Partial vs General equilibrium lumps of labour

Does an increase in productivity cause labour demand to increase or decrease?

The answer to that question, and how we go about answering it, depends on whether we are talking about one small sector of the economy (partial equilibrium), or the economy as a whole (general equilibrium). (I was doing general equilibrium in my previous post).

If you start with the answer for one small sector, and just add it up across all sectors, you get into a total mess. That's the Fallacy of Composition. What's true for each of the parts isn't necessarily true for the whole.

Let's simplify massively. Ignore land and capital. Labour is the only factor of production. And let's assume all labour is identical. And let's assume constant returns to scale, so if you double labour employed you double output produced. That lets us focus all our attention on the difference between partial and general equilibrium, and ignore everything else that might complicate the story.

Suppose apples are a very small part of the economy. Suppose a new invention doubles the productivity of apple producers. What happens to employment of apple producers?

When the cost of producing an apple halves, the price of an apple will also halve. That's true under perfect competition. (It's also true under monopoly, and monopolistic competition, if we assume the elasticity of demand for apples is constant.) If the price of an apple halves, the quantity of apples demanded will increase.

If the elasticity of demand for apples is greater than one, the quantity of apples demanded will more than double when the price halves. So the demand for labour to produce apples will increase when productivity doubles.

If the elasticity of demand for apples is less than one, the quantity of apples demanded will less than double when the price halves. So the demand for labour to produce apples will decrease when productivity doubles.

That's the answer to the partial equilibrium question. It's simple. But did you notice all the implicit assumptions I slipped in there?

I assumed wages stayed the same, when I asserted the cost of producing apples would halve. But if the price of apples halves, workers' cost of living falls slightly, so they should be willing to supply the same amount of labour at a slightly lower wage.

I assumed the prices of other goods stayed the same, when I talked about the effect of a fall in the price of apples on the quantity of apples demanded. But if wages fall, because all workers can now buy cheaper apples, the price of other goods might change too.

I also assumed incomes stayed the same, when I talked about the effect of a fall in the price of apples on the quantity of apples demanded. But if wages and prices are all changing, because apple productivity has doubled, and if employment might be changing too, it is very unlikely that real income would stay the same.

All my implicit assumptions are likely to be false. The things I assumed constant will probably all be changed by a doubling of apple productivity. But if apples are only a very small part of the total economy, the effects of a doubling in apple productivity on economy-wide wages, prices, and incomes will be very small. It's OK to ignore them.

But you obviously can't ignore those things if you are talking about a doubling of productivity across the whole economy.

In the partial equilibrium experiment, what was driving the results was a decrease in the price of apples relative to other goods, which caused an increase in the quantity of apples demanded relative to other goods. That won't happen at all if the productivity of producing everything doubles. Because the price of everything will halve relative to wages. So all the analysis in the partial equilibrium experiment is totally useless in the general equilibrium experiment.

And it's all the things I ignored, in the partial equilibrium experiment, that become the only things that matter in the general equilibrium experiment.

Throw away the partial equilibrium analysis. It's not just wrong; it's totally useless for the general equilibrium experiment. Start from scratch.

The productivity of labour doubles for everything. Relative to (hourly) wages, the cost of producing everything halves. And so the price of everything halves relative to wages. Or wages double relative to prices. Same thing. Real wages, which represent the amount of goods you can buy with an hour's labour, must double. (Remember, I assumed labour is the only factor of production, so there's no capital or labour income to worry about. And if that bugs you too much, just read "labour" as shorthand for "labour, capital and land", and "wages" as shorthand for "wages, capital rentals, and land rentals".)

Output per unit of employment has doubled. Will output double, and employment stay the same? Will employment halve, and output stay the same? Will it be a bit of both? That depends.

"Maybe people can't afford to buy twice as much stuff?" That argument is totally wrong. We get our incomes from producing and selling goods. If the value of goods bought doubles, the value of goods sold doubles, and income from goods sold doubles too.

