Bryan Caplan  

Answer for Question from My Last Ph.D. Micro Midterm

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Despite the lack of a consensus in the comments on the right answer to my micro midterm question, I maintain that there's just one right answer.  The key point - and the reason I emphasized the words virtually and before long - is that as consumption approaches satiation, workers reduce their hours of work to prevent themselves from actually reaching satiation.  More technically, as workers approach satiation, their labor supply curves start to "bend backwards."  The result is that rising labor demand stemming from rising productivity raises wages yet reduces employment.  From my answer key:

What happens:

Output: Output continues to rise slightly as labor productivity keeps going up, approaching but never reaching the satiation level.  If output hit satiation, people would stop working; but otherwise the tendency of greater productivity to raise output remains.

Employment and wages: Increasing labor productivity raises labor demand, and as workers approach satiation, their labor supply curve starts to bend backwards.  The result: Wages go up, but employment declines as satiated high-wage workers switch from labor to leisure.

Real Interest Rates: As the intertemporal GE consumption model at the end of the Week 2 notes explains, positive time preference (β<1) and growing income (g>0) guarantee a positive real interest rate.  Since the question says, "Labor productivity continues to improve," there is no reason to say that real interest rates rise; all we can say is that they remain positive.

Note: The question says "virtually satiated," not "completely satiated"; furthermore, nothing in the question suggests that consumers would remain satiated if there were a drastic fall in output.  It is incorrect, then, to claim that output and employment would fall to zero.  Even if this were so, though, wages would still go up, because in GE workers earn their marginal product. 

Furthermore, no matter what happens to output, there's no reason to think that real interest rates would fall.  If labor productivity is rising, workers who feel almost satiated today should expect to feel even more satiated next year, so interest rates would still be positive!

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The author at Pure Pedantry in a related article titled Interesting Comparison: Economics and Relativity writes:
    I caught this interesting sentence over at Marginal Revolution: as consumption approaches satiation, workers reduce their hours of work to prevent themselves from actually reaching satiation. More technically, as workers approach satiation, their labor... [Tracked on March 25, 2009 10:55 AM]
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Joe Marier writes:

What, you didn't include the opportunity cost of leisure time in the equation? I account for that in my deep psyche every day of my life!

Matt writes:

I didn't explain the why's, but sounds like I got it right on the first two.

I guess what you wanted was that as people near satiety, consumption growth will slow so that they never actually get there, just like prices rise on a declining stock so that it never actually runs out. You might say that the unsatisfied part of us is a source of utility, or at least of utility growth, and we don't want to lose that.


Zac writes:

I'm mostly satisfied with your answer. I assign myself 30% of available points. I agree I was in error to say real interest rates would fall.

I still wonder, though, about what sort of weird behaviors would emerge if people really thought they were almost "satiated" or could ever possibly be "satiated." I think people realize that no matter what they will always want more or something else. I think if they thought there was a bundle of goods that they could possibly have that would satiate them, and they almost had it, and would have it soon, they would sharply raise output in order to get it, and only then would their labor supply curve start to bend backwards (dramatically).

Philo writes:

You said not just that people were approaching satiation but that they would *reach* it (“before long”). Granting that, I maintain that it would be indeterminate what they would do then. By hypothesis they already have all the *leisure* they want, so they would not be motivated to switch from working to leisure. Rather, they would lose motivation altogether; they would cease to “act” in the ordinary sense.

Note that people want not merely present consumption but the assurance of future consumption. To be really “satiated” they would have to be absolutely certain of a fully satisfying supply of future consumption goods. Absolute certainty implies that the goods are expected to be available *without work*. (*Of course*, this is unrealistic.)

Mike Hammock writes:

What happens if consumers' preferences for leisure are also satiated?

Steve Roth writes:

Excellent question! I don't have time to take the full test, but consider this thought experiment:

During the next year, computer-driven nanotechnology delivers the means to turn a pile of dirt into 1,000 Christmas dinners--or anything else into anything else.

