Do the varieties of apple exist before the process starts, but are produced in zero (or minuscule) quantities at high fixed cost? If so, then the increase in scale production of the "new" varieties reflects a fall in average price, meaning real GDP has increased. You describe the new varieties as exogenous, but if you endogenise them - by assuming that they could be developed earlier, if anyone could be bothered to invest the capital in doing so - then perhaps you can treat this as a price fall. Alternatively we could question the assumption that the price will remain the same. If people prefer variety, wouldn't they be willing to change their labour-leisure tradeoff to buy more apples with more labour? Finally, if the economy produces only apples, how are people "getting richer" if the total apple productivity (in either quality or quantity) isn't rising? I guess maybe GDP could rise continuously during the period that N varieties are consumed, and then make a step fall when variety N+1 is introduced, but that doesn't sound right either. Regardless of the theory, I do agree with Luis's anecdotal observation. I think there have been calculations of the number of SKUs available in the modern economy (in the billions) and that this figure is supposed to be rising.

If audiences want to hear political gossip, surely that's what they will listen to, whether the BBC broadcasts it or not? Of course it would be great if the BBC spent more on More or Less-style analyses of political claims. But if they got rid of their political correspondents would viewers turn over to More or Less - or would they turn over to ITV, Sky and twitter?

I can see that in principle this is true. But is it in practice? In reality we know very little about the payoff functions, beliefs and information available to other players. We don't even know that much about our own! Therefore we make moves fairly blindly, and (if we are especially sophisticated) use those moves to learn a bit about the other players. Though by the time we've learned much, the game has changed and it might not do us much good. We could in principle model the possible payoff functions and information sets of the other players as a probabilistic distribution and determine the optimal moves accordingly - but in practice that is neither achievable, nor do people really even try to do it. In certain cases the game is simple enough that we can model the equilibrium outcome rather than the steps to get there (though it can still be instructive to imagine the actual causal chain from, say, a gas pipeline explosion to the ultimate effect on the equilibrium point of the petrol market). But in many other cases, we can't, and these are in fact the cases which never really reach an equilibrium - or not in sensible human timescales anyway. Maybe sometimes you can move the definition of "simultaneity" up a level. In physics [I can't remember if physics analogies are frowned upon here] there are plenty of problems which do not reach a static equilibrium - eg pendulums or waves on a string. But if instead of saying that the atoms of the string reach equilibrium, we say that the _waves_ reach equilibrium then we can say how the length and tension of the string and the energy of its vibration codetermine the amplitude and frequency of the waves. However, I don't think economics does normally take this explicit step - and even then, I'm not sure that the majority of economic problems can be handled that way either. So if the point is: are simple microeconomic problems better modelled as simultaneous, non-Artsie-linear systems, then sure. But all of economics? Or the interesting problems of economics? I don't think it's the best philosophy. [as mentioned above, I understand that Leijonhufvud's work is partly based on this argument]

There are some different phenomena mixed together here. Overconfident CEOs - are successful because they convince us they _do_ have merit. We can this as a second-order effect; rather than being a direct product of economic exchange it arises from our cognition and beliefs _about_ economic exchange. In order to make decisions about exchange we need to use available signals to estimate what the outcome of that exchange might be. Thus, people have an interest in manipulating those signals independently of their interest in developing absolute merit. Jedward and Brick on the other hand are successful directly because of their lack of merit; we all benefit from a positional good of kinds by being reminded of our superiority to them. This might even be a third-order good: it's not that they are of direct value to us; or that we think they might be; it's that our perception of their lack of value influences our perception of our own potential value to others. Boris Johnson and George Galloway on the other hand do have a genuine merit, in that they help people to reveal their identity to themselves. Again this might be a second-order effect, in that it doesn't directly produce anything of value but just influences their audience's perception of its own value - but they do that particular job better than most of the other potential candidates who are available for it. I guess Chris's argument is that this is not based on any talent they have, but simply on their similarity in merit/value to their mediocre audience. I don't think this is quite enough to explain their success; they also have a genuine skill in communicating this audience's particular prejudices and inanity back to itself. What binds all these together is that the modern economy is as much symbolic as real; much of the utility in our life experience comes from our guesses about future value, contingent events or other people's happiness, rather than objective physical experiences. In a symbolic world, we cannot fully communicate (and therefore cannot experience the world completely) without symbols that are negative or self-referential as well as positive.

