### Minimum Logic

The question is often raised: “Why would you ever want to raise the minimum wage when you could raise the earned income tax credit instead?”. In other words, if you’ve got a choice between two ways to increase the effective wage rate, why would you choose the one that reduces employment over the one that increases employment?

Paul Krugman has an answer. He’s argued on numerous occasions that the EITC and the minimum wage are complements, not substitutes — that is, each makes the other more effective. So, according to Krugman, once you’ve raised the EITC, the case for a minimum wage hike becomes stronger, not weaker.

Here’s his argument: When you raise the EITC, more people enter the labor market. The increased supply of labor tends to drive wages down, which transfers some of the benefit from the workers you intended to help to the employers and/or consumers who you presumably care about less. To prevent this perverse consequence, one needs a hike in the minimum wage.

The other day, a colleague (who I’m not naming because I’m not sure whether he’d want to be quoted) pointed out that this argument makes not a shred of sense. Here’s why: Any effective minimum wage (that is, any minimum wage set above the wage rate that would prevail in an unregulated market) suffices to do the job Krugman wants it to do. At best, then, Krugman has made an argument for having some minimum wage, not a case for raising it.

Here’s the picture:

Suppose the minimum wage is set at \$5 an hour, just a hair above the unregulated equilibrium. Now we raise the EITC by the amount of the vertical blue line. Ordinarily, this EITC would drive the wage rate down to \$3 an hour. But the wage is not allowed to fall below \$5 an hour, so workers continue to earn that amount, plus the entire EITC. That is, they earn the amount at the top of the red line (which is the same length as the blue). Had the minimum wage been \$6 or \$7 or \$8 an hour instead of \$5 an hour, workers would have pocketed exactly the same 100% of the EITC.

Of course you might want to increase wages still further, and you can do this by increasing the minimum wage, but now you’re right back to the question: “Why would you ever want to raise the minimum wage when you could (further) raise the Earned Income Tax Credit instead?”

Because my sympathies are always with the underdog, I did my best to defend Krugman. Namely: the existing minimum wage of (let’s say) \$5 might be effective in some labor markets (where the unregulated equilibrium is \$4.50) but not in others (where the unregulated equilibrium is \$6). Krugman’s argument is (as shown above) invalid in the first market, but could still carry water in the second. So if you’re constrained to have a single minimum wage that applies to both markets, you might want to raise it to \$6.

Of course, even to make this work, you have to ignore a whole lot of economics, including this: If you increase the EITC in a market with an effective minimum wage, you’ll get a whole lot more workers competing for the same limited number of jobs, and this competition must continue until all of the benefits have either been dissipated or transferred to employers, who are now able to demand harder work and offer fewer perquisites. In other words, even if you go out of your way, as I have, to make sense of Krugman’s argument, you still end up with the same ironic bottom line: His stated goal is to prevent the benefits of the EITC from being transferred to employers, and to this end he proposes a policy whose certain effect is — to transfer the benefits of the EITC to employers. It’s almost enough to make you wonder whether he even bothers to give a minute’s thought to this stuff any more.

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#### 12 Responses to “Minimum Logic”

1. 1 1 Harold

There are two justification for a minimum wage that I can see. You believe either:
1) The market is efficient, but you want those at the bottom of the wage heap to have more. In this case, EITC would seem to offer advantages if combined with a minimum wage at the rate that would prevail in an unregulated market.

or
2) The market is not efficient, and the lowest wage earners are getting less than they should in an ideal market. In this case, the employers are the very people you would want to stick the costs to, and minimum wage is a better option.

I think a lot of non economists believe 2, so a minimum wage is very attractive.

The evidence that minimum wage does not have the impact on jobs that efficent markets predicts is not conclusive, but supports hypothesis 2.

2. 2 2 nobody.really

If you increase the EITC in a market with an effective minimum wage, you’ll get a whole lot more workers competing for the same limited number of jobs, and this competition must continue until all of the benefits have either been dissipated or transferred to employers, who are now able to demand harder work and offer fewer perquisites.

This is in the nature of price controls generally. If government says that you can’t charge more than \$X for a “car,” then we can expect that over time a “car” may decline in quality. If government says you can’t charge less than \$Y for an airline ticket between NY and LA, you may find airlines competing in terms of legroom or numbers of peanuts distributed or sexy flight attendants.

So if you say employers can’t discriminate by paying blacks less than whites, you may find employers accommodating their interest in racial discrimination by seeking to hire more whites. Wisely or not, this has not discouraged the US from adopting policies punishing firms that pay blacks less than whites. I surmise that eventually firms run out of qualified white candidates, and eventually stoop to hiring exceptionally well qualified black candidates.

