The English for "rentier" is rentier, at least in British English.
Tony Stark, Bruce Wayne, and Paris Hilton are all heirs of billionaires who are also managers (Hilton manages fragrances, while Stark and Wayne are industrialists)
Really? Stark is the only one of those who seems to be more than a figurehead. I mean, Wayne spends so much time being Batman he can't be managing much. Even Stark is more of an inventor than a manager. And as for Hilton, give me a break.
Yes, let's make rentier buzz as the new "entrepeneur" of French capitalist loanwords.
Also boulevardier is better than hipster.
The problem isn't that rentier isn't an English word; it's that it isn't a common English word. We can solve that problem by using it as often as possible. I promise to do my part.
Actually, until now I didn't know how to pronounce "rentier"--I thought you might pronounce the -er at the end--but Piketty inspired me to look it up. The British and American pronunciations here actually sound very similar. I was surprised that the first syllable was pronounced "ron" rather than "ren."
The Murdoch children are all inherited wealth rentier-managers. Rupert too, actually, though his inheritance was cut into by inheritance taxes (ooh foreshadowing).
Yes, rentier is an english word, the same way that "heighten the contradictions" is an english phrase, not common. Infuriating that French-sounding words are alienating, but they are so for many people here.
Ms Hilton is a manager in economic terms, heightening the contradiction with newscasting popular culture that equates "manager" with "productive person."
Oh, the US book is set in Garamond, nice choice.
So I have a question going back to chapter 6, on the capital labor split. (Maybe I should just go back and read that post & thread).
Sometimes when talking about the labor/capital split, he talks about capital's share of the national income, meaning how much of the money that gets made each year goes to the people who put in the capital and how much goes to the people who put in the work. That's how he talks about it on page 39, when he refers to the question of "how should income from production be divided between labor and capital," and how he talks about it on page 220, when he says that "numerous studies mention a significant increase in the share of national income going to profits and capital after 1970, along with the concomitant decrease in the share going to wages and labor."
But for most of chapter 6, when he talks about the capital/labor split, he talks about how much capital contributes to the production, not how much it gets out of it. On page 216, he introduces the idea that the capital labor split is said to come from the marginal productivity of capital, that is how much more stuff gets produced for each unit of capital invested (in tools or machinery, or whatever.) The idea of the elasticity of the substitutability of capital and labor is about how easily you can increase production using either more workers or more tools. The whole discussion here is about what capital gets done, not how it gets rewarded.
But these two ideas are different, right? It may be that in some firm the additional investment of capital increases production by 5%, but the investors demand 20% more of the profit--paid through dividends or whatever--because they are greedy bastards and can get away with it.
Am I right in thinking that Piketty is equating the productivity of capital with capital's share of the profit? If I am right, why is he doing this? Is it a general economic assumption of the rationality of markets? Is it more definitional, so that the marginal productivity of capital is just defined as the share of the profits capital receives? (If so couldn't you increase your productivity simply by demanding that you be paid more?)
Also, I can do chapter 10.
Ms Hilton is a manager in economic terms, heightening the contradiction with newscasting popular culture that equates "manager" with "productive person."
I'm sure she is some narrow taxonomic sense, but, like the Murdoch children, they're only in their actual managerial jobs because of their inherited wealth. There has to be a meaningful Piketty sense in which their job income is return on capital rather on labour.
7. I think that Piketty is assuming here that profit is all the income from production and sales that is not used for maintenance, rent and wages. And taxes? If the shareholders demand a greater dividend than can be covered by this, then the company will go tits up in short order, because it will be unable to meet its expenses.
9: Still, if you drive down wages, and increase profits, you increase capital's share of the income, but you haven't really increased the productivity of capital. It is not the case that the company would have produced less if less capital had been invested.
Yes, driving down wages is an alternative to investing, but there is a lower limit to how far because, theoretically, your workforce will go and work for somebody who offers slightly higher wages. In practice of course we encounter the question of monopolies: if Walmart is the only employer in town, then they can pay what they like and the employee's only recourse is to leave town. They shouldn't actually pay starvation wages, because killing your labour force off is counter-productive, but they can get close. P. believes that the pitchfork will come out if they try that too much, but I've seen no evidence.
Still, whichever strategy they use, greater investment or minimised costs, the profit remains income minus outlay and paying dividends which exceed that is the high road to bankruptcy. In some jurisdictions it's illegal.
