Should informal sector be subsidised?

are internationally traded and their prices are exogenously given.The production
functions of all the three sectors satisfy constant returns to scale. All the three sectors
use labour and capital as inputs. Capital is measured in physical unit while labour is
measured in efficiency unit. The intensive production functions of the three sectors are
given by:

Xu = Lufu (ku)                       ..........(1)

Xi = Lifi(ki, h)                          ..........(2); and

Xr = Lrfr (kr)                            ..........(3).

Where Xj is the level of output of the jth sector,Lj is the level of employment in the
jth sector ,kj is the capital intensity of the jth sector and h is the worker’s efficiency.
Worker’s efficiency depends upon the wage rate they receive. Higher wage implies
larger efficiency of the worker and such efficiency-wage relation is more pronounced
in the low wage level. It is assumed that the worker’s efficiency is equal to unity above
a certain level of wage (W*); and both the urban formal wage rate and the rural wage
rate are higher than this level in the initial equilibrium. Thus, worker’s efficiency is
equal to one for both the rural sector and the urban formal sector and hence are
independent of the wage rates there. However, for the urban informal sector, the wage
rate is very low and is less than that level in the initial equilibrium. So the labour
efficiency there is positive but less than unity. Also this efficiency varies positively
with the wage rate in the informal sector._The efficiency wage relation in the informal
sector is given by:

h = h (Wi)                         .........(4)

Following restrictions are imposed on this efficiency function :
(I) h′ (Wi) > 0 for Wi<W^*;   (II) h (Wi) = 1 for Wi > W^*.

All the market are assumed to be perfectly competitive and the representative firm is
assumed to maximise profit. CRS property of the production function and the
equilibrium of a competitive firm implies the equality between the price and the unit
cost. Profit maximisation in the informal sector also implies the minimisation of cost
of one efficiency unit of labour. The long run equilibrium of a competitive firm implies
that price is equal to the unit cost. Hence we have the following equations :

Pu = Cu (Wu,R)               ∙∙∙(5);

Pi = Ci (Vi.R)                  ...(6); and

Pr = Cr (Wr, R)               ...(7).

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