"But can we all co-ordinate on the new equilibrium where we all buy twice as much stuff and all have twice as much income?" That argument has a point. It's not totally wrong. For example, if each of us wants to save part of any increased income by hoarding money, rather than spending it, we will not co-ordinate on the new equilibrium. Output will stay the same, and there will be a 50% unemployment rate. The policy solution is to (approximately) double the money supply, so people hold twice as much money in their pockets, and will be willing to spend all their income, rather than hoard money, when income doubles. (Or, if all prices halve, the value of the existing stock of money could double that way instead).

"But maybe people just don't want twice as much consumption?" OK, that's entirely possible. Let's take the extreme case, and assume that people just don't want any more stuff at all, even if it were free. So firms, in aggregate, are simply unable to sell any more stuff. "Oh my God! Doesn't that mean there will be 50% unemployment? Doesn't that mean we have to launch a big advertising campaign to dupe people into wanting to consume more stuff? Or else have mandatory work-sharing, where the government forces everyone to work half-time?"

No. If people don't want to consume any more stuff, why would they want to keep working the same amount and earn double the income than they want to spend? If they enjoy leisure, they wouldn't.

In the "nightmare scenario", where people just don't want to consume any more stuff, labour supply will halve, at the same time as the demand for labour halves. There is a 50% reduction in employment. But that's not the same as 50% unemployment. People simply choose to work only half as much as they did before. Each individual prefers to "spend" his extra riches on lesure, rather than on extra consumption. No worries.

But there is one scenario that does worry me a bit. Suppose people enjoy working. Not for the extra consumption that the extra income can buy, but simply because they enjoy doing something they think is useful. And they hoard their money income, simply because they can't think of anything they want to buy with it, but don't want to stop working. And money is no longer merely a convenient medium of exchange, but a signal of how useful and productive a member of society the holder is. A bit science-fictiony perhaps. But I can't rule it out on theoretical grounds. The demand for money might be unbounded.

Comments

[Sandwichman]

"That depends." Truer words never spoken!

Nick, Nicely framed. This looks very much like it's going into Luigi Pasinetti territory. I'll elaborate this later, after work.

[Nick Rowe]

Thanks Sandwichman. I shared a house with Luigi for 6 months, many decades ago. Lovely man. Except he did tend to burn the toast every morning, and set off the smoke alarm! But we have very different theoretical perspectives.

[bill woolsey]

What are the wages earned by hunters?

I am sure it varies, but generally, the wages are negative. You pay to go hunting.

But isn't hunting a core economic activity of human beings for millenia? Why don't
we have mass unemployment of hunters?

Anyway, if people want to earn incomes because it proves that they are spending
their time in socially useful activities, but they really are not, then there
is a problem. I don't think money demand being unbounded really desribes the
problem.

By the way, even if there are some people who countinue to work and and accumulate
money and have no use for the money ever, and money is of the outside variety, then
a decrease in money prices and wages still raise the real balances of some people
who still face scarcity.

With inside money, you may need negative real interest rates. These people who
want to work and accumulate money will pay for holding money. People who face
scarcity could borrow and consume now. While they must pay it back later, they pay
back less. Those who want to work and have nothing to consume will pay for it. If
the interest rate is sufficiently negative, they won't be able to afford to work. It
is more clear if you imagine negative nominal interest rates.

Of course, earning income and giving it away to people who have some use for it solves the
problem nicely too.

[Nick Rowe]

Bill: I'm glad you brought up the hunting example. It's one I've thought about in the past.

You see, we *can't* hunt any more. Sure, we can go out into the wilds and shoot things, and eat them. But it's not really *hunting*. It's not what hunting used to be. Really, we are now just pretending to hunt. It's no longer a purposeful activity the way it used to be. It's now something we do for its own sake, rather than as a means to an end. But we (sometimes) *want* to do something that's a means to an end.

Societies fall apart when their customary means-end relationships fall apart. Like the idle children of the rich. It took the English aristocracy many generations to learn how to keep themselves out of trouble, when they didn't need to work, or fight the French. They eventually made fox hunting a ritual. Siegried Sassoon, Memoirs of a fox hunting man.

