Monoposonistic Labor Markets, Minimum Wages and Employment - the Laffer Curve of Leftist Economics?
After having written this I realize that I think that the Laffer curve is still crazier of the two.
The Laffer Curve, of course is the idea that the relationship between tax revenue and the tax rate is reverse-u shaped, with end points at 0 and 1. If tax rate is 0, then there's no tax revenue. If the tax rate is 1 (100%) then no one wants to work (legally) and hence no revenue is collected. This leads to the conclusion that there is some "optimal" tax rate between 0 and 1 which will maximize tax revenues, and as a corollary, that if the current tax rates are higher than that then cutting taxes can actually INCREASE tax revenue. This is used by some on the crazy right as an argument that "tax cuts pay for themselves". However, even though the theory is sound and all, there's little to no indication that there are actual economies which have tax rates high enough so that cutting them would result in revenue increases. Maybe Sweden in the 80's, maybe really rich people in the early 1960's US. Maybe. Bottom line is that most serious economists don't think the Laffer curve idea matters for all practical purposes - you cut tax rates, you get lower tax revenues. (There should be a caveat here about demand side vs. supply side effects of tax cuts which maybe I'll write about later).
What does this have to do with the debate on minimum wages, which pops up with regularity of a sinusoid function? Well these debates usually go something like this:
Econ 101 - Higher minimum wages lead to lower employment because they raise the price of labor and when you raise the price of something folks buy less of it.
HetEcon - Oh please. Show me the empirical evidence. Oh, and Card and Krueger.
(a short, abusive, impolite and snarky conversation ensues about Card and Krueger and the potential shortcoming of it as well as that of follow ups and other studies)
HetEcon - Anyway. MONOPSONY!
And it's true. If you have a Monosponistic labor market then higher minimum wages COULD increase employment.
Basically, in a competitive market the marginal cost curve coincides with the labor supply curve and at the end of the day wages are equal to the value of marginal product. Mathematically, if firms take wages as given, and if Q(L) is firm's output as a function of amount of labor it hires and p is the price it receives for its product then its profit is given by:
-w*L $)
Taking the first order condition we get
} {dL} = w $)
which is the usual 'nominal wage equals the value of marginal product'
All this implies is that if wages are set above the market wage then firms have to adjust their hiring so that the VMPL above matches the set minimum wage. How do you get VMPL to equal a higher wage rate? Well, if there's diminishing returns to labor, you hire less workers, so that the 'marginal worker's' product is higher than it would otherwise be.
However, if firms have wage-setting power (and this doesn't just mean that firms can choose wages. It means that their choice is not constrained by competition with other firms) then the profit is written as
-w(L)*L $)
where now the wage rate is a function of amount of labor hired, w(L), since a monopsonist faces an upward sloping labor supply curve.
The firms choose the amount of labor to maximize their profits which mathematically means that they set the derivative of p*Q(L) (marginal revenue product of labor) to the derivative of w(L)*L (marginal cost):
Dividing through by w, rearranging and setting
where epsilon is the elasticity of labor supply, we get
which is a standard 'mark up' equation (parallel to a similar one for a monopolist).
The graph below illustrates this.
In fact we can write monospony wages as a fraction of competitive wages - the wages that would prevail in a competitive market:
where w^M are wages in a monopsonistic market and w^C are wages in a competitive market.
Note however that the mere existence of monopsony power does not guarantee that higher minimum wages will always lead to higher employment (as should be intuitively freakin' obvious). In fact, there's a limited range over which employment increases with minimum wages - between the original monopsony wage and the competitive wage:
After that it's downhill again. In fact, what we get again, just as with the Laffer curve is a reverse-u shape. The graph below shows how employment varies with the minimum wage in a monosponistic market:
So only if the minimum wage is somewhere between the monopsony and the competitive wage can increasing minimum wages increase employment. However, all this so far is pretty good news for minimum wage advocates. Let's go back to the equation
'Standard' estimates of epsilon - the elasticity of labor supply - indicate that it is fairly small, mostly less than 1 (this however is subject of some controversy). Even taking epsilon to equal one you can set minimum wages up to twice that of monopsony wages and still get increases in employment. So if the monopsony wage for unskilled workers in US is, say, 5$, you could set the minimum wages up as high as 10$ and get away with it.
Of course, there's a problem. The situation described above is that of a true "company town" where there's only single employer (*cough* gobemen *cough*) and it's work for'em or starve. But if you think about most unskilled jobs there seems to be plenty of competition. Even a very small town usually has five or six fast food joints, video rental places, coffee shops, retailers as well as a big box store or two. It'd would be quite a stretch to argue that that each corner McDonald's is a monopsonist in the market for unskilled labor, just like the Burger King that's sitting right across the street from it. So we need to modify the above equation to something more realistic, something like "monopsonistic competition" (by parallel with 'monopolistic competition')
(note that all through out this post we're playing along with the idea that labor markets are characterized by monopsony power and only considering to what extent)
There is one strand in literature which points to 'search costs' as a source of monopsony power, even when there's lots of employers. Workers have to physically search for jobs, be matched with their employers, search is costly, and once you're hired quitting your job is costly since it'll take you some time to find your next job. Well, as a former member of the minimum wage fast food industry, I seriously doubt that search plays a big role in these kinds of jobs. Once I literally quit my job at a Burger King (without giving 2 wks notice I might add. A bit crappy, but the manager was a real schmucko which is why I quit), walked across the street to a Wendy's, filled out an application and started my first shift the very same day.
