The electorate votes for a public sector which it thinks is of a size such that the marginal product of labour in both private and public sector is the same. (For a definition of marginal product, see ** below).
I.e. we all want a public sector of a size such that shifting a small amount of labour from one sector to the other makes what we believe to be little difference to our overall well-being. Thus any argument on the relative merits of public and private sector JG must proceed on the basis that the marginal product of labour in both sectors is the same, before JG is set up.
Now if JG is created JUST in one sector (say the public sector), the marginal product of labour in that sector will decline to below that of the private sector: not what the electorate presumably wants. And this phenomenon is reinforced by the fact that public sector is not good at employing the less skilled.
Thus, if the rules governing how public and private sector employers hire JG labour are the same, GDP is maximised for a given total number of JG employees.
Existing employers versus “specially set up schemes”.
Let’s assume JG is confined to the public sector. There is then a choice between allocating JG employees to EXISTING public sector employers or creating what might be called “specially set up” schemes. The latter were more or less what the WPA in the 1930s consisted of.
The advantage is using EXISTING employers is that it largely disposes of a big problem that afflicts the whole JG idea, namely what might be called the “skill mix” problem.
This problem was referred to by Malcolm Sawyer in a paper on JG. See under the heading “Functional Finance and ELR” in his paper.
The skill mix problem is as follows. If unemployment is well above NAIRU, much the best way of bringing down unemployment is a straight rise in demand, not JG. Therefor the real niche for JG is in dealing with “at or below NAIRU” unemployment. (Incidentally, I’m using the acronym NAIRU in a very loose sense: if you prefer “natural level” or Bill Mitchell’s “inflation barrier” idea, that’s OK by me. I’ve never had much interest in the differences between these quite similar ideas.)
So let’s assume unemployment is at NAIRU. Of course no one knows with any great accuracy what level of unemployment corresponds to NAIRU. But that doesn’t matter: the purpose here is to set up a JG system which is perfect IN THEORY, and that’s worth doing. The real world is one big mess compared to the world of theory, and JG in the real world might be such a mess that it’s not worth implementing. But that’s another matter.
Getting back the skill mix problem, the big problem facing an economy at NAIRU is the difficulty employers have in finding the types of labour they want on each local labour market. Thus any “specially set up” JG scheme (which by definition gets its labour exclusively or almost exclusively from the ranks of the unemployed) will have a skewed labour force: in all probability it will be biased towards the less skilled.
However, that problem is ameliorated if JG people are allocated to EXISTING employers. To illustrate, an employer with what the employer regards as a perfect mix of different skills can probably cope with a few more less skilled people if the price is right – i.e. if those additional less skilled people get the JG subsidy.
** The Oxford Dictionary of Economics defines “Marginal product” as “the extra output that results from a small increase in an input….”. Thus the marginal product of labour in a particular firm or sector of the economy is the extra output obtained from employing one extra person (or person hour) in that firm or sector.
Afterthought (same day): John Carney also refers to the skill mix problem.