Similarly, even if employers may initially respond to minimum wage laws/EITCs by demanding more productivity or eliminating perks, eventually they may find that they have no more productivity they can demand (within the limits of other constraints), and no more perks they can eliminate (ditto).

Recall that the minimum wage/EITC is intended to help workers with the least bargaining power. Presumably these employers are already demanding optimal levels of productivity, and providing optimal levels of perks, given their labor pool. True, the optimal levels (from the employer’s perspective) need not be the highest productivity or the lowest perks — but all else being equal, I’d expect things to tend in those directions. So, while I would expect employers to respond in the manner Landsburg suggests, it’s not obvious that they’d have a lot of room to maneuver here.

3. 3 3 Neil

I would add that if the minimum wage is binding, the EITC cannot increase employment. For the EITC to increase employment the employer’s wage must fall because the labor demand curve is downward sloping. If you want to increase both wages and employment, the minimum wage is counter-productive.

4. 4 4 travis

Given the logic that the EITC will drive job benefits down so that workers will be no better off (given a minimum wage or not given a minimum wage), what is the benefit of the EITC?

5. 5 5 Floccina

I agree with you about Paul Krugman’s reason but I think the real reason a smart economist like Paul Krugman would call for an increase in the minimum wage over the EITC is:

1. It is easier to get, because though it is a tax it is not so wide spread and hidden to most people.

2. You want to keep people to be under the illusion that they are not on welfare. Same reason for the bizarre structure of Social Security and FICA + matching FICA.
3. You want the owners of and management of (in the sort run) and customers of businesses who pay low wages to pay and not you. You might think of them as low class, cruel and rough people.

6. 6 6 Bennett Haselton

Can you link to an example of Krugman making this argument? I found a column from 2013 at
http://mobile.nytimes.com/2013/12/02/opinion/krugman-better-pay-now.html?referrer=
But it doesn’t make that specific argument in detail (that too much of the benefits of the EITC by itself will get transferred to employers)

7. 7 7 Bennett Haselton
8. 8 8 dave smith

Even more basic: layers of policies cannot change economic incidence.

9. 9 9 Bennett Haselton

I think there’s an error in the graph. If you combine the minimum wage with the EITC, the vertical placement of the red line is correct, but the horizontal placement (indicating quantity of labor) is misleading. Since the employer’s portion of the wage is \$5, the quantity of labor demanded would be determined by where the horizontal \$5 line meets the downward-sloping “D” line. That’s the amount of labor that actually gets performed (the lesser of quantity-supplied and quantity-demanded, which in this case is quantity-demanded), so the vertical red line should actually start at that point:
http://peacefire.org/new-eitc-graph.jpg
Would you say that’s correct?

Now you could also achieve the same wage rate purely by increasing the EITC. That’s the purple line I added to my graph. In that scenario, workers are earning the same wage they’d be earning in the min-wage-plus-EITC scenario, but there are a lot more of them earning that wage.

10. 10 10 Bennett Haselton

I made some new graphs showing the worker and employee surplus in the case of minimum-wage-plus-eitc, and in the case of eitc-only:
http://peacefire.org/minwage-and-eitc-versus-eitc.jpg

If my logic is correct, now you’re in a position to compare the two.

In both cases, the amount of the EITC subsidized by taxpayers is the EITC amount multiplied by quantity of labor performed, i.e. a rectangle whose width is quantity of labor performed, and whose height is the EITC amount.

So, comparing the second graph to the first, the amount of EITC billed to taxpayers looks about five or six times larger in the second graph (the rectangle would be about twice as wide and about three times as high).

The worker surplus, the dark-blue-enclosed region, is about 1.3 times as big in the second graph than in the first.

However, the employer surplus, the dark-green-enclosed region, is about 4 times as large.

So, in exchange for billing taxpayers about 6 times more, you’ve effectively increased the benefit to workers by about 1.3 times as much, while increasing the benefit to employers by about 4 times as much. This sounds like a plausible argument that the first scenario is more effective. Unless your top priority was to maximize the number of workers working at the higher wage, no matter what, in which case you’d prefer the second.

11. 11 11 khodge

I agree with #5 Floccina, point 3 with the further explanation that Prof. Krugman, an expert in business management, is familiar with the large pot of money called “profit” that each and every business has (sometimes at the bank, often times actually in a pot in the back office) that it is government’s responsibility to find, take away, and share with the rest of the country.

12. 12 12 Ken B

Like Travis in 4, I do not see why the argument does not apply even when there is an effective wage and the EITC is raised.

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