'Search' and 'matching' actually probably are far more important for highly skilled jobs where both the (relative to other markets) number of potential employers and the number of potential employees are small. Academic jobs are a good example. Medicine, law firms... all these are probably better candidates for this kind of monopsony than the industries actually affected by minimum wages.
(As a side note, let me be clear here. I don't mean to advocate any kind of minimum wages for academics. In fact I think a better model here is that of a double monopoly which means the distortions could off set each other).
But alright, alright. Can't we still have monopsony power even with lost of firms? Well, yeah. Here's the set up. Now the market wages depend not on the labor demanded by any one firm but all firms together. Say there's N firms in this market. An individual firm's profit function is then given by:
-L_i*w(\sum {L_j})$)
Taking derivatives with respect to L_i, setting it to zero and all that magic, we get:
So as not to get into all kinds of caveats let's just suppose that all firms have the same VMPL's (whether through productivity or prices or both). Then we can sum that sucker above over j and get
or
where now VMPL is sort of an average (across firms) value of the marginal product, and epsilon is the elasticity of TOTAL labor supply (rather than that faced by any one firm) with respect to wages. In effect, when moving from a 'company town' to a 'oligopsony' or 'monopsonistic competition' (that's the MC above) framework, the estimated elasticity of labor gets multiplied by the number of firms in the market. So now you can get convergence to competitive wages not just with a perfectly elastic labor supply curve (epsilon = infinity) (i.e. perfect competition) but also with a large number of firms in the market (N getting really large).
So now, if the monopsony wage is 5$, labor elasticity is 1 and there's 10 firms in the market (probably too low) then the maximum minimum wage which can be set without adverse effects on employment is 5.50$. With a, perhaps, more realistic labor elasticity of 1/2 it can go up to 6$.
Looking at it this way leaves very little room for minimum wages to increase employment, if at all, and even granting that labor markets are characterized by some amount of monopsony power.
So is this idea as bad as the Laffer curve? Probably not quite so much. One thing the minimum wage advocates might, just might, have on their side is 'standard' estimates of labor supply which are quite low (even though some folks argue that these are underestimated when using traditional methods. In fact I saw Edward Prescott start one of his lectures by saying "labor elasticity is 2". And there's other newer work which finds that that epsilon is much higher than previously thought).
But both ideas - the Laffer curve and the minimum-wages-raise-employment - are characterized by a lot of wishful thinking and a lot of unwarranted assumptions.
(and there are a couple studies, by Barro for example, which claim to have uncovered Laffer effects for some income groups in the 80's, which on the face of it are no more 'out there' than Card and Krueger).
(one other thing. The whole monopsony-as-reason-for-minimum-wage argument assumes that it's the market for unskilled labor which is most characterized by monopsony. But, as I partly indicated above, there's good many reasons to think that if you find monopsony somewhere, it's elsewhere. Which could, just could possibly be an argument for industry-specific minimum wages. And in fact, that's how them Europeans do it. But a general, blunt, un-targeted, federally mandated minimum wage law still wouldn't make much sense).
(I might have spelled monopsony as mono-s-pony above somewhere, since the spell checker don't know either one. Which is a market with only a single Equus Caballus, not a market with only one buyer. Sorry.)
The Laffer Curve, of course is the idea that the relationship between tax revenue and the tax rate is reverse-u shaped, with end points at 0 and 1. If tax rate is 0, then there's no tax revenue. If the tax rate is 1 (100%) then no one wants to work (legally) and hence no revenue is collected. This leads to the conclusion that there is some "optimal" tax rate between 0 and 1 which will maximize tax revenues, and as a corollary, that if the current tax rates are higher than that then cutting taxes can actually INCREASE tax revenue. This is used by some on the crazy right as an argument that "tax cuts pay for themselves". However, even though the theory is sound and all, there's little to no indication that there are actual economies which have tax rates high enough so that cutting them would result in revenue increases. Maybe Sweden in the 80's, maybe really rich people in the early 1960's US. Maybe. Bottom line is that most serious economists don't think the Laffer curve idea matters for all practical purposes - you cut tax rates, you get lower tax revenues. (There should be a caveat here about demand side vs. supply side effects of tax cuts which maybe I'll write about later).
What does this have to do with the debate on minimum wages, which pops up with regularity of a sinusoid function? Well these debates usually go something like this:
Econ 101 - Higher minimum wages lead to lower employment because they raise the price of labor and when you raise the price of something folks buy less of it.
HetEcon - Oh please. Show me the empirical evidence. Oh, and Card and Krueger.