Am I right in thinking that Piketty is equating the productivity of capital with capital's share of the profit?
Yes. At least, this is a criticism I've heard of Piketty, and I've read people like Krugman defend him on this practice, arguing that it's a useful starting point and approximation.
Is it a general economic assumption of the rationality of markets? Is it more definitional, so that the marginal productivity of capital is just defined as the share of the profits capital receives?
Yes to the first, no to the second.
Chris y seems to be arguing that it is a good assumption.
I'm sure she is some narrow taxonomic sense, but, like the Murdoch children, they're only in their actual managerial jobs because of their inherited wealth.
I feel like Hilton deserves a little more credit, it's not like she was given a Vice President role managing Hilton hotels, it's more like she created a celebrity persona that she was then able to convert into a cash flow. Yeah, it's a lot easier to become famous as a useless heiress if you are in fact a useless heiress, but it's not strictly necessary (I could imagine someone like her rising to fame despite being a fake).
12 last. I'd argue that it's a widespread assumption. I don't know enough to judge how good it is, but my instinct is to suppose, like Krugman that it's a useful starting point and approximation. I don't see what else you can do, although like everything else in economics it doesn't exactly describe the real world.
How much of this equation depends on making very optimistic assumptions about workers ability to fight back against efforts to drive down wages in most circumstances?
If your focus is economic inequality, you'd think that it would be important to note that workers in places like SE Asia aren't really in a position to negotiate for their fair share of company income. Heck, in the fishing industry in Thailand you've got real live slavery back in effect.
As an approximation, it hasn't been good for the last forty years at least, when labor's share of income has failed to track marginal productivity. Allowing economists their assumptions seems dangerous.
16. Are you talking about silly wages for top managers there?
9: Still, if you drive down wages, and increase profits, you increase capital's share of the income, but you haven't really increased the productivity of capital. It is not the case that the company would have produced less if less capital had been invested.
If you drive down wages and increase profits, in what sense haven't you increased the productivity of capital? If wages are lower then it takes fewer dollars of capital to create a certain amount of profit. (Or, stated differently, if the same amount of capital is invested, it will generate more profit than it would have with higher wages.) So each dollar is more productive.
8,13: Clearly they got the job through inheritance / nepotism, but there is a distinction between a pure rentier and an active manager, is there not? Are they turning up to work, firing people, holding meetings, all that other stuff that non-inherited managers do? Maybe some aren't, sure, maybe you can argue the income thus drawn has lost any connection with economic contribution, but they are working at a job.
I think its a worthwhile distinction because it seems like a huge cultural difference between 19c and Belle Époque values and today. Then the the thing you absolutely could not do was betray your common roots by seeming to try too hard, even if you were working like crazy and writing monographs on classical Greece in your spare time like Asquith. Today it's all eye if the tiger and working 70 hour weeks and doing triathlons to wind down. At least that's the public narrative, not sure what the Murdoch's are like at cocktail parties.
If you drive down wages and increase profits, in what sense haven't you increased the productivity of capital?
In the sense that you haven't actually improved the way the company goes about making stuff.
Suppose Widget Co. makes a million widgets a year and sells each for a dollar. Lets say further that they were able to make 250,000 of those widgets because they bought a new widget making machine with money from investors. Then the marginal productivity of the capital is 250 grand. That doesn't change if you are able to use near-slave labor and raise profits to 50%. The investors may be paid 500K, but they still only contributed 250K to production.
Isn't the productivity of capital measured by the profit generated per dollar of capital invested? That's how I would think of it, but I probably shouldn't be commenting since I haven't followed prior threads or read the book.
Using my definition, though, in your example, if the wage reductions were demanded by the investors, then the capital generated more than $250k in additional profit. It generated $250k from increased output and some additional amount through lowered wages.
7: If you assume not just equilibrium, but also the existence of an economy-wide production function, which tells us what GDP should be as a function of total labor input and total capital stock, then you can define a marginal productivity of both labor and capital. Multiply the amount of labor by its marginal product and you have the total income of labor, likewise for capital. If the aggregate production function takes a particularly simple form ("Cobb-Douglas"), the ratio of labor income to capital income simplifies and is just the ratio of their productivities.
This is of course assuming away bargaining, and so force and fraud.
Of course, it's been known since approximately forever that there is no reason in theory to assume there is an economy-wide aggregate production function, even if you start from pure neoclassical microeconomics (easier explanation; more technical one). It's been known for even longer that the supposed empirical evidence for Cobb-Douglas is rubbish (old demonstration, more recent review).
