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right, in the future, everyone will be an artisan baker / craft brewer etc. there have been articles in the FT about this recently, about macro implications of lots of smaller producers of more unique products, but can't seem to find them with a quick search.

Luis. Thanks. How empirically relevant is it, over the last few decades? I'm trying to remember when microbreweries really took off (probably different for different countries).

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.

I like the intuition behind this post, and how it sheds light on the concept of GDP.
One question - by what mechanism do we see the price of new apples equal that of the old apples? Wouldn't you likely see the more specialized new apples trade at higher prices and lower quantity than the old varieties? (Not because people like them more but because of returns to scale)

Leigh: if we consider an economy with perfect symmetry, so each variety has an equal number of fans (or each person prefers a basket with equal numbers of each to an unbalanced basket), then each variety will either be produced in exactly the same quantity at exactly the same price, or else not produced at all.

When doing macro (as opposed to partial equilibrium theory) it's hopeless asking whether the price of apples (the only good, by assumption) will rise or fall. In terms of what? It's easier to measure prices in terms of apples.

Labour supply might increase if people can buy an increased variety of apples with an extra hours work, but I am setting that aside, since I want to focus on measured productivity (number of apples per worker).

"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?"

That's the paradox. Think of a very simple Robinson Crusoe economy. He is "getting richer" in the sense that the shift in the production function from better technology expands his opportunity set, and so he *could* eat more apples and have the same amount of leisure as before, but he chooses to consume a greater variety of apples instead, so he doesn't seem to be "getting richer" as we normally measure it.

Whenever there is an improvement in technology it may be reflected in either an increase in quantity produced (more units of output from the same inputs)) or quality (same inputs produce better quality output). The first would be captured in GDP the second not.

Over the past 20 years televisions can not only be produced with (probably) less total labor inputs but the quality has also improved dramatically. A TV from 1997 may have cost the same as a TV in 2017 and so each one produced add the same amount to GDP (assuming its produced domestically!) , but the utility from watching in HD on a flat-screen TV is probably greater and this is not captured in GDP.

If only we could measure individual and social utility objectively then GDP (measured in utils) could capture both kinds of improvements.

louis: thanks. Realistically, since new trees produce only a small crop of apples each year, it takes time for new varieties to come down in price to match existing varieties. I'm skipping all that, since I'm thinking about a very long run process. The underlying model at the back of my mind is monopolistic competition, with each variety being produced by one firm, with a fixed cost, and horizontal Long Run Marginal Cost curve, and all firms facing an equivalent downward-sloping demand curve, and free Long Run entry, so P=ATC.

MF: Statistics Canada does try to capture improved quality, though it's not easy in practice. But I'm not talking about improved quality of apples here. The new apples do not replace the old apples; and both sell for the same price. Both apples have equal subjective quality on average, but some prefer new and some prefer old, and some like half of each.

@VaguelySteamy on Twitter sends us to this Hausman paper for the micro estimation.

> But it doesn't show up in the GDP data, or in rising wages or land rents.

I think your general point is that the GDP doesn't measure consumer surplus.

If we took your 'constant returns, more varieties' example and assumed monopolistic pricing, then prices would go up for the variety store and we'd account an increase in GDP for approximately the same total consumer utility.

This makes sense. We already know that GDP is an accounting exercise, just a usually-useful one.

If you look at the time dynamics, things get even wonkier. As you point out above, it will take some time for prices for new varieties to adjust to the long-run equilibrium. In the meantime, before firms complete market entry/exit, it will look as if the GDP has gone up and is falling to its pre-variety level. The new technology (apple varieties) has seemingly caused a recession!

Or the increase in the number of varieties of apples might be a random consequence of the pollination of apple trees. This introduces the possibility that some of the new varieties might be "worse" than the existing variety (varieties), and the "technical change" could be welfare reducing. Or at least that seems possible.

And @Market Fiscalist, one difference here is that the quality of apples hasn't increased. Overall, the average valuation of an apple is exactly what it was before, so there's no gross quality adjustment to make to a price index.

Consider an equivalent situation: all paint colours cost the same, and you need to paint your walls. How much measurable gain is there to you being able to select your favourite colour scheme?

Majro: "If we took your 'constant returns, more varieties' example and assumed monopolistic pricing, then prices would go up for the variety store..."

Stop. What are you measuring prices in terms of? And don't answer "money", because that just begs the question of whether the value of money stays constant, and what we mean by that. You gotta think macro, not partial equilibrium micro. Again, all apples have the same price, because I'm assuming a symmetric equilibrium between apple varieties.

