence inverse demand function is given by $p(q_i)=\bar{p}$. Better textbooks should actually also explain this if not with equations at least by saying in words that each individual firm demand is perfectly elastic. Hence a single firm cannot change price as demand would drop to zero above $\bar{p}$ and if price would be below $\bar{p}$ demand would be infinite. You can draw them perfectly elastic demand curve and then next to it inverse demand curve (unless you are dealing with students with high math background that do not need that).

Demand is a causal consequence of price, not the other way round.

This is simply empirically incorrect statement. It is well known that quantity demanded is endogenous so it is actually also other way around. Quantity demanded is both caused by price at the same time price is caused by quantity demanded. So the second part of your statement is not correct.

This is extremely well documented. In fact it is literally the textbook example of reverse causality/simultaneity that you will find in almost every econometric textbook.

Hence actually both Cournot quantity and Bertrand price competition models are wrong at the same time (save perhaps some special situations). Truth is empirically somewhere in the middle. Empirically in most cases firms simultaneously compete both on quantity and price at the same time (e.g. most firms neither just produce according to actual demand but produce in advance, nor they just passively take prevailing price as given).

Should I keep things simple and insist on just assuming quantity competition under Cournot, and additionally price-taking behavior under perfect competition, thereby risking to lose the connection to the real world and establishing a kind of shut-up-and-calculate culture (which might actually make sense for quantum physics, where it comes from, but hardly for introductory economics)?

I think there is a good middle ground. You can start by saying something like "today we are covering some simplistic models of market", "no model is realistic but undergraduate models are on purpose made extremely simple which makes them even more unrealistic". "Consequently take this model with a pinch of salt and don't take it at face value." You should do the same for Bertrand model by the way as discussed above, since empirically quantity demanded is not causally determined just by price.

By the way, as someone who studied astrophysics before economics, the concept of "shut up and calculate" is a valid concept in every science and in fact one could say it is even more valid in social sciences.

This concept was actually developed in physics precisely because quantum mechanics has myriads of different philosophical interpretations. Hence it is easy (especially for a student) to get lost in all of the philosophising and forget to actually learn how to do physics. Similarly in social sciences there are typically not just different philosophies when it comes to epistemology but even more economics (and other social sciences) are often intertwined with moral philosophy and so forth. Often people even bring their ideological biases when it comes to social sciences. In such environment, "shut up and calculate" makes even much more sense than in physics. Just teach students the tool they need math/statistics and let them explore questions like real life price vs quantity competition themselves.

Or should I start with a more realistic approach of price competition, talk about capacity constraints and capacity-then-price competition a la Kreps and Scheinkman (1983) to justify Cournot? And then explain that the limit case of Cournot with the number of firms going to infinity approaches a perfectly competitive market under some mild assumptions, thereby having to reverse the usual order of introduction of these models and also risking to overtax my students?

No this is didactically terrible approach. My advice:

• first cover simple unrealistic cases.
• after the above you can say that there is a way how to make the model more realistic by expanding it in this or that way (or if there is no time for this just tell students source where they can see the more realistic model).

Starting with the difficult problem will just result in confusion of students unless you are teaching honors class at a top university. If you are teaching regular undergraduates you cant just drop complex models at their head just like that. They wont understand most of what you are saying before going over the simple case anyway. In fact this is why textbook include all these unrealistic models. In most cases the unrealistic simple models are precondition for understanding the more complex models closer to reality.

I have variously tried both approaches, and mixtures thereof, but I have never been fully satisfied in the end. What is your approach and/or recommendation?

My approach to teaching undergraduate micro is as follows:

• Start class with a motivating example. Even if the models you have to teach do not adequately apply to the motivating example, starting with it helps students to get excited and it is good segue to actually explain caveats of the model since you can say why these models do not capture reality very well.
• Go over the simple examples first (of course what is simple depends what sort of university you are teaching at, if at major/selective university the simple example will be more complex than when you teach at some provincial university/community college etc).
• Use analogies from physics or biology. E.g. I really like to use the analogy about molecule of water not being wet but multiple molecules being wet whenever we talk about emergent properties (and economics is riddled with them). You can choose different example, just google example of emerging properties there are myriads of good examples out there. However, my advice is do not pick analogy for these from social sciences, the physics/biology analogies are always easier to understand than social science ones.
• Keep more difficult examples for second half of the class. If the examples are too difficult just learn main differences between the more complex model and simpler one and just describe it to the students.
• If students ask why they are learning unrealistic model, it is good to explain that they do not study economics just to learn how economy actually works but also to learn tools to be able later work as economists. The same way as nobody will ever ask you when will two trains meet in the middle between two cities, but such problems are good math practice problems, simple Cournot model is mostly a didactic tool. You have to learn to crawl before you can walk and to walk before you can run. It is nearly impossible to have carrier as an economics without being good modeller, even if you do pure empirical work you have to go through theoretical models to figure out how to structure your empirical model. Moreover, undergraduate econ students usually don't get enough math for some reason, so more opportunity to practice it is always good for them.

Answer 2

I add my experience, if it could be useful, but, of course, every teaching situation is different, and may require a different approach.