I don't think Piketty really needs any of this; you can read these bits as a for-the-sake-of-argument concession to orthodoxy.
16: To be fair to the marginal-product-Cobb-Douglas story, labor's share of income should have grown if and only if its marginal productivity grew faster than the marginal productivity of capital.
You always need someone to run the machine though. So the cost of the widget and therefore the return on capital always has a labour cost components. Unless robots/slaves.
Maybe some aren't, sure, maybe you can argue the income thus drawn has lost any connection with economic contribution, but they are working at a job?
Well my point is precisely that Bruce Wayne isn't working at his job as manager. He pays other people to do that work for him*. He's working at the (financially) uncompensated jobs of vigilante and playboy. Hilton seems to be that way too, but I'll be honest I haven't really paid much attention to her so maybe I'm being unfair.
* I realise this is pretty much the definition of manager. So much the worse for the definition, if that makes it fall on the labour side of the dichotomy.
For the Murdochs, they clearly do work for their pay, it's just no coincidence that they're (mostly) in positions of power in their father's company. I suppose I'm just wondering if some of the ostensibly surprisingly numerically smooth transition from feudalism to capitalism is a result of inheritance becoming about inheriting jobs rather than land.
23. Wherefore globalisation. As Helpy Chalk points out, they are in fact using slaves in some sectors. And robots in others. Ultimately the robots need human control, but far fewer humans than the old production line did.
21: Isn't the productivity of capital measured by the profit generated per dollar of capital invested
No, it's the extra output produced per extra dollar invested --- not the extra profit.
27 > 7? What then is the distinction, and does Piketty make it? The extra output must be measured at the price the product fetches on the market, surely.
22.last: Fair enough, I was sloppily conflating stagnant real wages with a declining labor share.
He's working at the (financially) uncompensated jobs of vigilante and playboy. Hilton seems to be that way too,
Wait, Paris Hilton is working as a vigilante? Does she have a costume and cool gadgets?
28: The definition of marginal product of capital is standard, I don't know if Piketty ever spells it out in the book.
The distinction might be clarified by a case like that in 7. Imagine a factor in Slightly Imaginary Scandanavian Social Democratic Utopia. For any given level of labor and capital inputs, it produces some outputs. Outputs are valued at market prices, defining marginal products. Because it's a SISDU, labor gets paid its marginal product.
Now build a copy of the factory in Tropical Hellhole X, with the same production function, but the workers crushed so they get paid next to nothing. (Or just very aware that the next-best job is being a starving peasant.) The marginal productivity of labor and capital haven't changed - you need the same amount of the inputs for a given level of output. At the same level of output, though, profit is much higher, and so is capital's share.
The usual economic assumptions, that every factor of production gets paid its marginal product, amounts to ruling out Tropical Hellhole X.
30. Fighting against shame and taste, sure.
22. That first link (the only one I've read so far) is fantastic.
Chainsaw Al inspired Uncle Frank? I knew it was worth it to keep reading these summaries without reading the book.
I started enjoying the book again with this chapter. It feels much more concrete, and the points salient. Plus, more history!
38. Is that a waxwork or has she smeared her face with vaseline?
The Ackerman article in 22 is very enlightening.
The Ackerman article in 22 is very enlightening.
Agree. The two Jacobin articles -- that one and this one are the two best single journalistic pieces I've seen on the book.
I might have to buy the book to finish it. But I really do want a paperback. Also three weeks isn't a long time for me to catch up.
22: In one of the earlier chapters Piketty explicitly discussed why Cobb-Douglas was nonsense.
39, 40: Ackerman is good, but Suresh's piece is the best single thing I've seen on the strengths and weaknesses of Piketty.
I don't think Piketty really needs any of this; you can read these bits as a for-the-sake-of-argument concession to orthodoxy.
Thanks, Cosma, that helps things a bunch. I'm tempted to print up this comment and put it in my copy of the book to answer the question I wrote in the margin on this topic.
I am so far behind. Being on vacation has made things worse, not better. Piketty just isn't lying on the sun on the dock material.
32,42: He also explicitly assumes rate of return is equal to marginal product of capital in chapter six p215-216. He precedes it by a few pages discussing situations where r!= MPK including monopolies and the USSR.