(I'm talking about politics here by the way)

The thing about paying for it is that you don't have to pretend to care about the other person's happiness any more. Liberating.

Two thoughts: First, should we expect investment to always be a high proportion of profits? In an economy where most people want to save for their future [for simplicity, let's assume saving is the same as investment], capital investment should indeed be more than 100% of profits, as the population will be net savers. Perhaps an older population wants to dissave and thus disinvest; taking its profits from prior investments and consuming instead of reinvesting them. If a higher share of capital is now owned by 65-year-olds than in the past, we might expect exactly this to happen. Overlapping generations models are all very well if the generations are homogeneous. The depressing thing is that capital being disproportionately held by 65-year-olds is both a consequence _and_ a cause of low growth, so this problem might become self-feeding. Although human capital is probably possessed increasingly by younger people, so the terms of trade on which the old buy services from the young might change and partly redress the balance. Second, and unrelated: Andrew Lilico's column yesterday, suggesting that we should increase interest rates to boost growth. http://blogs.telegraph.co.uk/finance/andrewlilico/100015883/the-bank-of-england-should-raise-interest-rates-next-week/ His argument seems to be either that there is currently too much investment and this will result in lower long-term welfare (which seems unlikely) or that low interest rates keep alive unproductive firms which should go bust, allowing productive ones to grow. Is that a plausible description of the situation today? (Tim's comment above hints at the same thing)

You overstate the case slightly. If everyone worked harder/smarter to find a job, one would expect job matching to improve, resulting in faster job offers (slightly lower unemployment), more productivity (and output) and a (perhaps small) multiplier effect which will create net new jobs. However this is a minor effect compared to the fallacy which Cameron appears to be indulging in. There is a more sinister interpretation. Perhaps Cameron knows full well about the fallacy of composition. Maybe he wants to create a division between those slightly more effective, skilled or hard-working unemployed people who will get the few jobs, and those a few steps behind who just miss out - and can then be blamed as feckless losers. Those who do get (or keep) a job will make the mistake of thinking "I worked hard like Mr Cameron said and I got a job, so if _she_ didn't get one she must be a lazy so-and-so". A recipe for class division and potentially, the creation of new loyal Tory voters. I don't really believe this; I just think Cameron says whatever he thinks sounds plausible and will get him re-elected. He probably suspects that nothing the state can do will make any (positive) difference - the simplest and most fundamental ideology of Tories - so it's just a matter of doing as little as possible and staying in power as long as he can.

When I read this two weeks ago I thought there was something missing, but I couldn't quite see what it was. I was just reminded to come back and look again by @stephenfgordon and @mattyglesias on twitter. I've realised that I didn't instinctively see the proposal as being anti-labour, or even as looking anti-labour to voters. A more sellable (or in Nick's term political-economy-compatible) proposal might be the following. Target a wage increase of not 2.5% but 4%. Based on expected productivity increase of 1.5-2% per year, this should be long-term equivalent to a CPI increase of 2-2.5%. Make sure CPI figures are still published so that people can see the difference between the two. Sell it to voters as a real-terms annual increase of 1.5-2% (plus whatever you get from being promoted or gaining more experience or seniority in the workplace - which every voter, being overconfident, will expect to happen disproportionately to them personally) As Nick hinted, it might seem to a macroeconomist like this is effectively equivalent to his proposal, but I think to a voter it's not. The 4% increase is better compared to pre-existing anchors than 2.5%. And a focus on productivity and showing the difference between CPI and wages would help to make the idea more popular. Am I wrong on the productivity figures? In the long run will it matter what the actual number is, once this expectation gets baked in? I'm not sure, but I think this proposal would be more politically achievable than Nick's, just because of that change in number.