Donald: I have never managed to figure out the sex lives of apple trees. They get pollinated from all over, and yet all the half-sibling apples on the same tree all taste the same. I did Google this once, but can't remember what the answer was. But it any case, if a new technology is worse than the old (everyone prefers the old apples to new, even at the margin) then the new technology does not get adopted. (Unless the old gets forgotten, like Roman concrete.)

Majro: I like the paint colour example.

OK, to to look at it slightly differently:

New ideas or discoveries can allow more utility to be generated from the same available inputs in three obvious ways

- More existing goods can be produced with the same inputs
- The quality of existing goods can be improved with the same inputs
- New goods get produced either because they have been newly invented/discovered or some of the gains from other goods get diverted into previously un-produced goods.

Your apple example seems to be of the third sort. The first type would be relatively easy to measure in GDP terms, the second harder and the third almost impossible. 2 and 3 would overlap to some extent (when does an enhanced existing product become a new product).

All seem to resolve to maximizing utility given the available combinations of goods that could in theory be produced.

Nick - We're talking about change here, right? Is GDP higher in period 2 than period 1? On introduction of a new variety in period 2, that variety has a higher price relative to the older variety, and the older variety has a lower price than it did in the prior period, GDP would appear higher. And over time, as the price of the new variety converges to the price of the old variety, that would show up as GDP growth. If we jump forward 100 yrs, statisticians will be somewhat baffled - people are consuming the same number of apples, but in different varieties, are we any richer? But if the statisticians were paying attention over the 100 yrs, they would see steady incremental growth in GDP. A weird result, no doubt.

MF: yes. Measuring 2 is hard, but Statistics Canada tries to do it. Measuring 3 is harder, but not impossible. You could ask people how much you would have to subsidise their food to persuade them to go back to eating only the food that was available 50 years ago. Or see the paper I linked above in comments.

louis: no. All varieties have the same price, by assumption. And it's pointless to talk about whether that price goes up or down, since what do we measure that price in terms of?

Re: microbrew variety
It is hard to count the number of craft beers as the various craft breweries are always experimenting, however the number of craft breweries isn't a bad first approximation. Typically a craft brewery will have one or two unique beers, and a number of standards.
For the US a lot of the regulations were nationwide and we have a fairly clear start date, that being 1979, the day after President Carter signed the home brewing deregulation bill. Some claim the real start date was in 1982 when CA and WA made brewpubs possible, but I don't think that would have happenned without the earlier deregulation.

https://www.brewersassociation.org/statistics/number-of-breweries/

Probably a bit off base, but the presumption is that those different varieties of apples don't lead to longer lived human beings. Obviously, apples do not contain enough of the nutrients that the human body needs so that one can live solely on a diet of apples. However, if those new varieties offer missing vitamins, minerals that are lacking in the current batch, GDP might be increased from the increased nutritional value that the variety of apples offers.

Also, there is the non-quantifiable effect on emotional fulfillment (sense of purpose) both from discovering those new varieties of apples, marketing them, and even teaching about them.

How boring would a biology class be if the only plant life out there was plain jane granny smith apples?

Nick Rowe is Gregor Mendel of economics?

Overall, I like the apple garden you are building. A couple of questions, some of them related to potential weeds in your garden (though I'm not sure which ones are micro-only):

Could it be more useful to view the different varieties as different goods? "Increasing returns to scale technology" suggests that each variety is produced using partly different technology (different tree type). And each variety might fill a somewhat different need, or fill a need in a different way, in each individual. To me this sounds like different goods.

My concern could have something to do with the tendency of economists to talk about goods and commodities as if the terms were interchangeable (I'd say the plain apples before variety entered the picture were commodities)? Across-the-board technological improvement could come from improved fertilizing, improved methods for picking the apples, etc, so that assumption probably works OK even if we saw the different varieties as different goods.

"Increasing returns to scale technology" also suggests that we could initially price an apple of a new variety ("special"; not better, but different) in terms of an apple of the existing variety ("plain"). The producer, and thus the society as a whole, faces a choice between growing, say, 100 plains or growing 90 specials. Want a special apple? You will get 9 for 10 plains (in a barter exchange). This, too, speaks for different goods, not just one good?

By the way, how narrowly do economists define 'price'? Can we say that in autarky the price you pay for the goods (or consumption) is the effort it takes you to get them? (For instance Keynes said once that in the end it all comes down to human effort and human consumption.)