(a short, abusive, impolite and snarky conversation ensues about Card and Krueger and the potential shortcoming of it as well as that of follow ups and other studies)
HetEcon - Anyway. MONOPSONY!
And it's true. If you have a Monosponistic labor market then higher minimum wages COULD increase employment.
Basically, in a competitive market the marginal cost curve coincides with the labor supply curve and at the end of the day wages are equal to the value of marginal product. Mathematically, if firms take wages as given, and if Q(L) is firm's output as a function of amount of labor it hires and p is the price it receives for its product then its profit is given by:
Taking the first order condition we get
which is the usual 'nominal wage equals the value of marginal product'
All this implies is that if wages are set above the market wage then firms have to adjust their hiring so that the VMPL above matches the set minimum wage. How do you get VMPL to equal a higher wage rate? Well, if there's diminishing returns to labor, you hire less workers, so that the 'marginal worker's' product is higher than it would otherwise be.
However, if firms have wage-setting power (and this doesn't just mean that firms can choose wages. It means that their choice is not constrained by competition with other firms) then the profit is written as
where now the wage rate is a function of amount of labor hired, w(L), since a monopsonist faces an upward sloping labor supply curve.
The firms choose the amount of labor to maximize their profits which mathematically means that they set the derivative of p*Q(L) (marginal revenue product of labor) to the derivative of w(L)*L (marginal cost):
Dividing through by w, rearranging and setting
where epsilon is the elasticity of labor supply, we get
which is a standard 'mark up' equation (parallel to a similar one for a monopolist).
The graph below illustrates this.
In fact we can write monospony wages as a fraction of competitive wages - the wages that would prevail in a competitive market:
where w^M are wages in a monopsonistic market and w^C are wages in a competitive market.
Note however that the mere existence of monopsony power does not guarantee that higher minimum wages will always lead to higher employment (as should be intuitively freakin' obvious). In fact, there's a limited range over which employment increases with minimum wages - between the original monopsony wage and the competitive wage:
After that it's downhill again. In fact, what we get again, just as with the Laffer curve is a reverse-u shape. The graph below shows how employment varies with the minimum wage in a monosponistic market:
So only if the minimum wage is somewhere between the monopsony and the competitive wage can increasing minimum wages increase employment. However, all this so far is pretty good news for minimum wage advocates. Let's go back to the equation
'Standard' estimates of epsilon - the elasticity of labor supply - indicate that it is fairly small, mostly less than 1 (this however is subject of some controversy). Even taking epsilon to equal one you can set minimum wages up to twice that of monopsony wages and still get increases in employment. So if the monopsony wage for unskilled workers in US is, say, 5$, you could set the minimum wages up as high as 10$ and get away with it.
Of course, there's a problem. The situation described above is that of a true "company town" where there's only single employer (*cough* gobemen *cough*) and it's work for'em or starve. But if you think about most unskilled jobs there seems to be plenty of competition. Even a very small town usually has five or six fast food joints, video rental places, coffee shops, retailers as well as a big box store or two. It'd would be quite a stretch to argue that that each corner McDonald's is a monopsonist in the market for unskilled labor, just like the Burger King that's sitting right across the street from it. So we need to modify the above equation to something more realistic, something like "monopsonistic competition" (by parallel with 'monopolistic competition')
(note that all through out this post we're playing along with the idea that labor markets are characterized by monopsony power and only considering to what extent)
There is one strand in literature which points to 'search costs' as a source of monopsony power, even when there's lots of employers. Workers have to physically search for jobs, be matched with their employers, search is costly, and once you're hired quitting your job is costly since it'll take you some time to find your next job. Well, as a former member of the minimum wage fast food industry, I seriously doubt that search plays a big role in these kinds of jobs. Once I literally quit my job at a Burger King (without giving 2 wks notice I might add. A bit crappy, but the manager was a real schmucko which is why I quit), walked across the street to a Wendy's, filled out an application and started my first shift the very same day.
'Search' and 'matching' actually probably are far more important for highly skilled jobs where both the (relative to other markets) number of potential employers and the number of potential employees are small. Academic jobs are a good example. Medicine, law firms... all these are probably better candidates for this kind of monopsony than the industries actually affected by minimum wages.
(As a side note, let me be clear here. I don't mean to advocate any kind of minimum wages for academics. In fact I think a better model here is that of a double monopoly which means the distortions could off set each other).
But alright, alright. Can't we still have monopsony power even with lost of firms? Well, yeah. Here's the set up. Now the market wages depend not on the labor demanded by any one firm but all firms together. Say there's N firms in this market. An individual firm's profit function is then given by:
Taking derivatives with respect to L_i, setting it to zero and all that magic, we get:
So as not to get into all kinds of caveats let's just suppose that all firms have the same VMPL's (whether through productivity or prices or both). Then we can sum that sucker above over j and get
or
where now VMPL is sort of an average (across firms) value of the marginal product, and epsilon is the elasticity of TOTAL labor supply (rather than that faced by any one firm) with respect to wages. In effect, when moving from a 'company town' to a 'oligopsony' or 'monopsonistic competition' (that's the MC above) framework, the estimated elasticity of labor gets multiplied by the number of firms in the market. So now you can get convergence to competitive wages not just with a perfectly elastic labor supply curve (epsilon = infinity) (i.e. perfect competition) but also with a large number of firms in the market (N getting really large).