I'm not really familiar enough to say confidently, but it seems like this nod to orthodoxy is quite useful for his overall argument. He can say capitalism, running in its usual, or even a fairly ideal way, produces widening inequality as a matter of course in many historical conditions. However, to critics of marginal prices, such as those on the left who hark back to Marx's labour theory of value, rent on capital is always squeezed from the blood of the workers, and not reflecting that in the model bakes capitalism in instead of showing alternatives. This is why they round back on the Cambridge capital controversy.
He precedes it by a few pages discussing situations where r!= MPK including monopolies and the USSR.
And yet so many monopolies. Or duopolies or triopolies or near as dammit. Small numbers of manufacturers and vendor who can make the market dance a bolero if they play the tune. If you want to buy a modern phone you can have Apple or Samsung or Apple or Samsung or Apple or Samsung or Apple or Samsung or one or two lesser beings which it's hard to buy stuff for. You can't go down to Mr and Mrs Sanchez' shop on the corner and ask them to knock you up a 4G phone in the back and you'll pick it up Friday. Apart from food at farmers' markets, what isn't an effective monopoly?
Yet the smartphone is only 10 years old. So of they are monopolies, or oligopolies, they are brief windows capitalizing on disruption, followed by obsolescence.
The other argument would be elasticity of substitution of goods and services. Yes, smartphones are basically a duopoly, but phone / data / music player services are available in many other ways, and this less direct competition provided pricing pressure.
I also think Piketty trying to put that in his model would be a pretty heavy burden for his research project to carry. Wouldn't he have to build or adopt a theory of monopolies, and a data set to show it was relevant? I'm sure that's worthwhile research, but how many paradigms to you expect person to shift at once?
If you want to buy a modern phone you can have Apple or Samsung or Apple or Samsung or Apple or Samsung or Apple or Samsung or one or two lesser beings which it's hard to buy stuff for
Smartphones are not a good example for this at all. You've got Apple, Samsung, HTC, Motorola, LG, Nokia, RIM/Blackberry, all on the shelves in your local Carphone Warehouse... and most of them use the Android OS which is dead easy to buy stuff for.
Wouldn't he have to build or adopt a theory of monopolies, and a data set to show it was relevant?
Yes he would. But his research project is already dedicated in part to the proposition that the assumptions prevailing in macro need to be rethought because they don't reflect the real world sufficiently accurately. It seems to me that the assumption that monopolistic distortions of the market can be hand waved away is one that needs to be rethought pretty early on, because the impact is fundamental. P. can write another book to address this, but he should at least put down a marker that he needs to.
49: I see your broader point. I have an HTC phone. But RIM is so dead.
51: Blackberries still alive and well in the corporate world. Good for another 3-5 years of pretty good rent at least I reckon.
The British civil service is currently replacing its blackberries. Dead phones walking.
This is the second or third hilarious example I've seen of how the British civil service is more dynamic and techno savvy than the multinational corporation that employs me.
I took 53 to mean replacing its Blackberries with newer Blackberries.
As in the fact that the British civil service is buying new blackberries is a clear symptom of its obsolescence?
I though 53 was supporting 52 by indicating another user of RIM phones.
No, something a bit more contemporary. Don't know why, they disable everything except calls, texts and email. They might as well use clam shells.
The British civil service is actually doing some groundbreaking shit with regard to IT these days. The e-Government framework that they are putting together with gov.uk is laying down the patterns that many of the other governments of the world will be copying in a few years time. Some solid public-sector innovation, that is.
Yeah, gov.uk was actually what I had in mind wrt dynamic and techno-savvy. It is genuinely cool. They have some good open data stuff too.
Given the state of public sector tech in other countries, its way ahead. Much better than the US, where somehow it seemed like a good idea for 50 individual states each to implement their own software for a health care exchange, because Federalism.
Gov.uk is brilliant because it integrates multiple levels of government, from the national level all the way down to the local level. As far as I know, no one else is doing that.
After all that waiting, I bought the book today. Discounted, at Costco.
46: Actually, in chapter 6, he argues that the equivalence follows from assuming perfect competition among capitalists. In the section "The Notion of Marginal Productivity of Capital," he gives an example of an agricultural society where 100 euros of additional land or tools produces an extra 5 euros per year of agricultural production (5% marginal productivity for capital), and then comments:
Under conditions of pure and perfect competition, this is the annual rate of return that the owner of capital (land or tools) should obtain from the agricultural laborer. If the owner seeks to obtain more than 5 percent, the laborer will rent land and tools from another capitalist. And if the laborer wants to pay less than 5 percent, then the land and tools will go to another laborer. Obviously, there can be situations in which the landlord is in a monopoly position when it comes to renting land and tools or purchasing labor ... in which case the owner of capital can impose a rate of return greater than the marginal productivity of his capital.