As a result, what currently requires 100 million people to produce suddenly requires only 100,000. (A thousandfold productivity increase.)

We know that humans' utility curve drops rapidly and starts getting very flat around $15K a year (maybe somewhat more, but...)

Only 100,000 people can provide all of today's high-utility goods. The other 99.9 million must compete in providing lower-utility goods.

The wage result, it seems, would be to increase wages for those 100,000 "high-value" workers, push the 99.9 million "low-value" workers into a lower wage scale, and hollow out the middle of mid-value workers.

Caveats and digressions abound. But I don't have time...

ryan yin writes:

Zac, I don't think he's saying interest rates aren't falling -- he's saying they're not negative. Consumption always grows, so interest rates are always above Beta, but interest collapses asymptotically to Beta.

Matt, it's not that you want to be unsatiated (by definition, you want more utility). This is just about diminishing returns; that last little increase in consumption is worth something, but not much, so every time you increase consumption a bit more, a little bit more leisure starts to look better. (But you're never satiated in leisure either -- you're asymptotically going to satiation in all goods, including leisure.)

RL writes:

BC says: "as consumption approaches satiation, workers reduce their hours of work to prevent themselves from actually reaching satiation."

This confuses (me, at least). First, it implies workers want to avoid reaching satiation. Why would that be? Second, it implies that the decrease in labor hours is due to the workers (choosing to cut back) rather than the employers (cutting them back), when I would have guessed that the hypothesized continued increase in labor productivity would have been the cause of employers pushing to either let workers go or ask for cut-backs in hours worked. Finally, as stated it implies that workers make micro decisions--how much am I willing to work--on the basis of macro calculations--I want to maintain the economy at the point where consumer satiation is being approached but not reached. That doesn't seem to be how people make decisions.

Arare Litus writes:

"I maintain that there's just one right answer."

You should test this: get your peers to answer, and if there is wide variation you must give marks back to your students (even better, instill even more knowledge into them)

After answering I thought that there would be wide variation among economists.

Arare Litus writes:

"Increasing labor productivity raises labor demand"

Should this not lower labour demand? If total demand is projected to decrease/stagnate, and it is easier to meet the demand, will there not be less need for workers?

Zac writes:

@Arare- When output per worker increases, workers’ contributions to firm revenue increase causing demand for workers to increase. If your output is determined by some combination of labor and capital, if labor becomes more productive you want more labor compared to capital. If capital productivity were increasing, that is when there is less need for workers.

Greg writes:

Interesting question, but isn't it far enough from reality to recall the "assume you have a can opener" joke? The US has the highest consumption, but Americans also work the most. Even more interesting, richer Americans work more, in general. Or maybe it's a u-shaped curve, with many poor people working a lot at low-paying jobs.

So maybe I'm missing the point, which is to test economic thinking. But if the point is also to provide a scenario that illuminates real life, I don't think it works. In the US at least, I could picture a world where we all live in houses with platinum-encrusted walls and personal robots but continue to work our butts off.

Arare Litus writes:

"workers reduce their hours of work to prevent themselves from actually reaching satiation."

I find this questionable - many people actually enjoy working.

I would love another post regarding this, as I am finding it hard to believe that employment would not involuntarily fall - causing the virtual satiation condition, that we start with, to be broken, I also expect wages to fall, further breaking the satiation trend.

Lord writes:

Your answer fails because it makes assumptions about the current state that are unlikely to be true. First, output rises only if the current production levels are below satiation levels, but it is far more likely that levels would already exceed those levels as production is filling both current replacement and expansion levels. As production approaches the top of the S curve, there is far more likelihood production which was built to satisfy the rapid growth slope is now redundant. Your argument collapses after that. Most of your commentators did better, but the answer is really dependent on the path to stable equilibrium so no one answer is valid.

