Let the utility of the i^th able-bodied citizen be

where w_i � 0 is weekly income, 0 � l_i � 168 leisure time per week in hours (I could equally well have taken labour time, but this would put me at odds with conventional labour market models). 0 � y _i � 1 measures i's preference for working ("labour preference", that is the satisfaction of the activity of working, irrespective of its remuneration).

Now, in Eu, the wage equation is

where h_i = 168-l_i is the number of i's working hours per week, w* the gross wage per hour of the job (usually unequal to the net wage, that is the wage after deduction of coupon cost), p_c the price per hour of a (part of a) Labour Right that gives you the right to work one hour a week (say during a year), and c* is the number of such coupons that every able adult citizen in Eu receives, say, every year.

Maximizing u_i after substition of the wage equations yields:

(Able adult citizens will supply more labour if the wage rate of jobs increases.)

(Able adult citizens will supply less labour if faced with increased coupon price.)

(Usually if an able-bodied adult citizen experiences an increase of her own labour preference, she will supply more labour.)

If we aggregate these findings to the market where all i's come together, the labour bank (if sensibly managed), controls c* in such a way that

where N (i=1, ..., N) is the number of able-bodied adult citizens and A* the number of "jobs" (measured here in labour hours per week). This condition states that the number of coupons in circulation exactly equals the amount needed to occupy all jobs.

There is an Equilibrium on this market only if:

p_c is endogenously determined by supply and demand on Eu's labour market, so:

All familiar "Pareto" and "efficiency" types of analysis of free markets apply to this (admkittedly at first glance somewhat counterintuitive) free market Labour Rights.

Of particular interest is the following theorem:

(The equilibrium price of the Labour Rights goes down when more Labour Rights come in circulation ceteris paribus.)

(If employment rises, Labour Right prices go down, ceteris paribus.)

(If able adult citizens increase in numbers, the Labour Right price will go up, ceteris paribus.)

We used Cobb Douglass as an illustration, the system assumes the familiar mathematical complications if generalized to larger classes of utility functions.