He then goes on to acknowledge that capital markets in more complex economies often fall short of the perfect ideal. It seems like he might be building up to an argument about the increasing concentration of capital creating more such distortions, but I haven't read far enough ahead to know if that's where he's going to go with this.
Still, the argument above is interesting, since we often think of the management of a firm as representing capital which then goes out and hires labor as needed. The above example argues that it could equally represent labor organizing together to negotiate for capital, which could be more representative of a startup, a sole proprietorship or partnership, or a co-op form of business.
I think there is still an aspect of bargaining theory that is being ignored here, though. If I understand the example correctly, the reason the capitalist can find a different laborer willing to pay more (up to 5%) for the extra land/tools is that it is still profitable for such a laborer to accept such a split. This discounts the possibility that all laborers will look at a capitalist offering tools at say 4% (80% of the marginal profit) and say "no, 80-20 is an unfair split" rather than "cool, an extra 1% profit for me."
It seems like he might be building up to an argument about the increasing concentration of capital creating more such distortions, but I haven't read far enough ahead to know if that's where he's going to go with this.
Nor have I, but it would be a major shortcoming if he doesn't. Even the mythical Econ 101 allows that much.
64.1: Actually, I've come up with an argument that under perfect competition, the marginal productivity of capital goods (with both it and output measured in monetary units) should always equal the discount rate. It's probably wrong but I've wasted a good part of the last few days trying to see the fallacy.
64.3 and also 65: It seems like he might be building up to an argument about the increasing concentration of capital creating more such distortions, but I haven't read far enough ahead to know if that's where he's going to go with this. It's certainly not a major part of where he goes later on, and in fact I don't think he goes there at all.
64.4: Thus Paul Samuelson: "Remember that in a perfectly competitive market, it really does not matter who hires whom; so have labor hire capital" --- quoted here by Bowles and Gintis, in a paper relevant to 64.last. (Actually lots of what Bowles & Gintis have done is relevant to 64.last.)
This seems vaguely to the point of Piketty's central thesis.
I always like it when Cosma's working on a grant.
Actually, I've come up with an argument that under perfect competition, the marginal productivity of capital goods (with both it and output measured in monetary units) should always equal the discount rate. It's probably wrong but I've wasted a good part of the last few days trying to see the fallacy.
Post the argument, I'd be curious to see it.
68: No grant, just five papers in need of revision, and otherwise in need of distraction.
69: Fine, here goes. Bear in mind that I am sure it contains an error somewhere, and pretty sure the error is idiotic.
1. Piketty measures capital in monetary units; in particular, everything is valued in current replacement prices, not in terms of what it historically cost to obtain.
2. If I own (or control) some firm and am trying to maximize profits, when will I increase my capital stock by some marginal amount, say $1? Clearly when the present value of the marginal increment to production this makes possible, m, is at least $1. Call the physical increment to my capital stock (tools, crucibles, workstations, factory space, chocolate-stirring robots) which I can purchase for $1, x.
3. If m > $1, then I would buy x physical units of capital and count myself very happy. But then I would have paid any price up to m, and the sellers of the capital goods could and should have raised their prices. Conversely, if m < $1, I will not buy x units of the good, and the price should fall.
4. I conclude that, in equilibrium, a marginal $1 of capital goods should always increase the PV of production by $1.
5. Assuming the extra capital good allows for the same increase in production in all periods and is infinitely lived, this means that $1 more capital increases production each period by $d, d being the discount rate.
6. Hence the marginal productivity of capital, dY/dK, should always be the discount rate d.
Step (5) allows for some variation in the marginal productivity if capital goods have finite useful lifespans.
I'm trying to adjust for multiple comparisons. I hate that because I never know where to stop counting.
When you get the right answer, obviously.
If m > $1, then I would buy x physical units of capital and count myself very happy. But then I would have paid any price up to m, and the sellers of the capital goods could and should have raised their prices. Conversely, if m
This only works if you assume that the sellers of capital good can engage in price discrimination. Imagine 5 buyers:
Buyer A: m=$1
Buyer B: m=$1.5
Buyer C: m=$1.5
Buyer D: m=$2
Buyer E: m=$3
The seller may price their product just under $1.5 to be able to sell to 4 buyers, and then buyers D & E make additional profit.