As you see, I'm trying to learn some economics. It takes time, because I have a liking for fundamentals.

John: thanks for that answer. CAMRA (Campaign for Real Ale) was taking off in the UK in the 1970's, IIRC.

Frank: yep. People might like variety for a lot of reasons.

Antti: "Could it be more useful to view the different varieties as different goods?"

Yes. It's impossible to draw a line between a different variety and a different good. The only reason to talk about different "varieties" is that it makes it mentally easier to imagine a simple macro model with a represent good/variety, with perfect symmetry, where each good/variety has the same production function (and hence cost curve) and the same demand curve, without assuming that all goods are identical so there's only one good. It's a multi-good model that is almost as simple to think about as a one-good model, because of that symmetry. Any equation that applies to one of the goods/varieties also applies to any of the goods/varieties; you just change all the subscripts and it still works.

We sometimes use "price" metaphorically like that, to note the analogy, but usually don't when we are being strict. When we are being strict, we say, for example, "in competitive equilibrium, for any two goods, the Marginal Rate of Transformation = the relative (market) prices = the Marginal Rate of Substitution". MRT is the slope of the production trade-off, MRS is the slope of the trade-off in preferences (the indifference curve), and Pi/Pj is the slope of the budget line in the market. Metaphorically they are all "prices".

We don't talk about "commodities vs goods" much. Instead we talk about, for example, perfect competition (where the individual firm faces a perfectly elastic demand curve because the good it produces is identical, in the eyes of consumers, to the goods produced by many other firms) vs monopolistic competition (where the individual firm faces a downward-sloping demand curve because no other firm produces a good that is identical). That's where the distinction matters; it's all about the elasticity of the demand curve facing a firm: is it perfect or imperfectly elastic with respect to relative price?

"Constant Returns to Scale" means if you double all the inputs you exactly double the output of a good/variety. "Increasing Returns to Scale" means output more than doubles. It's a statement about technology and production of a particular good/variety, not about demand and price (though it has implications for price).

If Q is output, and L is labour input, then:

Q=bL is an example of a CRS technology

Q=max{0,bL-a} is an example of an IRS technology (a is the fixed cost, so you must have L > a/b before you produce any apples at all.)

9 tree economy, each produces 100 apples per year.
Period one - Everyone produces A-type apples. GDP is 900 A-type apples (A-type apples are the unit of account). Everyone consumes 10 apples.
Period two - One tree is converted to produce 80 B-type apples instead of 100 As. People have a taste for novelty, so they are willing to give up 4 As on the margin for 3 Bs. Owner of B-tree gets 96 As and 9 Bs. Everyone else has 88 As and 9 Bs. GDP in terms of A-type apples = 908, so we see growth in the metric.
Period three - 3 more A trees converted to B trees, to the point where equilibrium price of A and B are the same. Economy produces 500 As and 320 Bs. GDP is 820 apples. However, we saw price deflation. Using period 2 prices, GDP is 927. "Real GDP" grew.
I guess the problem is this is all squishy and path dependent. All I'm saying is to extent people's revealed preferences show up in price signals in the short term, if those are picked up by statisticians that will have some effect on measured production in the long term, even if eventually prices equalize.

louis: interesting example, but very different to mine. Your consumers have a taste for *novelty*, which (presumably) dies away after they get used to the new good. If new goods have a temporarily higher price, reflecting that temporary novelty, GDP growth will overstate the growth in welfare.

> Stop. What are you measuring prices in terms of? And don't answer "money", because that just begs the question of whether the value of money stays constant, and what we mean by that. You gotta think macro, not partial equilibrium micro. Again, all apples have the same price, because I'm assuming a symmetric equilibrium between apple varieties.

I can measure the price in terms of other apples. Assume we have a generic 'Red Delicious' apple market and we introduce a single new variety ('Gala') with monopoly pricing that takes a small slice of the market.

Suppose the demand curve works such that we'd see 100 Gala/day sales at 1 Red Delicious : 1 Gala, but 95 Gala/day sales at 1.1 Red Delicious : 1 Gala is the profit-maximimizing price point for the monopoly firm.

With competitive pricing (long-term monopolistic competition with entry/exit), the GAP (Gross Apple Product) remains unchanged as per your example. With monopoly pricing (and short-term pricing with monopolistic competition), the GAP increases by 4.5 apples in Red Delicious units.