[Luis H Arroyo]

Nick, sorry, you confuse me.
Would not it be better to think in real terms? In 1990-2000 we had a prodigious decade thanks to innovations in computing. The prices of hardware & software fell steadily, and that reduced production costs of everything. Production costs fell in all sectors, and that increased production and employment.
Is not it an example of what you propose? GDP costs down, the real wage rises and (net) employment also; consumption rises, there is no hoarding of money.
I think it is easier to understand so than with your parable of apples.
Maybe I miss somthing? An increase of preference for saving?

[Lord]

The coordination problem seems to be much more difficult than anyone would have believed or we would not be where we are now. The pursuit of other policies is just the recognition of this and the damage that has been done in the interim due to this failure.

Money is power. The demand for that is unlimited.

[bill woolsey]

Lord:

The demand for something isn't the amount that people would accept as a gift.

The demand for money isn't how much money people wish they had or would take as a gift.

It is how much people want to hold, which means not spend now. It is not unlimited.

[CBBB]

I still don't believe most people can trade labour for leisure (unless they resign completely), except in the very long run. How long did it take western countries to get down to a 40 hour work week?

Also, what if the workers all have debt? Workers must work to pay down their debt so when productivity doubles, prices halve but the extra income is used to pay down debt not to buy the new output. Is this the same as the money-hoarding case?

I also don't think your final case is science fiction, and this would seem a good scenario in which to have forced retirement.

[Nick Rowe]

Luis: how do people respond when a productivity increase makes them richer, and increases their real wages? The income effect from increased productivity says there will be an increased demand for leisure. The substitution effect from increased real wages says there will be a reduced demand for leisure. The net effect could go either way.

Lord: the coordination problem (i.e. short run macroeconomic policy) can be difficult if there's a sudden big change in productivity. But most productivity changes for the economy as a whole happen slowly over time. Much easier to deal with. My thought-experiment of an overnight doubling of productivity across all sectors is purely hypothetical. Something like that would take 30 years.

"Money is power"? Nope. I really do mean money. You are talking about wealth.

CBBB: prices won't halve when productivity doubles. I didn't say that. What I did say was that prices halve *relative to wages*. More likely (unless monetary policy is bad) prices stay the same, and wages double.

"...but the extra income is used to pay down debt not to buy the new output". Nope. That's a fallacy of composition. If one person is in debt, another person is in credit. For every $1 borrowed there's $1 lent.

There are many ways an individual can choose shorter hours, even if others don't want to change. But if *everybody* wants to change, (which is the macro thought-experiment we're looking at here) it's easy.

[CBBB]

You're right it's a fallacy of composition, but not so much if consumption tends to be driven by workers and creditors want to hold money.
You say increasing the money supply should solve the problem of people wanting to hold excess money, but in the United States the Federal Reserve has driven interest rates very low and still the demand for money is not satisfied.

[Luis H Arroyo]

yes, true

[Sandwichman]

"Does an increase in productivity cause labour demand to increase or decrease?"

Nick,

I've extracted passages from Chapter V of Pasinetti's Structural Change and Economic Growth that address your question in interestingly parallel, as well as theoretically different, ways to your brief sketch above. The comment machine here won't take my long comment so I've posted it at ecological headstand.

http://ecologicalheadstand.blogspot.com/2011/01/partial-vs-general-equilibrium-lumps-of.html

[Nick Rowe]

Sandwichman: what is Luigi's labour supply function? (there's not enough on Google books for me to find it). At the top of page 89, he suggests that the demand for existing goods may become surfeited. Suppose it does. Why should anybody *want* to work? How could workers have a surfeit of consumption, and involuntary unemployment at the same time?

This sounds exactly like the nightmare scenario I already addressed above.

Now if his/your answer is "because people want to save (rather than consume) part of their income", then OK, what's the savings function? Does savings (and investment) depend on the rate of interest? And why would people want to save, if they will be even more surfeited with consumption in the future?

[Sandwichman]

Nick, I'd also have to consult the book for his labour supply function. I read it about six years ago. I can say with some confidence, though, that it is pretty obviously not the labour-leisure trade-off model.

Why would anyone want to work once they have a surfeit of existing goods? Fear of unemployment or other unanticipated future hardship. Plus the fact that the labour market isn't structured so you can dial your hours of work up and down like a water faucet.