68 reminds me that I have about a week to invent some kind of marvelous, exciting new form of outreach that will make the government happy enough to deign to pay half of a postdoc's salary.
76: high-energy physics modeling library for Scratch! Simulaitionmobile that you can drive around to underprivileged neighborhoods and let kids come up with their own solutions for field equations! A whirling disk of matter that occasionally causes a giant rock to hit the plastic dinosaur outside of the science museum! A special series of Keynote presentations that kids can make into custom gifs!
71: Is Piketty claiming equilibrium? 75 seems like one example where it has not been reached, but I'm not sure of the full technical implications of the term.
61 - At a previous job I (among other things) wrote the domain name application system for the .gov TLD. Man alive, I hope things have improved in that regard in the last ten years.
Cosma, I don't think anything is glaringly wrong with your logic. A Google search of "interest rate marginal product capital" seems to turn up this idea that there's an issue with casually converting between capital and consumer goods (I think, I could be badly misunderstanding something). The length of this discussion (part 1 of 4)suggests that there isn't a 1-sentence rebuttal to your Econ 101 argument.
Cosma, I don't think anything is glaringly wrong with your logic. A Google search of "interest rate marginal product capital" seems to turn up this idea that there's an issue with casually converting between capital and consumer goods (I think, I could be badly misunderstanding something). The length of this discussion (part 1 of 4)suggests that there isn't a 1-sentence rebuttal to your Econ 101 argument.
75: I think then D and E should keep buying capital goods, until m falls to $1. (This presumes that the returns to physical capital are eventually decreasing. If it was constant or increasing, I'd need to do some actual work to see if there was an equilibrium.)
I think then D and E should keep buying capital goods, until m falls to $1.
Hmmm, I understand the theory, but I think there are obvious reasons why that won't work.
But, really, let me step back for a moment before trying a longer response. I'm just making the standard argument about consumer surplus, and trying to apply it to consumers of capital good. Consider Brad Delong's summary
In a standard economic transaction it is no mystery where the value to both sides comes from. When I buy a double espresso from Café Nefeli for $2.25, the coffee is more valuabe to me then $2.25 is. Were I to consider only the experience and not worry about fairness consideration--that is, if I did not worry about thinking that I was turning into a chump--I would pay $5.00 for a double espresso (if Café Nefeli were the only possible place I could get one and if that is what they charged) and count myself happy. And sometimes $10.00.
He does not then conclude that he could continue buying espresso until he reaches a point at which the value is only $2.25. He stops buying once his coffee needs are satisfied. I think a lot of capital goods are like that -- if you need one corporate headquarters, there isn't much reason to build two just because you got a good deal on the first one.
83: Well, consumers are also subject to a budget constraint. The standard theory is that you are supposed to keep buying more of everything until you hit your budget constraint, and then move along the consumption frontier so that the last, marginal dollar you spend on anything gives you just as much utility as the last, marginal dollar you spend on anything else. (If the marginal dollar of espresso gave you more micro-skinners than the marginal dollar on yoga instruction, you'd be happier drinking a bit more espresso and learning a bit less yoga.)
Whereas a firm that buys more inputs, produces more, and sells it, has actually come out with more money than before. If the second head-quarters really would lead to an increase in production over the cost of the headquarters, the profit-maximizing firm should build it. It should buy more of all inputs until marginal products equal marginal costs on all dimensions.
4 is true, but I don't think 5 follows. 4 hold under rational expectations when markets clear. 5 would hold for a no-growth economy where you are exactly at the steady state. You would have to be born there, though, since if you're not at the steady state the optimal path is to converge towards it but you don't reach it in finite time. (It does hold in the limit, though.)
(The formal model is the Ramsey-Cass-Koopmans model.)
85: How does (5) not follow from (4) and the definition of present value?
Wait, by discount rate do you mean the short-term interest rate? Then yes, they're always equal.
(I was thinking you meant the amount you discount future utility versus today, though future cash flows makes more sense given the context.)
87: Yes. (Discounting utility would mean imposing a utility function for money.)
You can axiomatize time-separate utility, a la the state-separable utility of von Neumann-Morganstern. Then you can compare utility at one time with utility at another time.