THE EQUIVALENCE OF LITTLE-MIRRLEES FORMULATION OF SHADOW WAGE AND UNIDO APPROACH

In the UNIDO approach, the optimal shadow wage is given by,

W* = P_A + s* (P^INV - 1)W       ...         ...         ...         (9)       

Where  s* is the capitalists' propensity to save; W is the wage and  P^INV measures the price of investment in terms of consumption. Assuming that the propensity to save of capitalists is unity (s* =1) and all wages are consumed, equation (8) may be written as:

 W* = P_A +  (P^INV - 1) C          ...         ...         ...         (10)     

Where (P^INV - 1) C represents the present value of aggregate consumption lost              assuming (P^INV >1) because of  increased consumption of workers which reduces saving for future consumption.

Now from above for the two approaches to give equivalent cash flows, whichever numeraire is taken, P^INV must be equal S₀ , so that the equation (9) may be written as:

W* = P_A + (S₀ - 1)C                ...         ...         ...         (11)

Now Little - Mirrlees formulation of the shadow wage from equation (6) is:

W* = P_A +  (1 - 1/S₀)(C-m)     ...            ...      ...         (12)     

Which, on the assumption that  P_A = m , may be written as:

W* = P_A / S₀ + (1 - 1/S₀)C      ...         ...         ...         (13)     

Comparing equation (12) with the UNIDO equation (11) , it can be seen that the UNIDO formula is  S₀ times the Little-Mirrlees formula because the UNIDO numeraire is 1 / S₀ times as valuable as the Little-Mirrlees numeraire.

The calculation of the shadow wage will be different according to the two approaches assuming (P^INV = S₀ ) only to the extent that they classify goods into traded and non-traded in a different way and that the standard conversion factor (SCF) to convert    non - traded goods into world prices is not the reciprocal of the shadow exchange rate (SER) to convert traded goods prices into domestic prices.