So now, if the monopsony wage is 5$, labor elasticity is 1 and there's 10 firms in the market (probably too low) then the maximum minimum wage which can be set without adverse effects on employment is 5.50$. With a, perhaps, more realistic labor elasticity of 1/2 it can go up to 6$.
Looking at it this way leaves very little room for minimum wages to increase employment, if at all, and even granting that labor markets are characterized by some amount of monopsony power.
So is this idea as bad as the Laffer curve? Probably not quite so much. One thing the minimum wage advocates might, just might, have on their side is 'standard' estimates of labor supply which are quite low (even though some folks argue that these are underestimated when using traditional methods. In fact I saw Edward Prescott start one of his lectures by saying "labor elasticity is 2". And there's other newer work which finds that that epsilon is much higher than previously thought).
But both ideas - the Laffer curve and the minimum-wages-raise-employment - are characterized by a lot of wishful thinking and a lot of unwarranted assumptions.
(and there are a couple studies, by Barro for example, which claim to have uncovered Laffer effects for some income groups in the 80's, which on the face of it are no more 'out there' than Card and Krueger).
(one other thing. The whole monopsony-as-reason-for-minimum-wage argument assumes that it's the market for unskilled labor which is most characterized by monopsony. But, as I partly indicated above, there's good many reasons to think that if you find monopsony somewhere, it's elsewhere. Which could, just could possibly be an argument for industry-specific minimum wages. And in fact, that's how them Europeans do it. But a general, blunt, un-targeted, federally mandated minimum wage law still wouldn't make much sense).
(I might have spelled monopsony as mono-s-pony above somewhere, since the spell checker don't know either one. Which is a market with only a single Equus Caballus, not a market with only one buyer. Sorry.)
posted by YouNotSneaky! at 2:30 PM
60 Comments:
Extremely interesting and useful post as usual and very reasonable and valid points. Minor semantics point: shouldn't we call it a wage 'mark-down' (since that is what it is as e/(1+e)<1) -- analagous but the reverse of the monopolists 'mark-up'?
I am also curious to understand how labor supply elasticities are estimated in this context. The elasticity of supply that matters to the firm ought to depend on the market structure -- as your revised formula suggests (N*e rather than e enters the formula). But in practice do econometricians take the market structure into account in their estimates (it would seem they'd need to estimate as structural model), or are they just taking household-level estimates of labor supply response?
The latter would seem an underestimate. For instance even if every household supplied labor perfectly inelastically ('e'=0) we might expect the elasticity of supply faced by an individual firm to be positive since if burger king raises its wages it can expect a positive supply response as McDonalds and Wendy's workers quit their jobs and walk across the street as you did to to work at Burger King.
So I'm just curious to know where those 'e' estimates come from.
Yeah, but if you flip it and solve for price you get the standard "mark up over marginal cost" formula.
As far estimating labor supply elasticities - I'm a bit on the macro side of things so I'm not really sure how micro people do it. Of course, whatever the actual labor supply, a perfectly competitive firm will act as if it's facing a perfectly elastic supply (i.e. a wage taker) so I don't know how one goes about separating the market structure from the elasticity. Seems like you'd have to first assume a given market structure and then estimate it given that set up. Which means you could be off if the actual mkt structure is different than the one you assumed. I dunno, those crazy applied labor people should known though.
This comment has been removed by the author.
Oops! Never mind the previous comment. I can't do supply AND demand before 9 AM, it seems. :-)
Anyway, both with monopsonist and competitive markets, you're on the labor supply curve, i.e. all that want to work at that wage, do. With an out-there wage, you get unemployment. Maybe the difference is mostly semantic though.
Nah, it's an important point - we can estimate the elasticity of aggregate labor supply with panel or time series data but what matters in a monopsonistic market is the elasticity of labor supply facing an individual firm. At that point you've got to put some structure on the data - basically make a judgment call of what the actual market competition looks like.
I didn't mention it in the post, but the model presented there, where firms choose amount of labor they wish to hire, taking the hiring decisions of other firms as given, and being aware that the total amount of labor hired will determine the wage rate is a "Cournot" style model of imperfect competition. If instead firms actually set wages then you get the standard Bertrand result (assuming homogeneous firms and all that) that wages will converge to competitive levels even with only two employers in the labor market (i.e. even though there's only few employers, individually, they still face perfectly elastic labor supply curves). You can relax that by differentiating firms by work-environment, safety, or location (that's sort of how those search models generate the monopsony power result) and get something similar to the above.
Another thing I didn't go into is that in general the number of firms N, will be a function of the wage rate too, as well as some kinds of fixed cost of entry. So firms will enter until profits are down to zero (normal accounting profits). Then even with a minimum wage within the monopsony-competitive range (which would normally increase employment) there's two effects going in opposite directions. First there's the regular monospony reducing effect which tends to increase employment as in the model in the post. But second there is exit out of the industry so even though each firm hires more workers there's now fewer firms so overall employment can go down even within this range. In the end it ends up depending on labor supply elasticity again as well as the slope of the marginal product curve.