In a more realistic sense, this sort of reasoning does uncover problems with equating GDP and well-being. The water coming from your tap has a negligible contribution to Canada's GDP, but any world in which it isn't there is far worse for everyone (also diamond/water paradox). Competitive markets maximize consumer surplus, but GDP measurements – save for minor corrections for technological changes – can't measure this.

Nick - maybe novelty was the wrong term. I think the logic holds if you just say the consumption utility function has declining marginal utility with respect to each variety. So the first B apple may give less satisfaction than the first A apple, but less utility than the 9th A apple. It's another way of saying people like variety.

Majro: GDP has been rising extremely fast if we measure it in terms of computer chips, but falling if we measure it in terms of caviar. It all depends what good we use as numeraire. Normally we use a basket numeraire for real GDP, but even then, which basket -- current or previous period's, (Laspeyres or Paasche) or a Fisher geometric average of the two? (And it gets hairier still with new goods, which had an infinite price in the previous period.)

That's why I assumed a symmetric equilibrium where all varieties of apple have the same price, precisely to avoid all those index number problems which distract from the main point.

There is a huge conflation of use-value and exchange-value in this post. Let me demonstrate where this can cause people to go wrong.

Imagine an economy that uses perfectly supply-inelastic meteorite fragments as money. The total aggregate supply available to the economy never changes (across human timescales).

In this scenario, on average it will be impossible for a typical person to accumulate more meteorite fragments. What one person accumulates (perhaps by luck, or by skill, it doesn't matter), another must lose.

Investing meteorite fragment money in a line of production in the hopes of gaining a profit in terms of meteorite fragments would, for the typical person, be foolish.

This is despite the fact that the production of everything else in the economy, such as apples, could be made more efficient or of higher quality or volume. All of that would increase the utility, the enjoyment, the pleasure available to people. But none of that would allow a typical meteorite fragment holder to increase his exchange-value in terms of meteorite fragments.

Investment in production might make sense anyways--but only in order to produce directly useful things for the producer's own consumption, not for re-sale. Producing for re-sale would be silly. You'd get back, on average, no more meteorite fragments than you invested. Could you barter your produce for more real goods? Yes, but so could you have just as easily hoarded your meteorite fragment money, allowed it to appreciate against the greater quantity of real goods being produced, and "barter" your meteorite fragment money for more goods.

And yes, society would have more real wealth due to your investment, so the "purchasing power" of each of your meteorite fragments would increase. But even so, you would have been better hoarding your meteorite fragments than making an uncertain investment only to get back as many meteorite fragments back...or, what is the same, a bundle of real goods that, for exchange-value purposes (not necessarily use-value purposes), would be worth the same.

Another difference between exchange-value and use-value: exchange-value has an objective existence. Use-value is entirely subjective.

For example, let's say the going price for a loaf of bread is $2. Let's say that bread is on sale somewhere for $1. I eagerly buy a loaf of bread.

Have I "profited"? The sense in which I have "profited" depends on what I go on to do with the bread. If I consume the bread, then I might have profited in terms of personal subjective utility. Maybe the bread's tastiness was more useful to me than $1. But if I consume the bread, then my holdings of exchange-value have absolutely decreased by $1. I know have $1 less social advantage, social credit, with which to obtain new things. If I had intended for my bread-buying to be a self-financing business, I will find that this business has been unprofitable in the exchange-value sense when I go to re-invest in the buying of another loaf of bread and find that I am short the money needed. Only if I had re-sold the $1 loaf of bread for something like $2 would my actions have been profitable in the exchange-value sense.

So, when you ask, "Does GDP increase if we gain merely a larger variety of apples," you need to specify to me: in the use-value sense, or the exchange-value sense. In the use-value sense, absolutely...although it would be difficult for me to quantify just how much because prices measure exchange-value, not use-value. If you are asking in terms of exchange-value, then I would say, "No."

I think the whole concept of "hedonic adjustments" and of "real GDP" itself are bogus. To measure exchange-value, only the nominal prices are relevant. But not just any nominal prices! Of course, if you used nominal dollar prices, that would be misleading. But you have to use some sort of nominal prices.

The explanation for this would take a lot more space to explain, but the thesis I would argue is: if you want to measure exchange-value across time, calculate the aggregate prices of output in terms of gold or some other commodity money. Add up the nominal gold-prices of goods and services produced in an economy. If your larger variety of apples fetches more gold on the market, then yes, GDP has risen.