That's exactly the point. In her letter, she shows that Adorno is translatable into a very comprehensible sentence without losing any meaning. Which makes her own example, for which she won the Bad Writing prize, all the more egregious. Here's that beautiful lump of prose: The move from a structuralist account in which capital is understood to structure social relations in relatively homologous ways to a view of hegemony in which power relations are subject to repetition, convergence, and rearticulation brought the question of temporality into the thinking of structure, and marked a shift from a form of Althusserian theory that takes structural totalities as theoretical objects to one in which the insights into the contingent possibility of structure inaugurate a renewed conception of hegemony as bound up with the contingent sites and strategies of the rearticulation of power.

The problem is that fund managers are living in a certain kind of fantasy world where they think they have a right to a 20% increase in capital value on whatever assets they feel like buying. Thankfully there are also people (or regulations) that force them to pay attention to downside risk too, which is why they're hanging into all those Treasuries they hate. "Mom, I hate crossing the road at the traffic lights." "Well do you want to be hit by a car?" "No." (much pouting ensues, followed by a crossing at the traffic lights)

This is suggestive but not conclusive. Benford's law depends (as you would expect) on the distribution of data being tested. For instance, we might not expect to see Benford's law applying to the scores in basketball games: the nature and length of the games results in lots of 5, 6, 7, 8 and 9 initial digits, some 1s, and hardly any 2s or 3s. One could argue that competitive pressures would drive corporate results to be correlated with each other to a greater extent than in a random power-law distribution. Or, even if the figures are partly influenced by the managers of the companies, this might be a financially oriented management strategy (e.g. invest sufficient, or work one's salespeople hard enough, to ensure a 10% sales increase each year). I'm not certain that this would result in a Benford's law violation but it is mathematically plausible. When a data trend is simply going up over time it is very hard to ascribe it econometrically to any particular cause. Maybe the data regarding individual industries which are mentioned at the end of the article are clearer. But the alternative causes above could also fit quite well with booms and bubbles in each industry. Or maybe it's fraud after all. I'm not saying that never happens!

Your 9-point scale is a good outline of the spectrum from fiscal to monetary intervention. There are certainly adjacent steps on the scale which are not equivalent. Your example in a later comment is a good one: "Suppose the government buys a brand new office chair. That's fiscal. Suppose it buys a chair that was produced 5 minutes ago? 5 hours ago? 5 days? 5 weeks? 5 months? 5 years? 50 years? Someone's got the cash, and will want to replace the chair." In fact, this example shows why the two policies are different. There are lots of old office chairs which would not be replaced if the government bought them. In fact, there are lots of chairs in abandoned office buildings which would be brought out and dusted off to sell to the government if Congress passed a cash-for-chairs scheme. This is an argument both for and against fiscal policy. For, because buying newly produced chairs is better than buying old ones (antiques?). Against, because it shows how easy fiscal policy is to game. Behaviourally, this is explained by some kind of status quo bias/risk aversion - as a business I might hang onto equipment just in case it comes in useful - its net present value is slightly greater than zero. But it doesn't mean that I would replace it if someone bought it. Now that should not be true of government or corporate bonds because they are liquid, with a clear tradeable value. But it will definitely be true of investment in, or lending to, small businesses, which is not fungible. It will be true of many fiscal interventions. There are a few reasons why intervention at step 1 will not be equivalent to intervention at step 9 - most of which I think arise from the leap from step 8 to 9, because old and new projects are only equivalent in a limited subset of the economy (liquid corporate bonds and some equities). Which is not an argument for or against step 1 relative to step 9. Either might be right. Each has different positive and negative impacts. Each is reversible to a different extent, has different political acceptability, raises different credibility questions, and creates different kinds of incentives. You've demonstrated quite well why they are not as different as they might instinctively feel. But they are different, and perhaps these essentially political questions of credibility and incentives are the main reason they are different. Is there really a difference between an "excess saving theorist" and someone who believes in "excess hoarding of money"? I think I have been persuaded by you that these two are the same, but that's from a starting point of some macroeconomic naivety. What is the alternative theory?