Workers can have a surfeit of consumption and unemployment at the same time because the ones who have the surfeit are not the ones who are unemployed and the ones who are employed are afraid of becoming unemployed, so they work longer hours than they need to for current consumption to "save for a rainy day". Why would defensive saving depend on the rate of interest?

From the employers' side there is a considerable wedge of per-employee costs that create a perverse incentive to resist hours reduction -- in addition to the competitive bias in favor of long hours that S.J. Chapman noted 100 years ago. Lars Osberg wrote about the artificial incentives for longer hours created by public policy in a 1997 advisory report to the Federal Minister of Labour.

[Too Much Fed]

"But there is one scenario that does worry me a bit. Suppose people enjoy working. Not for the extra consumption that the extra income can buy, but simply because they enjoy doing something they think is useful. And they hoard their money income, simply because they can't think of anything they want to buy with it, but don't want to stop working. And money is no longer merely a convenient medium of exchange, but a signal of how useful and productive a member of society the holder is. A bit science-fictiony perhaps. But I can't rule it out on theoretical grounds. The demand for money might be unbounded."

Sounds realistic, think Warren Buffett and others. Would that throw the retirement/leisure market out of balance?

[Too Much Fed]

"The policy solution is to (approximately) double the money supply, so people hold twice as much money in their pockets, and will be willing to spend all their income, rather than hoard money, when income doubles. (Or, if all prices halve, the value of the existing stock of money could double that way instead)."

So do you want to double currency or double the demand deposits created from currency denominated debt? From a budget perspective, it matters.

[Sandwichman]

See bottom of page 80 for Pasinetti's labour supply function.

[Sandwichman]

Nick,

Your question has started me thinking about "partial vs general equilibrium labor supply functions". I'll have to spend a bit more time working it out but the rough outline is that the canonical model assumes a proportional relationship between hours and income. However, individually, quasi-fixed costs would have the greatest impact on income, suggesting a more than proportionate decrease in income for any decrease in hours. Collectively, however, the Chapman theory of the hours of labour would suggest a less than proportionate decrease in income (in some cases an increase in income) for any decrease in hours.

[Nick Rowe]

Sandwichman: I had a look at the bottom of page 80. As far as I can tell, the supply of labour is exogenous. That's a big problem. Here's why:

Let me massively simplify Luigi's model.

Robinson Crusoe can catch 1 fish per hour. He wants to work for 8 hours per day (that's his labour supply function). He wants to eat 6 fish per day (that's his fish demand function, or consumption function). He really can't eat a 7th fish, because 6 fills him up.

Conclusion: Robinson Crusoe will suffer a 25% unemployment rate, due to deficient demand. To solve this economic problem, the government needs to step in and either impose a 6 hour day, or else tax him 2 fish a day which the government eats.

Which is an absurd conclusion, of course. But that's what happens when you specify a labour supply function and a consumption function independently. They need to be consistent.

[Lord]

What is true in the long run is not necessarily true in the short and what is true in normal times is not necessarily true in crisis. Wealth during normal times but liquidity during crisis. Solvency is not enough, and even enough to liquidate all debt may not if the option value becomes too great. In the long run and normal times this is moot and there is no reason to prefer liquidity other than option value.

[Nick Rowe]

Sandwhichman: Fixed costs. Yep, there are a lot of fixed costs. The simplest assumption is a production function like Y= a(L-b). Y is output, L is hours labour, and a and b are parameters. You have to work for b hours before you begin to produce anything at all.

b could be the time travelling to work. Or the time getting up to speed at work in the morning. The solution is to have a wage paid on L-b hours, but high enough to compensate the worker for the fixed costs. Or, insist the worker work a minimum s hour shift.

That's why we would see 3 days at 6 hours each rather than 6 days at 3 hours each. Labour supply and demand functions have a "lumpy" equilibrium. We don't work every third minute of every day. We take off evenings, weekends, a month's holiday, a year out, early retirement.

[Sandwichman]

"Which is an absurd conclusion, of course. But that's what happens when you specify a labour supply function and a consumption function independently. They need to be consistent."

