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
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