Saturday, 25 July 2009

Deadweight losses (updated)

You do get some odd economic arguments from non-economist at times. The following comes from comments by Draco T Bastard on the posting Back to the future: electricity privatisation at The Standard:
The supposed dead weight loss that monopolies bring are actually brought about by people trying to maximize profit. This has been proved (google Steve Keen, economist). As the government doesn’t need to make a profit that dead weight loss doesn’t exist.
This is wrong for a number of reasons.

The reason for a deadweight loss is that output is below the perfectly competitive level of output, call it q(c). I am assuming that no one wants to produce at a level greater than q(c) to avoid outright losses. I will also assume here that the price is read off the demand curve so that all output is sold. The reason for output being below q(c) doesn’t matter. Whether the firm is maximizing profits or not there will still be a deadweight loss if output is below q(c). For example, assume that q(c) is 10 and the monopoly level of output, q(m), is 5. Then any level of output between 5 and 10 will not maximise profits for the monopolist but will result in a deadweight loss. So not maximising profits does not mean no deadweight loss. What results in no deadweight loss is producing the perfectly competitive level of output.

Note also that both monopolists and competitive firms maximise profits. But only one results in a deadweight loss. So having firms maximise profits doesn't mean there will be a deadweight loss.

Even state owned firms need to make (non-negative) profits, in that their revenues have to at least as large as their costs of production to avoid any subsidies, and their implied taxes.

Bastard goes on,
Monopolies are actually more efficient than competition due to several factors: Economies of scale and having only to deal with itself and the customer (rather than several independent competitors and the customer) being the most notable.
Now here I'm guessing (the "Economies of scale" bit) that Bastard is assuming a natural monopoly and thus you get the standard result that a single firm is the most efficient form of production. Note that the whole discussing is about electricity and I'm not sure that electricity production is a natural monopoly and thus the natural monopoly arguments don't apply. Natural oligopoly may be.

Update: Bastard goes on to say,
And my description of dead weight loss is spot on – it is profit.
No I'm not making this up!


Steve Keen said...

Dear Paul,

Draco is correct and you have some reading to do.

In a nutshell, the mathematical argument behind the Marshallian argument in favour of competitive firms over monopolies is based on two mathematical fallacies.

The first is the proposition that a competitive firm faces a horizontal demand curve at the market price. The fallacy behind this under the conditions assumed in the Marshallian model was pointed out by George Stigler in 1953 (see PERFECT COMPETITION, HISTORICALLY CONTEMPLATED Vol 65 p. 8 footnote 31), but as usual:

(a) economists don't refer to papers that contradict their beliefs; and

(b) Stigler, who was a staunch champion of neoclassical economics, believed that he found a way around this conundrum in any case in the argument to which the footnote was made--that though Price does in fact exceed Marginal Revenue for a competitive firm, the equating of Marginal Cost to Marginal Revenue means that Price will converge to Marginal Revenue as the number of firms rises towards infinity.

This argument is perfectly correct, but there's a twee problem: the behaviour Stigler assumed, of equating Marginal Cost to Marginal Revenue, which economists call "Profit Maximising Behaviour" does not in fact maximise profits.

The actual profit maximising formula is:

MR-MC = (n-1)/n * (P - MC)

where n stands for the number of firms in an industry, and the other terms have the obvious meanings.

I've pointed this out in a number of academic papers that are available on my website, including:

(2004). “Deregulator: Judgment Day for Microeconomics”, Utilities Policy, 12: 109 –125.
(2006) (with Russell Standish, UNSW) “Profit Maximization, Industry Structure, and Competition: A critique of neoclassical theory”, Physica A 370: 81-85.

The second fallacy is the one relating to comparing the aggregated marginal cost curves of a competitive industry to the marginal cost curve for a monopoly, something which neoclassical economists blithely do in their textbooks without ever asking themselves under which conditions such a correspondence would be true. Mathematically there are two cases where it will apply--where marginal costs are constant and identical, and where marginal cost is a function of the number of firms in an industry in such a fashion that a way that a small firm would actually have a cost advantage over a monopoly if it could produce at the same scale.

As pointed out in one study I cite in that Utilities Policy paper and referred to here, there are good reasons why a monopoly might be expected to have a lower marginal cost function than a number of smaller firms operating in its stead.

Matt Nolan said...

"The first is the proposition that a competitive firm faces a horizontal demand curve at the market price"

Perfect competition is based on the assumption that the individual firms quantity is so small that their impact on price is negligible. Yes dP/dqi<0 but it is assumed to be sufficiently close to zero that we can treat it as such.

"The actual profit maximising formula is:

MR-MC = (n-1)/n * (P - MC)"

As perfect competition assumes "many firms" (read infinite) n-1 converges to n, implying that P=MR.

This is the same assumption as above - in the "perfectly competitive case" we need many tiny firms - it isn't realistic, it is an ideal we use for comparative static purposes.

"The second fallacy is the one relating to comparing the aggregated marginal cost curves of a competitive industry to the marginal cost curve for a monopoly"

This is more of an issue. In order to make the markets comparable we could assume:

1) Marginal costs are flat
2) Cost increases in the industry are due to underlying factors (quality of land which is scarce), not the number of firms.

However, economists have always accepted this reasoning which is why we have pushed the idea of natural monopolies.

The purpose of "perfect competition" is to look at a situation where, given the cost function of a monopoly and the market demand curve, the "surplus" created is as large as possible. Now the actual choices of a monopoly do not match this, so there is some "deadweight loss" to society.

Strategic interaction makes matters more interesting, yes. But as long as we keep the limits of the counterfactual in mind it is a useful exercise.

Paul's criticism was of this:

"As the government doesn’t need to make a profit that dead weight loss doesn’t exist."

That is wrong, very wrong, extremely wrong. Ultimately, if the government commits to making the quantity that maximises surplus at the price that satisfies demand then there will be no deadweight loss - but I don't know how the hell they're going to do that.

Paul Walker said...

Damn it Matt, I wanted to say that! :-)

Matt Nolan said...

Couldn't help myself Paul :)

It was an opportunity to talk about micro - I don't get many of those opportunities in my field :D