MODELO DE MERCADO

It has already been mentioned that the informal sector firms primarily produce intermediate inputs for the formal sector through an institutional arrangement which is known as subcontracting. As the informal sector depends on the formal sector for marketing its output a common contention is that the informal sector lives or dies with the formal sector. It is worthwhile to theoretically examine the validity of this

Page | 64 conventional wisdom. In the following section we do this exercise using a three-sector

Harris-Todaro model with an urban informal sector.

We consider a model of rural-urban migration with three sectors: rural, urban informal and urban formal sectors. The rural sector produces an agricultural commodity, X , using labour and a sector-specific input land, the latter earning a return i. The urban informal sector produces an intermediate input, Y for the formal sector with the help of labour and capital. In the rural and the urban informal sectors, labour market is perfectly competitive and the wage rates are W and _X W , respectively. The capital market facing the urban _Y informal sector is imperfect. The interest rate on capital, R, is a positive function of the amount of capital borrowed and a decreasing function of the policy parameter, . An increase in implies a credit subsidy to the informal sector that lowers the interest rate.

Therefore, we have ( _KY , )

RR a Y  , with (R/a Y_KY ) ; and 0 (R/)0. (3.73)

Let us now explain in details the capital market dichotomy which is a salient feature of the developing economies. The functional form of R(.)suggests that capital cost in the informal sector increases with an increase in the amount of capital borrowed. In the absence of any significant provision for organized (formal) credit, the informal sector has to mainly rely on informal credit market for financing the costs of capital.

TheR(.)function with (R/a Y_KY )0 and (R/)0 is a possible way of formalizing the informal sector’s lack of access to the organized credit market. The idea is that the economy is endowed with a given amount of capital. SectorsX andZhave access to or connections with the owners of capital and they work out a rental rate,r, which is the competitive rate. The informal sector lacks this connection. Hence we can conceive of a set of middlemen who borrow capital from the capital owners at the competitive rate, r and then lend them out to the workers in the informal sector at a higher rate given byR(.), with (R/a Y_KY ) . This means sector 0 Ycan get an additional loan at the cost of a higher interest rate. This implies imperfection in the

Page | 65 capital market. Similar treatment of credit market imperfection is available in Datta

Chaudhuri (1989), Gupta (1993) and Chaudhuri (2000) etc.

Lending of credit to the informal sector borrowers is always risky. There is a high probability of default of loans. The risk of default may arise due to many reasons. First, there is the risk of involuntary default owing to unforeseen circumstances (unemployment, disease, death of the borrower etc.). Hence the borrower simply may not have sufficient money at the time of repayment of the loan. Secondly, there is possibility of voluntary default: the borrower may take the loan, not use the fund for production and refuse to repay. In developing countries where the legal machinery is not so strong and functions slowly, the risk of default is high. The larger the volume of loan, in order to cover risks, the higher the interest rate the informal sector lender would charge. See Bottomley (1975), Basu (1998) and Ray (1998) in this context. Nonetheless, in Appendix 3.1 we have shown mathematically why the informal interest rate,R, is an increasing function of the volume of loan and a decreasing function of the government’s credit subsidy.

Finally, the urban formal sector faces a perfect capital market but a unionized labour market. The unionized wage in this sector,W, is greater than both the rural and the informal sector wage rates. In particular, we have W W_X W_Y. There are two production divisions in the formal sector. Division Z produces a final manufacturing commodity using labour, capital and the non-traded input, Y. Another division,M , produces at least a part of the requirement for the input in order to avoid complete dependence on the informal sector. The price of commodity Y is determined domestically while final commodity prices are given internationally. The technology for producing the intermediate good, Y , is identical in both sectors and coefficients of production in all the three sectors are fixed so that the a_jis are technologically given.

However, this is only a simplifying assumption. Finally, commodity 1 is chosen as the numeraire.

