Kinked demand curves

What does the aggregate demand curve for labour look like? I ask because the evidence seems inconsistent.
On the one hand, the minimum wage seems to have had a small (that's small, not zero) effect in cutting demand for labour. This suggests demand is price-inelastic; a rise in price cuts it only slightly. The demand curve is steeply downward sloping.
On the other hand, quite big inflows of immigrants have only tiny effects on wages. A big rise in supply doesn't affect wages much. That suggests demand is quite elastic - the curve's flattish.   
So, which is it? It could be both. Maybe demand for low-skilled labour is price-inelastic but demand for average workers (immigrants) is more price-elastic. If so, the aggregate demand curve is kinked.
Casual empiricism lends credibility to this. Many low-skilled jobs are in industries like care homes, pubs or hairdressing, where offshoring or capital-labour substitution is diffcult. So demand for workers in these industries should be more price-inelastic than demand for other jobs.
But equally, casual empiricism suggests there might be more than one kink. You rarely hear of big-earning lawyer or chief executive jobs being offshored or replaced by technology (sadly).
So perhaps the demand curve for labour is inelastic at high and low wages, but elastic in the middle.
This raises at least three questions:
1. Could my optimistic view about the economic effect of immigration be wrong? Maybe if the labour supply curve shifts out far enough, it will cross the inflection point at which the demand curve becomes more inelastic. If so, further big immigration will cut wages a lot.
2. If the demand curve is (at least doubly) kinked, does macroeoconomic analysis of the labour market make sense? Jobs and workers differ in important respects, so why aggregate them? Feel free to throw in the backward-bending supply curve as an extra complication.
3. Does this help explain the apparent economic insecurity felt by much of middle England (and I guess middle America) despite a healthy macroeconomy? If labour demand is elastic in the range of wages that many people earn, then middle-income workers are vulnerable to supply or demand shocks, even if high and low earners are less so; this paper (pdf) by Dani Rodrik is a neat discussion of this. 

Comments

[dsquared]

could be that there is no demand curve for labour? yes I think it could.

[chris]

It's 20 years since I almost half-understood Sraffa - you don't really expect me to go back to him, do you?

[Bob B]

Could it be that migrants include a lot of non-competing groups?

A few years back I was exchanging what for me was an instructive series of emails in a web forum with a qualified psychiatrist and dedicated muslim who originally came from Afghanistan? I can't imagine him having much impact on the demand for minimum wage labour.

As for there being no demand curves, does anyone seriously imagine that the buyers in the supermarket chains think that way and make shelf-price decisions accordingly?

[dearieme]

"aggregate demand curve for labour": what if the "curve" is subject to hysteresis, with one limb applying in good times and the other in bad? I wouldn't be surprised if the minimum wage has done pretty modest damage during the latter years of the Lamont Recovery, as we surely ought to call it, but will do dreadful damage when next we are in, and trying to recover from, recession, the Brown Bust.

[Bob B]

Something in the press a little while back reported that the minimum wage had been rising faster than average earnings and suggested that it is only now starting to bite. As reported, one sign of this was that wage differentials at the bottom of the earnings spectrum are starting to be compressed - which reduces the incentive to gain skills.

If supermarket buyers don't have much understanding of Sraffa, my guess is that they do have an intuitive appreciation of the principles of Ramsey pricing - according to which mark-ups relate to the inverse of the price electicity of demand.