By "It also charges this Congress to come up with an additional $1.5 trillion in savings by Christmas" I don't think it means the savings should happen by Christmas, just that Congress should come up with them by Christmas. Presumably they will mostly be back-loaded towards the end of the ten-year (is it ten years?) remit of the super-committee. Of course the announcement of the future cuts might have a small contractionary effect, but that's a bit of a Ricardian equivalence argument, and I don't think we really believe in Ricardian equivalence round here...do we?

I posted here earlier, but my comment seems to have vanished - I assume there was a posting problem, as I got some kind of error on my first attempt. This is surely a matter of degree - there is no absolute answer. Yes, labour is not entirely fungible; but people do have some flexible skills. Half of the current unemployed had jobs three years ago, so they're not completely unemployable. Their skills are not all applicable to just any construction project, but they're not entirely useless either. Simple hydraulic Keynesianism won't work, because it does distort incentives; but if designed right it will work much better than no intervention at all. The Austrian insights of heterogeneous labour supply and price signals certainly have some truth; so do the Keynesian insights that some components of demand are driven by aggregate income and that money spent out of labour income does have an effect on whether resources suboptimally sit idle. Does unemployment create value by incentivising people to retrain and redeploy themselves to new industries? Sure. Is it value-destroying because it makes it harder for people to demonstrate their skills credibly to new potential employers? Yep. Which effect is stronger? That's surely an empirical question, and the data in studies like the Mercatus one might help us to answer it. My philosophical view is that there is no such thing as no intervention: even if the government doesn't do anything directly, that project manager in the quoted comment might still get hired away by another private company; value is always being both created and destroyed by factors outside of our control. I think that (well-designed, carefully targeted) intervention can have positive effects; but it does need to be applied with caution, recognising the risks of misdirected resources and bad investments. Government should be humble, using market signals as far as possible to help it work out which public goods have a positive net value.

Duncan noticed something similar yesterday: http://duncanseconomicblog.wordpress.com/2011/08/30/bank-failure-macroeconomics-keynes-hayek-marx-minsky/

...there's an awful lot of poor lost souls wandering around the internet who have just discovered the marvellous truth of I=S as an accounting identity, and think they have found some magical philosopher's stone... I suspect this is because the definitions of S and I are not quite intuitive to non-economists (and even to some economists, perhaps). Imagine I earn $100 and put $10 in the bank, but the bank hasn't yet found a business to lend it to, so it hasn't been "invested". An intuitive way to describe this is: S=10, I=0 - oh look, S=I is violated! Of course S is not really 10, because my saving is cancelled out by the bank's borrowing (or the bank's shareholders' borrowing if you like). That's without even getting into the question of whether the $100 is actually income. People who think in the above way (which is not unreasonable given the normal use of English language) are inevitably going to be surprised by the assertion that S=I. This will lead to one of two responses: "don't be ridiculous, your economic theories of 'equilibrium' and 'rationality' are obviously wrong" or "wow, look at this amazing fact I discovered. Isn't the world a strange place? I will now show off my new cleverness to my unenlightened friends/fellow bulletin board readers." If they were taught the technical meanings of S and I, or even that there are technical meanings, their amazement and confusion would quickly dissipate. Admittedly it would probably be replaced with boredom; good luck getting most of those people to read and understand this post. Thanks though - it's a good refresher, especially for those (like me) not formally trained in economics. I'm sure I have made similar mistakes in the past.

My whole livelihood comes from selling willingness to pay estimates. Not for environmental goods, admittedly...at least not yet. We act as pricing consultants for a range of companies. It's extremely valuable to them to know what people will pay for their products. Though I'm not sure I am ready to tell Daniel the answer to his question...

To expand slightly on this: most classical economic equilibrium models are continuous in most variables - this makes them much easier to work with for the modeller, and for rational agents it is usually a natural assumption. Non-rational or behavioural models (I'd include sticky-price or sticky-wage models in this) may well have discontinuous features. For instance, the very fact that wages are sticky means that a change in wages of 0 is special, and would not be expected to have similar effects to a change of 0.01%. What you're talking about here is a shift from a rational model to an only-slightly-irrational model by a change of parameters; my intuition is that this change should be continuous and not fragile, but I could be wrong.