One of the commentators in the Cafe Hayek discussion (a pro min wage one), holymoly, pointed to a lit review paper by Bhaskar, Manning and To. Well, those guys also have a paper which explores this in detail.
The reference for the lit review paper is:
Bhaskar, Manning and To (J. Econ Perspectives, 2002, 16(2), 155-174. (http://www.ingentaconnect.com/content/aea/jep/2002/0000
I don't have the reference for the paper with exit and entry handy (i.e. I'm too lazy to look it up right now) but it's referenced in the JEP paper.
hmmm, deduct a couple of points for equivocation between "leftists" and "hetecon" there in your initial dialogue. Also, of course, that monopsony argument for a minimum wage isn't heterodox at all; it's neoclassical (I think that the usual argument by left wing American neoclassicals is that the stickiness is a result of health care arrangements rather than search costs btw).
The PEN-L view of the world with respect to minimum wages is, as far as I've seen, that profit rates are positive, that labour is hired as a result of a production function, not a demand function, that production functions are complicated and gnarly things which are often quite locally inelastic in labour, and therefore that the majority of the impact of a minimum wage is on profits rather than labour. (This was certainly the interpretation of the Card/Krueger piece the last time it came up, and IMO it makes sense as AFAICS a burger joint has to have the tills manned at lunchtime more or less no matter what).
Then there's the more interesting long run dynamic argument in which we can have a discussion about whether minimum wages incentivise substitution of capital for labour (presumed "bad for the workers") or the development of higher-valued-added industries (presumed "good for the workers"). But that's the heterodox debate, and as usual it is more interesting than this monopsony stuff.
Dsquare, what do you mean? -- The demand function for labor comes out straight from the maximization of the profit function w.r.t. factor quantities.
As for profits, the national accounts share says it all, doesn't it? And much of that is sweat capital and arbitrage, both of which are activities vital to a contemporary economy.
Elasticities make sense at the margin. You say you need people at the tills, but are those the marginal workers? Plus, you don't need people at the tills... cash-reading machines are common these days. :-)
Yet, indeed, your last point is the most interesting. Minimum wages do imply a redistribution from unemployed outsiders to well-positioned insiders.
P.S. From a lefty p.o.v., minimum wage makes little sense because it's peanuts, compared with other policy instruments. So, what's the deal?
It's an emotional issue, that gets dragged to extremes because people invested so much in it, in terms of image and rhetoric.
It does come down to one's estimate of the labor supply curve. You made an assumption, but I'm not sure we have sufficient evidence to know whether this assumption is a reasonable one. Incidentally, I made a similar argument over at Angrybear as to why the current minimum wage for America Samoa should not be increased. Such call me a Pelosi apologist.
Dsquare, what do you mean? -- The demand function for labor comes out straight from the maximization of the profit function w.r.t. factor quantities.
well in neoclassical economics it usually does, but that's the result of a number of important assumptions (which Radek would no doubt argue can be relaxed while staying within the neoclassical paradigm, but which are invariably relaxed outside it). Viz:
1. One of those inputs is "capital". Lots of people don't think that there is a meaningful aggregate measure of capital; this is the whole critique of the John Bates Clark marginal productivity theory and the general conclusion is that the critique is valid and the theory ain't.
2. Even if I spot you the inputs, each individual firm's maximisation program is a programming problem, not simply that of maximising a function. If labour is a slack variable at the optimal point, then there isn't a single demand-for-labour schedule for that firm, and there is no guarantee that this problem will disappear in aggregation.
My point about the burger bars is precisely that there aren't any marginal workers. Unless and until someone invents a burger-flipping machine or a customer-serving machine, then a rise in the minimum wage will either require you to close your burger bar down, or to more or less wear the increase. The option of keeping your burger bar open, but with fewer workers, doesn't really work unless your processes weren't optimised to begin with. So the question is one of how many firms in the economy have such low value-added that they would indeed close down as a response to introduction of a minimum wage. Empirical evidence seems to suggest "not many", or at least "not many, compared to the normal variation in the economic cycle".
This comment has been removed by the author.
Why are the CCCs relevant here? You can go as disaggregated as you want, where's the issue?
CCC is not *just* about aggregation. The point is that there is no natural unit of capital in the way that the man/hour is a natural unit of labour power. Because of this, you don't know how much capital there is in your production process unless you know the rate of profit. It follows pretty easily from this that you don't know the marginal product of labour except conditionally on a profit assumption. It is the height of bad manners to talk about reswitching on another man's blog, so I won't, but the possibility of reswitching rather dramatises this point; a heterodox economist would not in many cases admit the existence of a single labour demand schedule.
Given that for most businesses, especially in retail and services, wages are the biggest expense, theoretical counterexamples where firms are wage-insensitive are just that, theoretical oddities.
I don't believe this is what the empirical work shows.