Tired writes:

Demand has a ceiling and productivity increases without limit. Eventually there is only one worker working one microsecond per eon. He doesn't care what wages are because he's buying from himself. Pundits bewail the "deflationary
pressures". Interest rates fall to the smallest number convenient to the accounting system.

If, on the other hand, productivity increases, but approaches a limit (sounds crazy, but not as crazy as the demand suppositon), you will terminate at a steady state economy. Interest rate will be zero -- why borrow when tomorrow will be the same as today?

ryan yin writes:

I think you have to remember the set-up to the question -- "People occasionally argue that Western consumers are virtually 'satiated.'" The point of the question is that you're supposed to assume for the sake of argument that's true (and then show that even if we're epsilon from satiation, we never get to satiation).
You're saying that labor supply curves do not, in point of fact, bend backwards -- that might be right, but that just means you're preemptively rejecting the claim that people are virtually satiated.

liberty writes:

I don't think your answer was better than some of the answers in the comments. I would also like to see what some of your colleagues would answer - especially if we could see a cross-section of Keynesians, Austrians and others.

Arare Litus writes:

Zac- "When output per worker increases, workers’ contributions to firm revenue increase causing demand for workers to increase."

But the condition is of plateuing demand, so there is no incentive to increase production - if you expect to make X wigets/year forever and the number of empolyees needed to do this falls, then the number of retained empolyees should fall. Is not increased demand of workers only a good assumption when you are in a scarce situation and demand is high, and where you must try to reduce your bottleneck condition? [Note: this is likely why unions could blossom - at one point semiskilled workers were the limiting factor, so it was worth throwing money at them; now skilled labours are worth more, so unions are not "worth it"].

I think that the underlying conditions mean that employment must fall, and thus wages as expectations are broken & competion begins.

The answer to this question is weird. The reason why I think your answer is weird is because you don't mention if this is a lifetime preference. Another reason is because in neoclassical microeconomics we are trained to think of things in equilibrium, whereas the agent you speak of never reaches equilibrium - as the representative agent "prevent[s] [itself] from actually reaching satiation."

Bryan, please comment on this!

Troy Camplin writes:

So I guess introducing unstated variables into the equation isn't a valid approach? I suspected not, but decided to be a smart-aleck and introduce them anyway, since in the real world, even if people began to approach satiation, something new would be introduced, and people would want that. One could also raise the question of what if you had people who liked to work, and therefore wouldn't want to have more leisure? And what if their leisure produced something? What, then, do we mean by 'leisure'? I write plays and do scholarly work. I'm not being paid for doing them, so is that leisure activity? What will actually change in my life if I get an academic position that allows me to do these things and get paid to do them -- other than the fact that I will then be able to pay my bills for a change?

Michael Kolczynski writes:

Darn, I lost my notes from week 2.

I still need an answer Professor Caplan!

Maximum Liberty writes:

Perhaps I over-read the question, but these words -- ". . . before long, they will have everything they want. Assume this claim is correct . . . ." -- meant to me that, in the very near future, people have everything they want. So I analyzed it from that perspective, completely ignoring the period of time before they reached satiation. I suspect that means I would have gotten half credit at best.

I'd have assumed that the question meant that, even at satiation, people would have to continue working in order to replace things that wear out and to continue buying services that are provided for set periods of time. That is, I assumed a stagnant level of consumption, not that consumption stopped.

I think that means that the labor supply curve bends backwards, but labor supplied never gets to zero. Wouldn't it be unit elastic? The total wages earned would be stagnant and the wage rate would rise, so labor supplied must fall by exactly the right amount to cause total wages to remain unchanged.

I think it also means that output as such stagnates; improved labor productivity goes entirely to additional leisure. Unless you count additional leisure as output, then g=0 but beta is still greater than 1, so interest rates are still positive.


Lord writes:

Another problem is leisure is assumed to be an unalloyed good, but it is as likely as anything else to become satiated meaning at least some people will work even if they have no desire or need to spend. This in combination with little to no expansion needs would lead to falling interest rates.

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