Nick, Any abstraction will be more or less absurd if applied to purposes other than its intended one. In this case, Pasinetti was using the abstraction to demonstrate that the alleged choice between more consumption or more leisure is not a mere choice but a necessity, if unemployment is to be avoided. Given those results the income leisure choice model is no less absurd because its alleged consistency between labour supply and consumption is both tautological and based on a fallacy of composition.

But more on this later. I'm on my lunch break.

[Sergei]

Economy-wide productivity increases all the time. Does it mean we should ignore its effects on employment which is quite chaotic?

[Nick Rowe]

Sandwichman: As far as I can tell, there are no prices (wages, interest rates) in Luigi's model to which labour supply and goods demand could respond. Suppose we assume neither the supply nor the demand for apples depend on the price of apples. It's not surprising if we end up with either an excess supply or excess demand for apples. The role of prices is to coordinate the individuals' plans so that all plans are mutually inconsistent. If you simple *assume* that prices don't affect people's plans, then those plans will almost certainly be inconsistent.

[Sandwichman]

"As far as I can tell, there are no prices (wages, interest rates) in Luigi's model to which labour supply and goods demand could respond."

Nick, You've got to be kidding!

Section 9 of Chapter V is titled, "The dynamic movement of physical quantities and relative prices." So how do you suppose Luigi could discuss "the dynamic movement of relative prices" without prices? I'm waiting for my Marshall McLuhan moment. Luigi, where are you when I need you?

[Nick Rowe]

Sanwichman: sure, there are relative prices between the different goods produced. That's not the issue here. Does labour supply depend on the real wage, in some sort of consumption leisure choice? If not, you are straight back to my Robinson Crusoe example. There you don't need any relative prices, because the only good is fish.

[Too Much Fed]

Why are my posts deleted this time?

[Travis Fast]

No labour supply does not rely on the real wage (as in the real wage is not determinate of the level labour supply). It must be counter intuitive.

[Nick Rowe]

TMF: I unpublished your comments because they were cluttering up a good discussion. Too many comments, missing the point, rambling off in all directions.

Travis: why would people want to work longer hours if there were nothing they wanted to buy with their wages?

My view of (involuntary) unemployment is this: the unemployed want to work because they want to buy things with their wages. Firms won't hire them because the firms can't sell the stuff they can produce, and workers won't buy the stuff because they can't get hired. It's a Catch 22 coordination failure that causes unemployment. It's not caused by everybody already having everything they want.

[Travis Fast]

Let me clarify. And I will do so empirically because I really do not have much patience with mental experiments untethered from data. We know a couple of things empirically. During recessions wages in real terms decrease or stagnate but the labour supply initially increases then decreases. When the upswing moves into high gear labour supply increases with real wages. Historically we also know that in the case of the US lower real wages were tracked by increasing not decreasing participation rates (a robust twenty + year trend). So which is it the income or substitution effect? Theoretically you do not have any way to say whether income or substitution effects rule unless you break your labour supply functions up sociologically.

Nick you keep demanding that if it can't be put in work leisure terms it is just a dumb fish argument. Try a labour supply function where 60% of the workforce has no discretionary trade off to make both in terms of consumption and hours and the next 30% has varying degrees of a discretionary trade off to make but with no real capacity to choose their hours, and the last 10% with some.

Your imagined labour supply amounts to a homogeneous workforce that can both choose their income and leisure preferences. It just ain't so. Change your priors.

[Sandwichman]

We seem to be caught in some kind of a chicken/egg controversy, here, Nick.

In reply to your earlier questions. Yes, I interpret labour supply in the model as ultimately depending on "some sort" of consumption/leisure choice -- just not the same sort the customary automatic adjustment based on exogenous (and mysteriously prescient) preferences for consumption and leisure. Consider that we are dealing here with technical change and that a key element in income/leisure choice is the introduction of new kinds of goods.

Returning to your Robinson Crusoe example, R.C. wants to eat six fish per day and he can catch one fish per hour at time t. But at time t+n he can trade one fish a day for cell phone service that didn't exist at time t. Now he wants to work seven hours a day because with a cell phone, he won't be so isolated during those seven hours as he previously was during the six hours.

