Deadweight loss, debunking, and strawman micro

In a recent post, Paul Walker criticises the idea that “deadweight loss wouldn’t exist if we had a government monopoly”. He is right but in another idealistic sense the idea of no dead-weight loss is also correct right.

If the government acts as a monopoly we will still have dead weight loss, as it comes from the “loss of surplus” relative to the situation where “surplus” is as large as possible (given demand and the monopolies cost structure).

But if government blatantly sets price equal to the marginal cost of the last unit dead weight loss will melt away. This does not imply that profit is dead weight loss in any sense of the word, and it does not tell us that the solution will be “dynamically efficient” (where is the incentive to invest, to develop), but it does tell us that a government that is behaving this way could achieve the “perfectly competitive” price and quantity.

However, this is all 100 level stuff that I don’t particularly care about. My interest lies with the “debunking of microeconomics” that Steve tries to achieve on Paul Walker’s blog.

His critique of “standard micro theory” is two-pronged:

Perfect competition is wrong because there are strategic interactions,
The cost structure of a monopoly and a “perfectly competitive industry” are likely to be different.

Perfect competition and “strategic interactions”

Straight off the bat here let me say that parts of this may step up to 200 level economics here, so lets hope my aging mind can keep me on the straight and narrow (Steve’s paper on the issue is here) 😉

Now, BY ASSUMPTION perfect competition is the study of a situation where there are no strategic interactions between firms. There are “many firms”, many is a not particularly technical way of saying that each firms individual choice of quantity has a practically no impact on the market price. No matter how much additional milk a farmer produces the “market price” for milk is unchanged – and as a result the production decision of one farmer does not change the production decision of other farmers.

Do strategic interactions matter when looking at the actual performance of a market, hell yes! But the purpose of perfect competition isn’t to “describe a certain market” – it is to illustrate a situation where “surplus” from the market is maximised so that we have something to compare the market (and other counterfactual markets) too.

The cost structure of a monopoly and an infinite number of tiny firms is different

Yes, yes it is. And if someone was actually planning to split the industry into an infinite number of firms this would be important 🙂

But again, the purpose of perfect competition is to give us an idea of the “highest surplus” in the given market. The cost structure we should look at IS the monopoly cost structure. By doing this we can compare the outcome of the “monopoly” to an outcome where the monopoly aims to maximise total surplus in the economy.

Conclusion

Attacking perfect competition because it doesn’t represent an actual market is a strawman for attacking microeconomics.

Strategic interactions do matter, they do have an impact on the quantity in the market, and the size of any “deadweight loss”. But hell, industrial and microeconomics have been using this knowledge forever.

Steve’s idea that MR=MC is wrong is in itself wrong. Why? Well in the case of strategic interaction (in individual demand) the MR is a function of the other firms response to any change in quantity by our firm, as it all occurs through the “price level”. Deep down marginal revenue is just the extra revenue associated with a very small increase in firm output – the reaction of other firms to this change in output impacts on the price our firm gets and so is part of the “marginal revenue”

To take his own words he says firms are profit maximising when:

$P+n q(i) \frac{d P}{d Q} - MC \left( q(i) \right)=0$

He says that this illustrate MR>MC as he believes $MR=P+q(i) \frac{d P}{d q(i)}$ (as it is with a monopoly). However, lets split out his equation a bit by looking at the change and assuming that we have reaction functions $q(j)\left[ q(i)\right]$ – such that $q(j)$ where $j$ new $i$ is a function of $q(i)$ . In this case we find:

$P+q(i) \frac{d P}{d q(i)}+q(i) \sum_{j \neq i}\frac{d P}{d q(j)} \frac{d q(j)}{d q(i)}-MC\left( q(i)\right)=0$

where $q(j)$ is the quantity produced by other firms.

When we frame it this way we can see that all that matters is how the other firms output impact on the price our firm faces – it is still part of what I would term the “marginal revenue” calculation.

The MR here is larger than the one we would have gotten from his previous equation (as both the inside terms are negative), but it is still the marginal revenue.

Update: Paul Walker discusses a paper that criticises these ideas further.

Update 2: Paul Walker discusses a critique that Steve provides of a comment I put on Paul’s blog. I would note that the individual firms behavioural relationship is the correct thing to look at – and although a bunch of things converge to zero as the number of firms tend to zero economists blatantly assume that “strategic interaction” term converges to zero more quickly. If it didn’t, the equilibrium of the game often wouldn’t be stable as either the choice to enter or what to produce often would not converge.

Update 3: BK Drinkwater also shows some skepticism regarding Steve’s claims.

Paul Walker says:

July 27, 2009 at 12:19

Thanks Matt. I think you have said everything I was going to. By the way Chris Auld at the University of Calgary has a short paper on “Debunking Debunking Economics” which points out the errors in the Keen argument. Available at http://jerry.ss.ucalgary.ca/debunk.pdf.

rauparaha says:

July 27, 2009 at 13:12

Is there a LaTeX plugin for WordPress? Cos I have no idea what those equations are saying. Of course, even if they were well formatted I may still have no idea 😉

Matt Nolan says:

July 27, 2009 at 13:16

@rauparaha

I do not know 😛

It is just the total derivative of the profit function methinks.

July 27, 2009 at 13:21

@Paul Walker

Interesting thanks

July 27, 2009 at 13:37

@rauparaha
See here at BK Drinkwater’s blog. But this is for Blogger and I don’t know if it works for WordPress. Some learning by doing.

July 27, 2009 at 13:40

@Matt Nolan

FYI the total derivative with respect to the firms own quantity of course, sorry – I just realised that might not sound clear, in fact it might not even be clear in the post.

July 27, 2009 at 13:51

I tried out the WP Latex plugin, but it only does inline maths. Anyway, your maths is readable now but you might want to check I didn’t miss any brackets and change the equations at all 🙂