This paper explains the impact of output subsidy to the informal sector on urban unemployment and domestic factor income in a mobile capital model where urban formal wage is endogenous and the informal sector has global exposure.Informal sector; Subsidy

Bandopadhyay, Titas Kumar

English

Research Papers in Economics

  1 
 
                                                   1 INTRODUCTION: 
This is the first sentence of my introduction.  My paper examines the impact of subsidy 
policies, given to the informal sector,on urban unemployment and domestic factor 
income. At the present juncture, it is well known to all development economists that the 
informal sector provides jobs to many unemployeds. This is true irrespective of the 
level of development.At the same time, it is also observed that huze unemployment also 
exists in many countries where informal sector plays important role in the employment 
generating activities.One question obviously comes: why such huze unemployment 
exists even when the informal sector is very large? Fields(1975,1989) and Gupta(1993) 
have explained this1. This paper explains such co-existence in terms of consumption-
efficiency hypothesis of Leibenstein(1957). The basic idea of the consumption-
efficiency hypothesis is that a worker’s efficiency is positively related to the wage rate 
he receives. This is generally valid in the case of low income workers who consume the 
whole wage income and suffers from malnutrition. The employers use this wage as an 
instrument of profit maximisation and the optimum wage appears to be unique and 
independent of other economic variables. This wage rigidity at the  equilibrium level 
explains involuntary unemployment. 
The development literature shows that from time to time Government of many small 
countries have given output subsidy to the informal sector to combat unemployment, to 
enhance informal employment and to uplift country’s welfare. The present paper tries 
to  explain  theoretically  the  impact    of  such  policy  on  urban  unemployment  and 
domestic  factor  income  where  urban  formal  wage  rate  is  endogenous  and    urban 
informal sector is internationalised.. The trade unionism of many developing countries 
may lead to endogenous urban formal wage rate.We also observe in many developing 
countries that the products of the urban informal sector are also globally traded.2 Our 
main  finding  is  that  subsidies  given  to  the  urban  informal  sector  lowers  urban 
unemployment and raises domestic factor income.The result provides adequate basis 
for Governments’ subsidization program for the urban informal sector. At present, this 
is very important when global tendency runs against subsidies 
Section 2 develops the model and gives the results. Section 3 concludes. 
                                            2. THE MODEL   
We consider a small open economy consisting of three sectors: urban formal sector(u), 
urban informal sector (i) and rural sector (r). The goods produced in the three sectors   2 
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).   3 
Where Pj is the producer’s effective price of the jth good, Wj is the wage rate in the jth 
sector,R is therental rate on  capital, Vi is the cost of one efficiency unit of labour in the 
urban informal sector, Cj is the unit cost of production of the jth sector.3  
The cost of one efficiency unit of labour in the urban informal sector is given by: 
Vi = (Wi / h(Wi)    …(8). 
The condition for minimisation of  unit cost of labour (expressed in efficiency  unit) is 
given by 
(h′ (Wi) Wi / h (Wi) ) = 1  …(9) 
Workers migrate form the rural region to the urban region; and a fraction of the urban 
labour force remains unemployed. The migration mechanism is of Harris-Todaro 
(1970) type. Thus, the labour market equilibrium is given by the equality between the 
actual rural wage rate and the expected urban wage rate. The Harris-Todaro (1970) 
migration equilibrium condition is given by the following equation : 
Wr = Wu (Lu/ (L-Lr) ) + Wi (Li / (L-Lr))    … (10), 
where L is the total labour endowment of the entire economy,Lj is the level of 
employment in the jth sector.We assume that the total amount of capital stock (KD ) and 
the size of labour force are given. Capital is fully employed. However, there exists open 
unemployment of labour in the urban region. Capital is perfectly mobile among the 
three sectors 4
 . Thus, we have a common rate of return on capital in all the three 
sectors. The full utilisation of capital stock leads to the following equation :  
kuLu + kiLi + krLr = K       …(11) 
It is assumed that the urban formal sector  is more capital intensive than the rural sector 
in value terms . 
The level of urban unemployment(U) is given by : 
U = L-Lu-Li-Lr          (12) 
The total factor income(Y) of the economy is given by 
Y = WuLu + WiLi + WrLr + RK    … (13) 
And is equal to the national income in the absence of any tax or subsidy imposed on 
factor income. Using Equations  “(10)” and  “(13)”   we get,  
Y  =  WrL   +   RK                                          …  (13a) 
urban formal sector’s wage rate is assumed to be endogenous.  Urban formal wage rate 
is positively associated with the urban informal wage rate and the rural wage rate and is   4 
inversely related to the urban unemployment. Thus , the urban formal wage function is 
given  by :  
Wu = Wu (Wi , Wr , U)                                                      …      (14) 
Where (δWu  / δWj ) > 0  for  j = i , r  and (δWu / δU ) <  0.  
We follow Khan (1980) to justify the equation “(13.1)”with the help of Calvo (1978) 
and  Stiglitz  (1974).  Calvo  (1978)  has  emphasised  the  role  of  trade  unions  in  the 
determination  of  urban  formal  wage  rate.  Calvo  (1978)  assumes  that  trade  unions’ 
utility depends on the wages received by their members and on the alternative sources 
of  employment.  Thus,  if  we  assume  that  labourers  in  the  urban  formal  sector  are 
unionised the increase in rural wage rate, Wr (urban informal wage rate , Wi) makes 
rural employment (urban informal sector’s employment ) more attractive to the trade 
union members. As a result , the utility of the trade union falls. Hence , the trade union 
demands higher urban formal wage rate , Wu , to  maintain the same level of utility . 
The effect of urban unemployment on urban formal wage rate can be explained in terms 
of the labour turn – over model of Stiglitz (1974) . Stiglitz (1974) has shown that , as 
unemployment falls , it becomes easier for the workers to quit and take other jobs.  
Thus the quit rate rises ; and this raises the cost of recruitment of new workers and the 
indirect training cost of labour. To combat these increases , firms must pay higher 
urban wage when quit rate rises due to the reduction in urban unemployment. Thus , 
urban formal wage rate and urban unemployment vary inversely.This completes the 
equational structure of the model. 
Equation “(9)” yields equilibrium value of Wi . Then Equation “(8)” determines the 
value of Vi and Equation “(4)”  determines the value of  h . We get the value of R from 
Equation “(6)” , given Pi and vi . Equation “(7)” yields the value of Wr , given Pr and R. 
Equation “(5)” determines Wu , given Pu and R . Thus , we get the values of  ku , ki and 
kr from the Equations “(14)” , “(15)” and  “(16)” . We can solve for equilibrium value 
of U from Equation “(13.1)” , given Wu , Wi and Wr . The levels of employment in the 
three sectors Lu , Li and Lr are obtained solving Equations “(10)”,”(11)” and “(12)” 
simultaneously.  Finally , we get the value of Y from Equation “(14a)”. 
                            