Even the most obfuscated, perverse production processes that don't admit smooth functional representations there are maxima of sorts, with marginal conditions of sorts.
Yes, but "of sorts" here might not meam "of the right sorts that can form the basis of a labour demand schedule".
Sorry about that. I deleted my comments because I was unsure about what you mean, so I thought that it's best that I don't insist.
Anyway, there are natural units for shovels and office building space and so on.
I think I overstepped myself in claiming that linear programming problems don't have marginal conditions - you're clearly right that they do, even the slack factors (but the slack factors have zero marginal productivity).
I can't do the advanced math but: in everyday experience when the minimum wage is raised the first thing that happens on the price/demand graph is what would have happened anyway: the demand curve keeps creeping up nominally in step with consumers gradually getting their wages adjusted for inflation. Prices creep carefully along behind, so as not to alienate consumers.
The federally mandated minimum wage is so (objectively) low (it was $9.50/hr in 1968 when average income was half of today's) that I think you can assume intuitively a gigantic amount of monopsony at work.
The minimum wage is so low that it has effectively shipped minimum wage jobs out of the country (caused native born workers to no longer be employed at that wage level). When Bush I's minimum wage raise went through McDonalds was experiencing 70% employee turnover every 90 days. These days I see the same smiling Mexican faces behind fast food counters (also Chinese in San Francisco) year in and year out.
And want about redistribution of demand towards businesses that minimum wage earners might potentially patronize (if they could afford fast food!). Since Illinois minimum wage rose from $5.15 to $7.50/hr, business has picked up substantially in my neighborhood (also recently upgraded) Mac's -- the noticeable increase being very "third world".
Also since $7.50/hr arrived here, some native born workers actually started showing up behind the counter.
Even if a $10/hr minimum wage costs left some jobs behind, doubling the wages of those still on the job would be a huge boon for lower income families.
Raising the minimum wage from $206/wk to $500/wk would add all of 3.5% cost to GDP output (and presumably no more to inflation not counting other wages pushed up) -- the simplest, most effective anti-poverty (poverty ending program really) ever.
If we could somehow have predicted to Americans of 1968 that, by early 2007, 25% of our workforce would be earning less than LBJ's minimum wage, the only thing they could have imagined happening would have been a small nuclear war, multiple depressions or plagues. We would have to explain that average income doubled but that he race to the bottom can be just as catastrophic. It is time to begin seriously shoring up the bottom as much as possible (while considering instituting federally mandated sector-wide labor agreements or the (e.g., French) equivalent -- the OEDC standard for ending the race to the bottom; see http://ontodayspage.blogspot.com/2007/11/had-adam-smith-lived-to-see-1800s.html).
Dsquared,
It might be bad manners but I've been looking for a clear exposition.
Usually, all you can find online is "numerical examples" and comments about the "neoclassical parables" and the like. The literature assumes a familiarity with other literature and so on.
If someone is trying to find a *theoretical/formal/modeling* introduction to the several aspects of inter-temporal production, it turns out very hard, next to impossible.
Even Samuelson's A Summing Up is mostly numerical examples and it simply assume that people are familiar with a lot of terminology, Bohm-Bawerk, this long-run he's talking about, etc.
(Sorry, YNS!, about the off-topic message.)
Ay, you've guys been busy while I was sleeping. Also it's Thanksgiving here so I have food to eat and all that. Anyway.
Monopsony analysis might be squarely within the neoclassical tradition but these days it's mostly invoked by heterodox-type people. Like EPI or what not.
Also, backloading food into trucks, strictly speaking isn't nonconstant returns to scale but rather economies of scope. As long as we're nit picking each other.
And we're essentially talking about a single industry or a couple of them. So there's much less need for 'capital aggregation' or the problems associated with it. I'll tell you what a unit of capital is: a grill, two fryers, a soda machine, two registers, drive through equipment and a mop. That's pretty much the standard "basket of capital" that a franchisee purchases from the mother corporation (there is some choice, size of grill and all that). So I think in this case we can definitely measure capital. The other part of your argument though I guess is that there's limited possibilities for substitution between capital and labor which would give rise to a downward sloping marginal product curve (and as I said before, as long as workers are homogeneous (which just means you're definining things accurately) you can always define something like a marginal product. Additional product or something.
Again drawing on my vast experience in the industry I think however that there are substitution possibilities. Maybe not between capital and labor (given a fairly standard package of fixed capital) but between labor and quality or labor and cleaniness. Either in a burger joint, there's lots of 'non-essential' task, like mopping. So minimum wage rises, you fire a workers but now have your remaining workers mop once every week rather than once every two days. Your "health safety" rating might go down. Or you have your remaining workers prepare more of the food ahead of time during slow times - so quality suffers. But of course that's what substitution is.
I'll try to answer more later.
You can always close (sooner) on Sundays or change from a 3-shifts schedule to a 2-shifts one. There are lots of ways in which you can reduce activity when wages are higher and those extra, slow Sunday afternoons are no longer profitable.