So how does the canonical labor/leisure model provide for Robinson's exogenous preferences for goods that didn't yet exist when his preferences were presumably formed (remember, they're exogenous)?

Meanwhile, back in the real world, I'm a shop steward and today I had two bargaining unit members approach me with issues about scheduling, namely management's presumption that it has the prerogative to override their time preferences. Contractually, in both cases management does in fact have the prerogative. Of course people can always quit and go elsewhere (where management also has the prerogative... and more so).

[Sandwichman]

"My view of (involuntary) unemployment is this: the unemployed want to work because they want to buy things with their wages. Firms won't hire them because the firms can't sell the stuff they can produce, and workers won't buy the stuff because they can't get hired. It's a Catch 22 coordination failure that causes unemployment. It's not caused by everybody already having everything they want."

Nick, I've read this paragraph over three times and I still can't find out how unemployment develops in your view of unemployment. How does unemployment go from 5% to 10% in your view of involuntary unemployment?

[Nick Rowe]

Sandwichman: on your last question, on how unemployment develops. Simplest story: Standard monetary disequilibrium story. Start in equilibrium, then suppose the demand for money increases (or supply decreases). Everybody stops spending money to try to increase the stock of money they hold. (This couldn't happen in a barter economy of course. The unemployed would just barter their labour for a share of the goods they produce.)

On Robinson Crusoe: Luigi says that there will be unemployment when people are satiated with existing goods, and maybe new goods could get them spending again. I'm saying that *even if* there are no new goods, there won't be unemployment.

The simplest way to introduce new goods into the utility function is just stick them in, with the price at infinity until somebody actually starts producing them.

[Sandwichman]

"The simplest way to introduce new goods into the utility function is just stick them in, with the price at infinity until somebody actually starts producing them."

Price at infinity? That's using price as a mere figure of speech. Why not just add epicycles?

[Nick Rowe]

Or just treat them the same way you would a rationed good, and set the ration at zero. Q=min{Qd,Qs} and in this case Qs=0.

[Sandwichman]

Nick,

Returning to your original question, two posts ago, how does your "standard monetary disequilibrium story" account for the American exceptionalism portrayed by the GDP and employment charts?

Here is Andrew Leonard's take on it:

"But none of these explanations gives a satisfying answer to the exceptionality question. Globalization and technological progress affect everyone, and presumably, there are crappy workers everywhere. We must look elsewhere for the difference that makes the U.S. special.

"How about this? In comparison to the rest of the G-7, the U.S. boast higher levels of income inequality, does a poorer job of educating its workforce, enjoys the double jeopardy of weaker labor unions and a sketchier social welfare net, and, at the government policy level, appears relatively more influenced by the financial sector than by Main Street."

Pasinetti's model is consistent with the explanation that policy differences are decisive.

[Nick Rowe]

Sandwichman: the monetary disequilibrium story is a story of why recessions happen. It says nothing about what happens to productivity in a recession. US exceptionalism is a separate question and puzzle.

I'm unconvinced by Andrew Leonard's explanation. All those things he talks about should cause lower productivity all the time. They wouldn't explain why productivity increases in a recession. And what about Spain, which was like the US in having procyclical productivity?

[Sandwichman]

So, one explanation for why recessions happen and another for US exceptionalism? I'll stick with Occam's razor. I'm not convinced by the "I'm not convinced" gambit. It takes a better explanation to defeat an explanation.

[Greg Ransom]

And then there is the time dimension.

What if people don't "horde" their money.

People will chose to lengthen production times only if they promise greater output.

Typically, with a larger cushion of wealth, people will chose to lengthen production processes in order to gain greater output.

So, when productivity increases, people will re-structure the TIME structure of the economy -- the capital structure of the economy.

This will have "macroeconomic" effects on interest rates, demand for money, labor coordination, and the relative demand for goods.

If you are going to go "micro" go for it ....

I won't hold my breath.

[Greg Ransom]

Did I really write "horde" for "hoard"? Heh!

[Greg Ransom]

Could have been worse ...

[Nick Rowe]

Greg: I was looking at that, and trying to figure out the correct spelling, wondering if I had it right!