                             3.COMPARATIVE STATIC EFFECTS 
 Suppose that Pi is raised due to subsidization to the informal sector. Then Equation 
“(6)” shows that R will rise , given Vi . Then Wr and Wu will fall , given Pr and Pu ( see   5 
Equations “(5)” and “(7) )”. Thus , ku’ ki and kr will fall. Equation “(11)” shows that (Lu 
+ Li + Lr ) will rise, given KD . Hence , U must fall to satisfy the Equation “(12)” .  
However, the Appendix shows that Lu , Li and Lr  may move in any direction .From 
Equation “(13a)” we can show that Y will rise if the fall in WrL isless than the rise in 
RK ; and this is satisfied if (dwr / dR) < - (K/L ) ; or if kr < (K/L) .Thus, we get the 
following proposition: 
Proposition :  A rise in Pi resulting from subsidization  to the informal sector lowers 
unemployment;  and  raises  the  total  factor  income  if  the  rural  sector  is  sufficiently 
labour-intensive.  However,  the  effect  on  the  informal  sector’s  employment  is 
indeterminate. 
So, subsidization to the informal sector raises total factor income; and hence national 
income may also improve even if the subsidy is financed by taxing the factor income. 
Such a strong positive argument for subsidization to the informal sector is not available 
in the existing theoretical literature. 
 
                                               4.CONCLUSIONS 
The paper has examined the impact of output subsidy given to the informal sector on 
urban unemployment, informal sector’s employment and on the domestic factor income 
of a small open economy where capital is perfectly mobile among the three sectors. The 
simultaneous existence of urban informal sector and urban unemployment has been 
explained  interms  of  efficiency  wage  theory  which  is  applicable  to  the  low  wage 
informal sector. Informal sector also produces traded goods and the presence of trade 
union in the urban formal sector makes the formal wage endogenous.This is highly 
observed  in  many  developing  countries  like  India  where  handloom  and  handicraft 
products are internationally traded and the trade union activities are flashing.  
Output subsidy given to the urban informal sector lowers urban unemployment and 
raises  domestic  factor  income  provided    that  the  rural  sector  is  sufficiently  labour 
intensive.  Its effects on informal sector’s employment is ambiguous.  
 
                                                  ENDNOTES  
1.  Fields(1989) explains this in terms of job searching and Gupta(1993) explains 
this in terms of agricultural surplus whose price is fixed. 
2.  The assumption that the urban informal sector produces internationally traded 
good has been found  in the models of Grinols(1991),Chandra and Khan(1991) 
and Gupta(1997).   6 
3.  The unit cost function,Cj(.) has three basic properties: it is negatively sloped 
and its slope is equal to –Kj/Lj , it is concave and it is linearly homogenous in 
factor prices(see Khan and Naqvi,1983). 
4.  We find this type of capital mobility in Chandra and Khan(1993). 
 