Page | 66 The usual zero-profit conditions are given by

X LX NX 1

W a ia  (3.74)

( , )

(+) (-)

Y LY KY KY Y

W a R a Y  a P

(3.75)

LM KM Y

Wa ra P (3.76)

LZ KZ Y YZ Z

Wa ra P a P (3.77)

All inputs are fully utilized. The full-employment conditions for land, capital, labour and the non-traded input are given by the following four equations, respectively.

aNXX N (3.78)

KY KM KZ

a Ya M a Z K (3.79)

LX LY LM LZ

a X a Y a Ma Z L (3.80)

YM a ZYZ (3.81)

Finally, the Harris-Todaro migration equilibrium condition is given by

( ^{Y LY LM LZ} ) _X

LY LM LZ

W a Y Wa M Wa Z

a Y a M a Z W

 

   (3.82)

Here the endogenous variables are: W W i P r X Y M and_X, _Y, , _Y, , , , Z. The policy parameter is  . An increase in  implies a credit subsidy policy to the urban informal sector.

Wis the exogenously given wage rate in the urban formal sector. Given W and P_Z, the equilibrium values of r and P are determined from equations (3.76) and (3.77). The _Y values of W i X Y M and_X, , , , Zare determined by solving equations (3.74) and (3.78) – (3.82) simultaneously. Once Y is known R is also known and hence from (3.74) W is _Y obtained. This is how the values of all endogenous variables are determined.

Now if a credit subsidy is given to the informal sector, takes a higher value.

Consequently, R decreases and W increases as_Y P and _Y r are determined from equations

Page | 67 (3.76) and (3.77). Sector Yalso expands by the process. As the informal sector wage,W , _Y

rises the expected urban wage for a prospective rural migrant, given by the left-hand side of (3.82), increases leading to a migration of labour from the rural sector to the urban sector. There is no reason for sectorZto change. Thus, the demand for the intermediate input remains unchanged. The intermediate input-producing division of the formal sector must contract as the informal sector now produces more of inputY. Thus, as a whole the formal sector (final good plus intermediate input) contracts while the informal sector expands. So the following proposition can now be established.

Proposition 3.8: A credit subsidy policy to the informal sector leads to an overall contraction of the formal sector while it expands the informal sector.

Hence, there may be cases where the urban informal sector may expand even if the formal sector contracts and the former is dependent on the latter for marketing its output.

Page | 68 Appendix 3.1: Derivation of the Rfunction

Suppose an informal sector lender finds that on average, fraction qof his loans is not repaid. It is sensible to assume thatqshould be increasing in the volume of loan,K , and _Y decreasing in the government’s credit subsidy, . As the volume of credit increases the probability of default is expected to increase while a higher provision for subsidized formal credit would lower the average cost of borrowing funds for the informal sector borrowers and it would be easier for them to repay their loans. So we write

( _Y, )

qq K  with (q/K_Y) and0 (q/)0 (3.A.1)

The income of the informal sector lender, denotedQ, is given by

(1 )(1 ) _{Y Y}

Q q R K K (3.A.2)

The effective informal interest rate net of the expected cost of default, denoted d , is as follows.

( ) (1 )(1 ) 1

Y

d Y q R

 K     (3.A.3)

Competition between sectors will ensure that in equilibrium the effective informal interest is equal to the competitive interest rate in the organized credit market. So in equilibrium we have

(1q(.))(1R) 1 r or,

( )

1 r q

R q

 

 (3.A.4)

Page | 69 It is easy to check that

(1 )

( ) ( ) 0

1

q r

R r

q

   

 ifq 0. (3.A.5)

So if the rate of default of loan,q, is positive there exists positive interest rate differential between the informal and the formal credit markets.

From (3.A.4) it is not difficult to check that

2

( ) [ 1 ]( ) 0;

(1 )

Y Y

R r q

K q K

  

 

   and,

(+)

2

( ) [ 1 ]( ) 0.

(1 )

R r q

 q 

  

 

   (3.A.6) (–)

Hence R is an increasing function of the volume of loan and a decreasing function of the credit subsidy.

Page | 70 Chapter 4