To fix our minds on the workings of this mechanism, it is helpful to imagine an institutional setting in which the attainment of this equilibrium could be expected. Solely for this purpose we shall investigate some fictitious possibilities.

The first possibility is to tax occupants of jobs in such a way that the tax sum suffices to pay transfer income t to P - J unemployed persons, where t is such that, w/t leads these P - J persons to prefer unemployment: suppose all jobs J have gross-wage wg =W/J, then the tax defined by

tax = w_g –w
is distributed over P - J unemployed, which makes transfer income t:

then, the relative wage can be expressed as

If the tax authority now gives al1 workers freedom to leave their jobs and register for a transfer income t, then tax is higher than equilibrium if more than P-J persons prefer to register, and it is lower than equilibrium if less than P-J persons prefer to register. Equilibrium tax, found by trial and error, is defined as that value of tax at which exactly P-J persons prefer to register. This already gives us some notion of the kind of system that would induce equilibrium, but in case of a relative wage above equilibrium, there is no place where an excess supply (the proportion of P-J that does not prefer to register), could go, since only J jobs are available.

We could further improve our economic science fiction by transforming the tax authority into a "Labour bank" which issues a total amount of J labour certificates entitling the holder to occupy a job. Each certificate consists of P coupons. The bank, however, distributes these JxP coupons evenly over all P persons, whereby every person receives only J coupons. If a person prefers employment, he will have to buy another number P-J of coupons, if he prefers unemployment, he can sell his J coupons to those who prefer employment. The price of the coupon on a free market now replaces the tax of our previous set up. If you choose for employtnent, your (net) wage w is given by

w = w_g – (P-J) p_c

where p_c is the market price of the coupon. If you choose for unemployment, your "transfer income" t is given by

t = J.p_c

Now, p_c is subjected to the law of supply and demand on a free market and the relative wage w/t is given by

The equilibrium price on the market for coupons really yields the optimum value for w/t: if p_c is such that w/t is above its equilibrium value, then more than J persons, at the given coupon price, prefer employment. Competition between coupon buyers raises p and thus lowers w/t. If p_c is so high as to render the value of w/t below its equilibrium level, then more than P-J persons prefer unemployment and competition between coupon sellers lowers p_c , thus raising w/t.