I'll tell you what a unit of capital is: a grill, two fryers, a soda machine, two registers, drive through equipment and a mop
I don't think defining some capital item of interest as the numeraire solves any of the Cambridge problems, because in order to define the marginal products you're still going to need to have some sort of commensurability between capital, labour and output. I suspect that the "additional product" concepts you're going to get out of the model you're suggesting here are going to end up with the marginal product of labour being either zero or the entire output of the bar, neither of which are particularly helpful for wage-setting.
Also, even with a fixed coefficients type of production technology without (or very limited) possibility of substitution this works in a similar way. In that case the marginal product curve will be constant up to some point and then discontinuously jump down to zero. So what will matter is where the supply and mc curves cross that thing. Generally the positive effect of min wages on employment is still bounded above at the competitive wage, except now, increasing min wages above competitive level will drive all the firms out of business causing a complete fall in employment. So I don't think this argument does much for the viability of min wages.
I think that's the normal case; that minimum wages in most cases have a zero or slightly negative effect on unemployment but are generally positive for "the working class" because a) they act as a poor-relation substitute for proper collective bargaining at the low end and b) they send out the message that Britain (etc) isn't really interested in being involved in low value-added activities.
Too much is made of marginal analysis by you economist lot - it's something that a few terms in business school could cure. I've been involved in a couple of decisions about shutting down operations and it was never marginal - it was always *really obvious* that that was what needed to be done. I have never seen (and don't think I've ever really heard of) a decision of that kind that could have gone the other way with a £1 an hour wage cut.
D^2, why do you insist that firms need to shutdown? That's the extreme case. The standard prediction is a reduction in activity (and employment).
Britain might not be interested, whatever that means, but what about the people who get fired because of it? They're interested, I presume.
What do you want to bargain? Profit's share in the NA is around 10% for the US, across administrations, over the last decades. Even in your wildest dreams, where you get an additional 5% to labor, is that worth the risk?
You told us your experience. Mine is from Romania and I can attest that social-democrat dreams of "collective bargaining" and "living wages" are far more unrealistic than marginal analysis.
Well, they have collective bargaining and living wages in Australia and Ireland too, so I think there may have been some other factors at work in Romania.
Profit's share in the NA is around 10% for the US, across administrations, over the last decades
nononooo. The national accounts include the government and overseas sectors. Doesn't it also subtract dividends and interest payments too? We're interested in factor shares here.
In this BIS paper it's more like 30% and rising; Sushil Wadwhani has 40% here.
http://www.bis.org/publ/work231.pdf?noframes=1
http://www.bankofengland.co.uk/publications/speeches/2000/speech103.pdf
Great post and comments. My macro students will read it next semester! Thanks-
don't you mean your micro students?
Dsquared, as far as I see, the paper you cite defined "profit's share" as 1 - wages, which is not what I have in mind. That way mixes up capital's share with pure profits.
As a first order approximation for the US, wages are 60%, capital services 30% and profits 10% (which includes sweat capital and other things we wouldn't identify with "pure profits") -- I'll be back with a reference.
Monopsony analysis might be squarely within the neoclassical tradition but these days it's mostly invoked by heterodox-type people. Like EPI or what not.
In 17 years at EPI (where I am no longer employed), I rarely if ever heard the word "monopsony" invoked in any context, let alone the minimum wage. If you search their web site for the word, you find it twice (once in a citation).
Notwithstanding youtoosneaky's Herculean exposition of monopsony and an undeniably interesting post & thread, it does not much apply to 'theLeft,' much less EPI. EPI's work on the topic is invariably empirical and does not make use of structural models.
-- the former MaxSpeak
I apologize for not responding. With thanksgiving travel and all I have limited internet access. So I'll let you guys sort it out.
Gabriel - I don't think we're in much disagreement on the numbers, just on whether we would call "capital's share" part of "profits" or not. The answer to that is going to depend on the application, but in this case I would say that capital share is up for negotiation in the same way that labour's is, so I'd be thinking about the 60/40 split.
I wonder if there is an adverse selection explanation of Card-Krueger -type results? If productivity increases with the wage for adverse selection reasons, might it not turn out that a minimum wage raises productivity (although not as much as it raises the wage- otherwise it would have been profit maximizing to pay a higher wage without a floor) enough that employment increases or stays the same?
In the US, factor shares have been 68% for "labor" and 32% for "capital" in the corporate sector, on average. It shows next to no long-run trend with big blips before and during WWII. There have been big low-frequency movements within "capital" (e.g. accounting profits up, nominal interest down, reflecting monetary policy). The accounting says nothing about whether these profits are accounting profits or economic rents; I take a labor matching-type view that it's something in between. (i.e. the fact that it's a return to investment so the asset-pricing relationships work out, but that it gets bargained over to at least a minimal degree, with lots of match-specific rents thrown in) The fact that it hasn't moved much in post-war US data despite large swings in minimum wages and union policy seems to tell us something though.