 
Appendix 
 
 
The total differentials of Equations (10),(11) and (12) are given by: 
 
WudLu +WidLi +WrdLr  =  (L- Lr)dWr – LidWi – LudWu  ……………………..(15); 
 
kudLu + kidLi  +krdLr =  dK –Lu dku –Li dki –Lr dkr    …………………….(16); and 
 
dLu  +dLi + dLr  =   --dU                 ………………………………………………  (17). 
 
 
The matrix form of these equations is : 










=




















-dU -  
dkr Lr    Lidki dku  Lu  dK 
dWu Lu    dWi   Li dWr     Lr)   (L
1       1       1
   
   
r
i
u
r i u
r i u
dL
dL
dL
K K K
W W W
 
 
 
Let D be the determinant of the co-efficient matrix of the endogenous variables in the 
system. So,we can write, 
 
D  =  (Wr –Wi) ku  -(Wu – Wi)kr + (Wu – Wr) ki 
 
If ku > ((Wu- Wi)/(Wr –Wi))kr, then, D >0 
 
Hence, dLu  = 1/D(((L –Lr) dWr –Li dWi – Lu dWu) (ki –kr) –(dK –Lu dku –Li dki –                   
 
                        Lrdkr) (Wi –Wr) – dU (Wi kr –Wr ki))……………………………(A.1) 
 
 
           dLi    = 1/D (((dK – Lu dku –Li dki –Lr dkr )(Wu –Wr) + (Wukr –Wrku ) dU – 
 
                       ((L –Lr) dWr –LidWi –Lu dWu) (ku –kr)…………………………(A.2) 
 
 
 
            dLr     = 1/D (((L –Lr) dWr  -- Li dWi –LudWu ) –(dK – Ludku –Lidki – 
 
                       Lrdkr)(Wu –Wi) + (Wiku – Wuki ) dU)……………………….(A.3) 
 
                                     Effect of a change in Pi 
 
Put dWi =dK =0 in the expressions (A.1), (A.2) and (A.3) and we get,   7 
 
dLu/ dWr  = 1/D (((L –Lr) – Lu(dWu /dWr))(ki –kr) + (Lu dku /dWr +Li dki/dWr  
 
                    +Lr(dkr/dWr))(Wi –Wr) – (Wikr –Wrki) dU/dWr)  > ,=,<  0 
 
 
dLi/dWr  =  1/D ((( -Lu(dku/dWr) + Li(dki/dWr) +Lr(dkr/dWr) (Wu –Wr) + (Wukr – 
 
                      Wrku) (dU/dWr) –((L –Lr) –Lu(dWu /dWr)) (ku –kr )) > ,=, < 0 
 
And (dLr/dWr)  = 1/D((( (L – Lr) – Lu( dWu/dWr)) (ku –kr) + (Lu(dku/dWr) + 
 
                    Li(dki/dWr) + Lr(dkr/dWr)) (Wu –Wi) +(Wiku –Wuki) dU/dWr ) >, =, < 0 
 
 
Now, (dLj/dPi)  =  (dLj/dWr) (dWr/dPi) for j = u,i and r. 
 
                                                                  References 
 
Bandyopadhyay , M. and M. R. Gupta(1995a) “Development policies in the presence of 
an informal sector : A note” Journal of economics 61,301 – 315. 
 
Calvo,G.A.(1978)“Urban  unemployment  and  wage  determination  in  LDCs:  trade 
unions in the Harris-Todaro model” International Economic Review 19,65-81. 
 
Chandra, V. and M. A. khan(1993)“Foreign investment in the presence of informal 
sector”  Economica  60, 79-103. 
 
Fields, G.(1975)“Rural-urban migration, urban unemployment and underemployment 
and job search activity in LDCs” Journal of Development Economics 2, 165-187. 
 
Gupta, M. R.(1993) “Rural-Urban migration, informal sector and development policies 
: a theoretical analysis” Journal of Development Economics 41,137-151. 
 
Harris , J. R. and M. P. Todaro.(1970) “ Migration, Unemployment and Development  
: A Two-Sector Analysis “ American Economic Review Vol.60, 126-142. 
 
 Khan,  M.A.  and  Naqvi,S.N.H.(1983)  “Capital  Markets  and  Urban  Unemployment” 
Journal of International EconomicsVol.15, 367- 385. 
 
Leibenstein, H.(1957)“Underemployment in Backward Economies”Journal of Political 
EconomyVol.65, 91-103. 
 
Quibria, M. G.(1988) “Migration, Trade Unions and the Informal Sector : a note on 
Calvo” International Economic Review29, 557-563. 
 
Stiglitz, J. E.(1976)“The efficiency wage hypothesis, surplus labour and the distribution 
of labour in LDCs” Oxford Economic Papers 28, 185-207. 
 
 

Should informal sector be subsidised?

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