When I studied the basic principles of microeconomics, a price-setting monopoly made perfect sense to me, but price-taking firms under perfect competition never did. No single firm can influence the market price individually, but collectively they do? Nobody sets a price for their product, but magically some "market price" falls from heaven?

When I was a first year student, I had the same question, as for perfect competition: "Yes, demand and supply, ok, but in practice, who fixes the prices? Where and when?" I didn't dare to ask this question to professors, because I feared it was too stupid. Only later did I realize that this was a central question in economic theory, not at all stupid.

Later, I've been teaching economics for several years to first year undergraduate students, at a Law department, so to students not very fond of economics. But this, and similar questions, arose frequently.

My idea, in such questions, is to tell the truth: that this is, in a sense, an unresolved problem, and these models are not 'realistic' explanation of reality. The essence of the question is, in my opinion, to explain to first year students the fundamental idea that economic theory is made of models, and to introduce them to the methods of economics and the nature of models, which are limited , abstract, and often unrealistic representation of reality. But, even with these features, they can be useful to understand the functioning of the economic system.

I agree when you say that monopoly or models in which there is a price setter are more easily understood by students, because are more similar to everyday experience. Perfect competition is a major problem, and there isn't an easy answer.

So, I sometimes choose to say to students, that asked the question, the truth, that perfect competition is a fictitious model, because by definition there isn't a 'price setter'. In perfect competition the theory resorts to an artificial expedient, that is the presence of an auctioneer, who fixes prices as if we were at an auction. The economic system in perfect competition works 'as if' there is an auctioneer (the 'as if' nature of an economic theory being an usual characteristic).

And that this 'auctioneer' is not, in general, explicitly mentioned in models, but it is, how can I say, lurking in perfect competition models.

And that it is a theoretical hypothesis that has a long and illustrious history and goes together with the idea of walrasian tâtonnement and the fictitious idea that exchange occurs only when equilibrium prices have been reached.

This is a subtle and may be tricky question to explain to first year students, as it requires, in principle, to explain the notion of equilibrium , the methodology of equilibrium analysis, and that there are models of non- tâtonnement on prices, and the subject is very complex, and there is an important literature about it, and so on. But I think that students can grasp the essential meaning, that is, that perfect competition is an abstract model that presupposes an auctioneer behind it.

And that models are always, in a sense, 'unrealistic': "the map is not the territory".

Answer 3

I used to emphasize that these simplistic models are not a good fit for most markets. I would give the example of commodity markets where individual companies have to behave almost like price-takers if the market is competitive enough, then I would explain why the product homogeneity assumption may be violated:

• the products are not perfect substitutes because of their characteristics (some examples are Pepsi/Coke, iPhone vs Android)
• the products are not perfect substitutes because of how/where they are being sold/marketed. (The other store selling the same product is distant/ is unknown to some consumers.) This is also a product characteristic, but a less obvious one, so it bears repeating separately.

If you want to explain with formulas: Kreps/Scheinkman is nice, but IMO too complicated for most undergrads, i.e., undergrads without above avorage math background. I think some simple version of monopolistic competition, e.g., Salop is pretty decent to get the ideas across. If you want to spend time on it you can also show how the decision variables may be switched up (to some extent), e.g., you can treat a company's price as a function of the quantity it wants to sell.

Answer 4

The market price is a price P such that the quantity demanded at P is equal to the amount supplied at P. I'm not clear what's not clear to you about that. Perhaps you could be more precise as to what you don't understand?

Imagine there's a set of buyers, and each of them have a quantity and a bid price. The quantity is how much they want to buy, and the bid price is the most they're willing to pay for it. All the buyers are sorted into a line, with the people willing to pay the most at the front. In front of them is another line facing the other way of sellers. Each of the sellers has a quantity and an ask price (ask price is the least they're willing to accept). The buyers are sorted with the people willing to accept the lowest price at the front.

The first person from each line approaches the first person in the other line. If the buyer's bid price is higher than the seller's ask price, then there's a sale. Whichever of them has the lowest quantity steps off to the side, and their quantity is subtracted from the other person's quantity. If they had the same quantity, then both of them step aside. Then, for each person who stepped aside, the next person from the corresponding line steps up. This continues until there's a pair of people such that the bid price is lower than the ask price. At that point, the market is at equilibrium, and the market price is the last bid/ask prices that cleared (note that for less liquid markets, there can remain some bid/ask spread).

This is a simplified version of how stock exchanges work. While more complicated markets don't use this process, the final market price is generally similar to as if this had. The market price doesn't "fall from heaven", it's set by the interaction of buyers and sellers. Each buying pushes the price up, and each seller pushes the price down.

Demand is a causal consequence of price, not the other way round.

Each person has some function f(P) such that if the price were P, the quantity they would buy would be f(P). Add all of those up over the whole market, and you get the demand function, or demand curve, for the market. There is a similar function for sellers of how much they would be willing to sell, given a particular price. The market price is then the result of the demand curve and the supply curve. The quantity demanded is an effect of the market price, but the demand curve is a cause of the market price.