64 It rules out the possibility of substitution between the non-traded input and other factors of
production in sector 3. Although this is a simplifying assumption, it is not totally unrealistic. This is partly justified by the fact that four tires are used to produce a car and one Brown tube is used for a TV set. In industries like shoe making and garments, large formal sector firms farm out their production to the small informal sector firms under the system of subcontracting. So the
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mobile between the two urban sub-sectors and labour is imperfectly mobile between the three sectors of the economy. But capital of type 1 is specific to sector 1. Let rand R
denote the returns to capital of type 1 and type 2, respectively. There is Harris-Todaro type of unemployment denoted by LU. The aggregate capital stock of the economy of
either type consists of both domestic and foreign capital. Incomes earned from foreign capital are completely repatriated. Let us now assume that labourers in the urban formal and informal sectors earn exogenously given wages65, *
3
W and *
2
W , respectively, while the wage rate in the rural sector,
W
1, is market determined. The three wage rates arerelated by the Harris-Todaro (1970) migration equilibrium condition where the expected urban wage rate equals the rural wage rate and * *
3 1 2
W W W .66Owing to the small open economy assumption the prices of the two final commodities are given internationally. But the price of the non-traded input produced by the urban informal sector, P2, is determined domestically by demand and supply forces. We assume that the urban formal sector is the import-competing sector of the economy and is protected by a tariff. Other standard assumptions made in the earlier sections are retained. Commodity 1 is chosen as the numeraire.
Some of the new notations used in this section are as follows.
j
K = economy’s aggregate capital stock of the jth type (domestic plus foreign), ( j = 1,2);
production is done in the informal sector firms while labeling, packaging and marketing are done by the formal sector firms. One pair of shoes produced in the informal sector does not change in quantity when it is marketed by the formal sector as a final commodity. Thus there remains a fixed proportion between the use of the intermediate input and the quantity of the final commodity produced and marketed by the formal sector. It may be noted that Gupta (1994) has used this assumption in the context of analyzing different expansionary policies of a duty-free zone in a developing economy. Chaudhuri (2003) has also made this assumption.
65The rigidity of the informal sector wage has been explained in chapter 4. 66 See footnote 28.
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Dj
K = economy’s domestic capital stock of the jth type, j= 1,2;
V social utility;
i
D consumption demand for the ith final commodity, i= 1,3;
Y national income at domestic prices;
M import demand for commodity 3.
A general equilibrium of the system is represented by the following set of equations .
1 L1 K1 1 W a ra (5.34) * 2 L2 K2 2 W a Ra P (5.35) * 3 L3 K3 2 23 3(1 ) W a Ra P a P t . (5.36) Full-employment conditions for capital of types 1 and 2 are as follows.
1 1 1X K aK (5.37) 2 3 3 2 2X a X K aK K . (5.38) The demand-supply equality of X2 implies that
2 3 23X X
a . (5.39)
For the sake of analytical simplicity, the number of workers in the economy, L has been normalised to unity. The labour endowment equation is then given as follows.
1 3 3 2 2 1 1 L L U L X a X a X L a . (5.40)
Introducing the informal sector to the Harris-Todaro framework would modify the labour allocation mechanism such that in the labour market equilibrium, the rural wage rate (W1) equals the expected wage income in the urban area. Since the probability of finding a job in the manufacturing sector is aL3X3/(aL2X2 aL3X3Lu)in the present case, then the expected wage in the manufacturing sector is *
3 L3 3/( L2 2 L3 3 u)
W a X a X a X L . Similarly, the expected wage in the informal sector is *
2 L2 2/( L2 2 L3 3 u)
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expected wage in the urban area (the manufacturing and informal sectors) is
* *
2 2 2 3 3 3 2 2 3 3
(W a XL W a XL ) /(a XL a XL Lu). Therefore, the labour allocation mechanism between rural and urban areas is expressed as
* * 2 2 2 3 3 3 2 2 3 3 1 (W a XL W a XL ) /(a XL a XL Lu)W , or equivalently, * * 1 L1 1 2 L2 2 3 L3 3 1 W a X W a X W a X W . (5.41) Following Beladi and Yabuuchi (2001) we assume that the wage in the informal sector is a constant fraction of the formal sector wage67 and is given by
* *
2 3
W nW (5.42)
where 0 n 1, represents the distortionary wage differential between the two urban sectors. It is assumed that the urban informal sector consists of many subcontract firms, and as explained in section 3.6, the workers employed do not get more than their reservation wages.
There are eight endogenous variables in the system: W r R P X X X1, , , , ,2 1 2, 3 and LU and
eight independent equations. The policy parameters are: K1 and K2.68 One can
obtainR and P2 by simultaneously solving equations (5.35) and (5.36). Using (5.37),
(5.39) and (5.42), equations (5.38) and (5.41) may be rewritten as the following, respectively. 2 3 3 23 2 ) (aK a aK X K (5.43) and