OK, I'll comment on point 1 - the existence of "fragility in the limit". This is the same as the mathematical concept of continuity. A function a(x) is continuous at a point c if the limit a(x: x->c) exists, and is the same as a(c). In this case, your condition of "fragility" means that the limit of inflation as f->0 is not the same as inflation AT f=0. Technically you are not talking about a function being continuous, but the behaviour of a model being "continuous" as one of its parameters tends towards zero. However, it's easier to write the definition in terms of the behaviour of the dependent variables in the model (e.g. inflation, prices). We're getting a bit meta, because we are not talking about whether the individual functions in the model are continuous (e.g. is inflation a continuous function of interest rates); we're talking about the behaviour of model variables as you vary the basic parameters of the model. But these can still be represented as functions - e.g. holding nominal interest rates constant at 1%, how does inflation vary as a function of the proportion of f, the fraction of prices that are sticky. I think that this particular function _is_ continuous in that variable, but that doesn't invalidate the concept of fragility - it is still a meaningful question to ask.

Rather than look at the reasoning of the f>0 example, I want to go back to the first "perfect" model: "The model predicts that if the central bank increases the nominal interest rate by 1%, the rate of inflation will instantly increase by 1% too" Without knowing the workings of the model intimately, my sense is that this can only happen because of an instantaneous fall in prices. Looking at it another way, if the central bank increases nominal interest rates, the money supply effectively falls (indeed this may be its mechanism for making interest rates increase). If the money supply falls, and money is neutral, prices must instantly fall. So the inflation happens, but from a lower price level. If this is correct, then the "limit" behaviour in your imperfect model is exactly the same - the "explosive deflation" of an instant reduction in the price level. So maybe the model isn't so fragile after all.

I agree that this would probably work to increase output, but I don't think it's Keynesian. It's the government using its market power to buy more stuff for the same price (reminds me of when some big retailers in the UK simply told all their suppliers that they expected an immediate 2% price cut or else they'd stop buying. Most caved in) Because the government is a big purchaser, this might have some macroeconomic effects - wage deflation, which may or may not be positive depending on your models, and increased real output. But I don't think it's Keynesian in any way - the Keynesian model depends on government borrowing to cancel out private attempts to save, and you have excluded that by assumption. It's just ordinary government intervention. (yes, there's a correlation between supporting government intervention and believing in Keynesian models. But that doesn't make this Keynesian) I do think this plan would have a monetary effect - it would increase velocity, to the extent that the newly-employed have a higher marginal propensity to consume than the already-employed. Does that count as monetary?

Ah - reading your reply to Scott, I think we are both saying the same thing.

From Part 2: "Hell, even I could do that. "Here are 10 bits of green paper per person. Unless I get all 10 back at the end of the year I will beat you up. How much will you give me for them?". "Nothing" is one possible answer, even if my threat is credible." I don't think "Nothing" is a realistic answer. I'll offer you something for your 10 bits of paper (and for 100 more of them) because I know I can sell them to other people who will need to give them back to you at the end of the year. The scarcity, combined with their practical application, creates value. I don't think this means that taxes are in themselves necessary to create a value in currency - taxes are just one of many ways to establish the network effect which you have described. And in Part 1, I don't believe taxes intrinsically give the currency value either. In this model, taxes are simply a way to reduce government borrowing - which reduces the broad money supply. But any other reduction in borrowing would have the same effect; if companies decided to fund more of their investment from retained earnings and less from borrowing; or if people bought houses with cash instead of mortgages. The value of the currency arises (partly) from the desire to use cash instead of debt - government is just the biggest of many agents who can independently make the decision to do that. Taxes aren't special.

There is no need for a causal relationship in either direction. Do chickens cause eggs, or do eggs cause chickens? Neither - the chicken-egg ecosystem is an emergent phenomenon from a world under evolutionary pressure. Despite how it sounds, this is the punchline to a joke about social scientists. It also does not mean we have to take the chicken-egg dialectic as it is given to us - we can intervene, co-opt it to make Nando's, or eliminate it with gradual work and domestication. Same with violent right-wing extremism.