Matthew: no. The exchange value vs use value distinction got sorted out in 1871 (do you know what I mean by that?). And the nominal value vs real value distinction is quite separate. And there is no conflation of use value with exchange value in this post. The whole point of this post is to give an example (increasing variety) where well-being goes up while real exchange value of goods produced stays the same. There are other well-known examples that we teach in first year economics, but this one is trickier to explain.

> That's why I assumed a symmetric equilibrium where all varieties of apple have the same price, precisely to avoid all those index number problems which distract from the main point.

I don't think of my comments as an index number problem, but instead more a mechanistic way of exploring your core point in this post. My reasoning goes as follows:

People are better off with a variety of apples (obviously). But how do we get a variety of apples? They arise because of an expectation of profit. In the short run, that profit can be realized (short-run of monopolistic competition), but in the long run there is no economic profit, giving us the equilibrium of your post.

People are better off, but this cannot be measured by tracking current-period exchanges. The market economy has generated a consumer surplus which is invisible to statistics.

This is different than a comparable situation, where we have different apple varieties because of an exogenous factor but everyone is indifferent. A space alien observing the markets would see the same set of exchanges as your variety-preference equilibrium, but there is no consumer surplus created by the variety.

This is not entirely dissimilar to your post from a few years ago about whether niftiness increases aggregate demand, although in this case the 'niftiness' is a personal preference rather than a general dominance of a new variety over old. (That's what makes it hard to aggregate, even!)

Majro: OK, I'm following you now, I think.

louis: OK. Let's simplify. New trees produce only a small number of apples, so there's a short run equilibrium with higher prices for new apples, and then prices of new apples fall as the trees mature and produce more apples, and we get to my equilibrium with all prices and all quantities the same in the long run. And that would create a problem for measuring real GDP, because even if the total number of apples stayed constant, the chain index would see the number of new apples rising and old apples falling, and would say that real GDP is increasing if the new apples are valued at previous year's relative price. But I *think* that problem is handled by the Fisher "ideal" price index, which is a geometric average of Paasche and Laspeyres.

I'm ignorant about Paasche, Laspeyres, and Fisher aside from what I can glean from these comments. Taking into consideration majro's points about short-term price incentives, the question I am left with is this: in light of the fact that relative prices are changing over time, it seems that measured GDP hinges on how frequently measurements are taken. Is that right or am I missing somethingm

Louis: you are right about frequency, but still missing something.

We want to measure how much the value of a basket of apples and bananas has increased between 2016 and 2017, adjusted for inflation. (Real GDP). There are 2 methods:

1. We can value both baskets at 2016 prices and compare them
2. We can value both baskets at 2017 prices and compare them

We get different answers from the two methods (unless both P's have changed by the same %, or both Q's have changed by the same %). A third method:

3. We take a geometric average of the two methods.

If we make the periods shorter and shorter (from decades to years to months to weeks) the two methods give closer and closer answers, provided there are no discrete jumps in the prices. We make each link in the "chain" index shorter and shorter.

We face exactly this same problem in measuring inflation, since the price level (GDP deflator) is defined as nominalGDP/realGDP. Same for measuring the CPI. This looks fairly good and simple.

Don't trust me on the above; I try to stay away from Index Number Theory, past first year.

Thanks for the economics lesson, Nick! :-)

You said: "When we are being strict, we say, for example, "in competitive equilibrium, for any two goods, the Marginal Rate of Transformation = the relative (market) prices = the Marginal Rate of Substitution". MRT is the slope of the production trade-off, MRS is the slope of the trade-off in preferences (the indifference curve), and Pi/Pj is the slope of the budget line in the market. Metaphorically they are all "prices"."

I took your "strict" to mean "not metaphorical". But then in the end you say that MRT, MRS and Pi/Pj are all metaphorically "prices". What is the non-metaphorical 'price'? Does it exist?

Antti: my mistake. MRT and MRS are metaphorical prices. Pi/Pj is the strict literal (relative) price.

OK, Nick. Now I'm wondering what Pi alone is? Is it the strict literal (nominal) price of good i? Or is the 'P' in front of both i and j just a way to say that this is about price, and the price of good i can only be expressed as Pi/Pj? If we say that the price of good i is $5, what we really mean is $5/$1, where good j is 'a dollar'?

Or should we just forget the nominal price?

Antti: yep. Since money (either as medium of exchange or unit of account) really plays no role here, it's easier to think of Pi/Pj as just Pij.