Another minor point that I've been trying to get a handle on. Based on my reading of it, the CCC implies that one can't aggregate _labor_ in an economically meaningful sense either. My grandmother can spend an hour baking cookies. I can spend an hour writing a paper. These are qualitatively different inputs. Just like capital can be very specialized, the same with labor. It's all a big index number problem that has no solution--basically we're trying to reduce a very high-dimensional problem into a lower-dimensional one. Is this a fair reading?
I do need to study the N.A. seriously at some point, but I distinctly remember Mankiw putting profits at ~10%, in his Intermediate textbook. Oh, well.
If perfect aggregation is your goal then you use Hicks' Aggregation Theorem: if some goods' prices change in equal proportion then there exists an aggregate good. There's also a result, by Diewert to the effect that small deviation from this lead to small deviations in the final result.-- But maybe this is not what you're aiming at. Hicks also has a restriction on the marginal rate of substitution for consumption goods to aggregate neatly.
Hi, great post.
I mentioned it on my blog:
http://tvhe.wordpress.com/2007/12/17/higher-minimum-wage-higher-employment/
I attempted to comment on how it might influence the firms choice of inputs in the long run without any maths. However it was a bit of a mess :)
This comment thread is long-dead, but I was interested in D2's arguments and have written some responses for my own benefit - so I thought I might as well stick them up here.
First on the idea that economists are too obsessed with marginalism. The standard argument is that even a small change will push somebody somewhere over the edge between hiring / not hiring or even closing down. The problem with what D2 is arguing here is, I think, if you want to argue that incremental changes in, say, the minimum wage do not effect anything because nobody is running a business where the decisions are that finely balanced, then you imply that so long as you raise the minimum wage in small increments, it never results in redundancies or closures. If you turn up the temperature slowly, nobody gets boiled.
On his other arguments: It seems perfectly sensible to suggest that some firms will take the hit (from a rise in the minimum wage) in profits rather than firing workers, and I'd be surprised if neo-classical models of imperfect competition didn't capture that effect somehow - but I'm not sure how much difference it makes to the basic argument - after all, at some point firms will decide they've taken enough of a hit as they want to, and start firing workers. It dampens the response, it does not eliminate it. I think it's also true that production functions are also often locally inelastic in labour, but unless all the firms in the economy happen to be locally inelastic around the current wage, you are still going to get marginal firms (whose production functions happen to be at a locally elastic point) who shed workers. What if firms (somehow) tend to gravitate to a state where their labour input is locally inelastic around the current wage? That just means that the minimum wage has to rise a greater distance before you get a meaningful short-run effect on employment - and when the critical elastic point is reached, the effect is likely to be more dramatic than the gradualist approach argued for by marginalists. Given that we do not know where the critical point of elasticity is, this argument does not entirely help those who would raise the minimum wage - it changes the shape of the risk. You could possibly argue for some form of gradualism - where raising the temperature slowly really does mean nobody gets boiled. Interesting to think about what proportion of modern Western economies are of a form where capital cannot be so easily substituted for labour (or off-shored?) and how that changes the response. It seems uncontroversial (to me) to think that the effect of raising the minimum wage depends on the level that it is being raise from; perhaps we are currently at a level where raising it does not make much difference to employment - hence we should raise it. And, while I'm not sure that debating the minutiae of running burger joints, are we so sure that larger outlets will not decide to shed some workers if the minimum wage rises, and tolerate longer queues?
Luis Enrique
Economics! Yay!
All hail Megan for resurrecting this zombie post.
I agree that small, nearly painless increments in wages will not push managers into shutting down. At least not until all of those small increments accumulate, and some new MBA comes along and says "Holy crap, we need to invest in some automation and we'll save 35% on our labor costs with an 18 month ROI"
And then the jobs go away.
Or the MBA comes along and says "Holy crap, we're barely making any money at those stores, we need to increase our prices."
Or the MBA says "Holy crap, we're barely making money at these three stores because their labor costs are so high. We'd be better off selling the real estate."
And then the jobs go away.
Re: the "crazy" Laffer curve,
As a non-economist, perhaps I am missing some technicalities of the debate, but I always assumed the importance of the Laffer curve was simply that tax revenues are negatively convex. That a static/first-order analysis is wrong, and we know in what direction it is wrong. That a nominal X% tax rise will probably not increase revenues X%, but less than that; and that a nominal X% tax cut will probably not "cost" (in lost revenue) the full X%.
Do you honestly dispute these corollaries of the Laffer curve? If not, then perhaps you should admit it's not so "crazy".
Whether or not "tax cuts pay for themselves" strikes me as a red herring; sure, the easy assumption that we are somehow always and axiomatically on the down-slope side of the curve is silly. I don't know who exactly genuinely makes this ultrastrong claim (some politicians in clumsy speeches, I suppose). But the Laffer curve doesn't and shouldn't have to somehow prove that "tax cuts always pay for themselves" in order to be interesting and relevant. The negative-convexity itself is IMHO an important and seldom-grasped (by laypeople) point to get across. Overwrought claims about the "craziness" of "the Laffer curve", which make it sound as the curve itelf is somehow incorrect (when, as you say, it is fully correct!), whatever the intent, do little but muddy the waters.
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