Sure, and if there's a time-lengthening in production, interest rates will (almost certainly) need to change, to re-equilibrate savings and investment decision. Because desired savings and desired investment depend on the rate of interest.

But look, I'm still trying to get people to understand step one. In an economy where there are no investment opportunities. So the only choice is consumption/leisure. Forget about the present/future consumption choice. We can't all agree on walking yet. So forget about running. I'm trying to convince people that that the labour supply decision and the consumption demand decision are simultaneous.

[Travis Fast]

But that is exactly wrong. The labour supply function is not smooth. The consumption function might be. There is more than a monetized economy running amok here. I know you guys hate this but society and socio-economic gradations they really do exist. Seriously I did not invent them: they have been observed over a seriously large duration in time. Really it is true. Really.

[Sandwichman]

There is that one scenario that worries Nick a bit: "Suppose people enjoy working." This possibility calls into question the arbitrary definition of work as a "disutility" or opportunity cost. If there's nothing else one would rather be doing, there's no opportunity cost.

But that's not one scenario -- it's two. The income-leisure trade-off model incorporates two complementary assumptions, that work is a disutility and that leisure is a utility. But as Robert Prasch points out, leisure is not necessarily a utility for people earning a below-subsistence wage.

This is not merely to say that the marginal utility of leisure declines with declining income. Faced with hungry children, eviction notices and a blighted environment, time off work may be experienced as irksome to the extent that extremely low wages induce more the supply of more hours of work rather than fewer. This result is consistent with empirical observations of labour-market participation.

I don't think this is the whole story. I would also argue for a wedge effect occurring in the average income range and I still intend to follow up on that analysis.

[Nick Rowe]

Sandwichman: "The income-leisure trade-off model incorporates two complementary assumptions, that work is a disutility and that leisure is a utility."

Nope. If we define leisure as time not spent working, then by that definition MUleisure = minus MUwork. For people choosing hours to maximise utility given their real wage, MUleisure/MUconsumption = W/P. If W/P is positive, then MUleisure/MUconsumption must be positive. If MUconsumption is positive, then MUwork must be negative.

[Sandwichman]

Nope? You're saying leisure is not considered a normal good in the standard model? The meaning of P is supposed to be self evident?

[Victor Galis]

"But there is one scenario that does worry me a bit. Suppose people enjoy working. Not for the extra consumption that the extra income can buy, but simply because they enjoy doing something they think is useful. And they hoard their money income, simply because they can't think of anything they want to buy with it, but don't want to stop working. And money is no longer merely a convenient medium of exchange, but a signal of how useful and productive a member of society the holder is. A bit science-fictiony perhaps. But I can't rule it out on theoretical grounds. The demand for money might be unbounded."

Let me make that a little less science-fictiony: replace "Suppose people enjoy working." with some or all of the following:

-Suppose social norms demand that people work full time.
-Suppose overhead per employee scales with number of employees but not hours worked per employee, and is significant portion of the cost of labor. (Or any other story for why firms would rather retain fewer full-time workers than let workers cut their hours equally.) AND less than half the workforce wants to retire.
-Suppose wages don't scale perfectly linearly with hours worked. (Say benefits packages only to employees that work full-time, overtime paid at higher rates.) This makes very few workers willing to cut back their hours just a bit as there's a major discontinuity between 40 hours worked and 39.

I'm sure there's other reasons why workers wouldn't cut back despite their demand not keeping up with production that make sense in the real world.

[Nick Rowe]

Sorry Sandwichman. I should have been more clear. It's not "*two* complementary assumptions". It's only one. That's what I was saying "Nope" to.

[Sandwichman]

OK, fair enough, Nick. There's an identity between the 'two' so they are, in fact, a single assumption. What I was trying to get at, though, is that we can look at that identity from the 'irksome leisure' perspective as well as from the enjoyable work one.

[Sandwichman]

So, here is my attempt at explaining the hypothesis as a quasi-fixed cost wedge impeding substitution between hours of work and numbers of workers.

http://ecologicalheadstand.blogspot.com/2011/01/partial-vs-general-equilibrium-labor.html

[Sergei]

"If we define leisure as time not spent working"

What is sleeping time? Is it really leisure or is it an extra dimension?