But, on the other hand, giving each good its own Pi is an easy way for the theorist to ensure that the matrix of Pij 's is mutually consistent, so it does not contain arbitrage opportunities (like Pij=1, Pjk=1 and Pki=2). And does not have absurdities like Pij =/= 1/Pji . If the price of 1 apple is 2 bananas, then the price of 1 banana must be 1/2 apples. The theorist needs a unit of account (which can be anything, even the proverbial "venus dust", which does not exist) to help keep his head straight!

Thanks again, Nick.

"The theorist needs a unit of account (which can be anything, even the proverbial "venus dust", which does not exist) to help keep his head straight!"

In a model of a monetary economy, would you say that if the price of an apple is $2.00 (luxurious varity!), then that price is a relative price of the apple (relative to dollars)? Or is it a nominal, not relative, price?

You see what I mean? If 'money' is a (special) good, then the price should be a relative price. If it is a nominal price (expressed in "venus dust" or "dollars"), then we should, in my opinion, conclude that the (abstract) 'unit of account' and the 'medium of exchange' are separate concepts. The MoE doesn't act as the UoA; the MoE is denominated in the UoA.

Antti: I was taught: that MoE and UoA are separate concepts (so the MoE and UoA can be two different goods); that the "numeraire" used by the economic theorist doesn't have to be the same as the UoA used by people in the economy (Keynes for example used labour as the numeraire in the General Theory); that the numeraire doesn't need to be a good in the economy (in which case the theory only determines relative prices, because nothing pins down the price of apples in terms of venus dust). Those are all non-controversial. A more contentious claim is that the UoA need not be an actual good. There is a literature on this, both historical and theoretical. It raises the question: what determines the price of apples in terms of venus dust, if people actually do use venus dust as UoA?

In my view, it's a bit like asking how the word "cat" can mean cat, and not dog? It's a convention. But conventions can change over time. Can the central bank control that convention using interest rates alone? And how do we define "the meter"?

This is a good illustration of the difficulty of measuring GDP growth due to the introduction of new goods. (I gave my undergrads a homework question on this recently).

In this case, I would say that the correct notion of GDP growth from increasing variety would be the increase in income (at the original selection of goods) that would compensate people for not receiving the new good.

For fun, I worked this out in a simple example. Suppose we have CES utility:

U = int_i(x_i^(1-1/e))

All apples have the same price (linear technology) which is normalized to 1. Income is Y, which is constant.

Then if there are N varieties of apples, the household consumes (Y/N) of each variety, and has utility:

U = N^(1/e) * Y^(1-1/e)

Then the increase in Y that compensates for an increase in N is:

dY/dN = (dU/dN)/(dU/dY) = 1/(e-1) * (Y/N)

One conclusion: this sort of growth experiences large decreasing returns in N. The growth rate per new variety is proportional to 1/N!

jonathan: good comment!

Take an example, where e=2 (plausible??). Then a doubling of the number of varieties is equivalent to a doubling of Y, in terms of its effect on Utility.

Maybe it's useful to thing of GDP along 3 dimensions: quantity, quality, and variety. Take food for example. Quantity and quality are not a lot different from what was available for our great grandparents; but variety has increased massively. How much would I need to subsidise your food to persuade you to eat only those varieties that were available to your great grandparents? If you say "80%", that is equivalent to food being 20% of the price it used to be.

Nick asked: "what determines the price of apples in terms of venus dust, if people actually do use venus dust as UoA?"

This is a good question. Hawtrey and Kitson have provided at least partial answers to it. I discuss them here:"A New Monetary System From Scratch, Part 1: Unit-of-Account and Numeraire".

A numeraire must be something that can have meaningful supply and demand functions (to determine its equilibrium value in terms of other goods, as Fama points out in a quote in my post). The abstract UoA's Hawtrey and Kitson discuss cannot be numeraires; they have no demand or supply, at least not in any literal sense. So an economist would need to use something else than the UoA as numeraire. But you say: "the numeraire doesn't need to be a good in the economy". Does this mean we disagree here?

If I say that 'a dollar' is a unit of account but that it cannot function as a numeraire because it has no supply or demand in the same (nor even in a similar) sense that goods have, do you agree or disagree?

Yes Nick, your last thought is correct. It is a well known fact in behavioral science that greater variety leads to greater consumption. Ceteris paribus, a greater variety of apples should lead to a greater willingness to work to produce more apples, and apple consumption should increase.

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