Foreign capital inflow and its welfare implications in a developing country context

In a small open developing country context, the author considers a three-sector general equilibrium framework and tries to find out the effects of foreign capital inflow on welfare of the country. Comparative-static results show that foreign capital inflow widens the skilledunskilled wage gap under some reasonable conditions, although it causes an expansion of the foreign enclave and the agricultural sector and contraction of the domestic manufacturing sector. Taking sector specific foreign capital, the authors find that foreign direct investment is beneficial in a free market small open economy in the absence of tariff. JEL D50, D60, F4, F63, O11


Introduction
The impact of foreign-capital inflow on the welfare of a developing economy has always been a subject of immense interest among the policymakers and the academicians. The famous Brecher-Alejandro's (1977) proposition, based on the theoretical works by Bhagawati (1958), Johnson (1967), andBhagawati (1973), is a benchmark in this context. The work of Brecher-Alejandro (1977) has successfully analysed the effects of foreign-capital inflow on the welfare of an economy. In a twocommodity, two-factor framework, characterized by the presence of full employment, they have shown that, if the relatively capital-intensive sector is protected by tariff and, the income from foreign capital is fully repatriated, then, an increase in foreign-capital inflow would cause a loss in welfare of a country.
However, the inflow of foreign capital cannot influence the welfare of a country if the import-competing sector is not protected. This is the famous Brecher- Alejandro's (1977) proposition of the trade theory.
The work of Khan (1982) has also thrown light on this in a Harris-Todaro's (1970) framework of urbanunemployment. The result of Khan's work also supports the Brecher- Alejandro's (1977) proposition. Beladi and Marjit (1992a) have re-examined the Brecher- Alejandro's (1977) proposition in a fullemployment model proposed by Heckscher-Ohlin-Samuelson, in the presence of an export-processingzone (EPZ) that uses the sector-specific foreign capital. According to their work, the inflow of foreign capital obstructs the national welfare if the country imports capital intensive goods while the importcompeting sector is protected. Contrarily, if the country imports labour intensive commodity, the expansion of the EPZ will make the country better off.
In an another work, Beladi and Marjit (1992b) have considered a three-sector model in which one sector is EPZ that uses sector-specific foreign capital in a subsystem proposed by Heckscher-Ohlin-Samuelson. In this model, skilled labour force is fully employed and the market of unskilled labour is characterized by the presence of unemployment. This work invents the conditions under which one can find out the negative effect of foreign-capital inflow on welfare of a country. It happens when the foreign capital is not injected directly into the import-competing sector, but it changes the composition of output in other traded sectors through the inter-sectoral reallocation of the existing resources.
The validity of Brecher-Alejandro's (1977) proposition has been presented by the work of Chandra and Khan (1993) in a Harris-Todaro's (1970) framework, where capital is mobile. They consider the presence of a 'flexible wage in urban informal sector', and establish that Brecher-Alejandro's (1977) proposition remains valid if the average capital-intensities of both the formal and informal sectors of urban area are higher than the capital-intensity of the formal sector of rural area.
Here, we are interested to find out the effects of foreign-capital inflow on the welfare of a developing country. More precisely, our main objective is to examine the impact of foreign-capital inflow on welfare of a developing country in a three-sector general equilibrium setting, the sectors being agriculture, domestic-manufacture and foreign-enclave. Moreover, we consider the domesticmanufacture as an import-competing sector (same as Brecher-Alejandro's (1977) proposition), whereas, other two sectors are considered to be the export sectors.
The paper is organised as follows. Section 2 describes the model. Comparative-static results are discussed in Section 3. Section 4 shows the effects of foreign-capital inflow on welfare of a small open economy. Finally, conclusions are made in Section 5.

The Model
We consider a three-sector small open economy in a neoclassical general-equilibrium framework. There are two sector-specific factors, viz., foreign capital, which is specific to foreign enclave and unskilled labour force, which is specific to the agricultural sector. There is no substitutability between domestic capital and foreign capital. There is full-employment in all the factors' markets. Both the products' markets and the factors' markets are assumed to be perfectly competitive and production function in each sector is CES 1 with CRS 2 and follows diminishing marginal productivities of all variable factors.
There is free trade of commodities.
The economy consists of three sectors, viz., the manufacturing sector (M), the foreign enclave (T) and the agricultural sector (A). S and L stand for skilled and unskilled labour-endowment respectively. K and F stand, respectively, for stock of domestic capital and inflow of foreign capital. Three sectors use different combinations of factor-inputs for their production, like, sector M uses S and K, sector T uses S and F, and, sector A uses L and K. Here, we assume that S is perfectly mobile within M and T; and, that of K is perfectly mobile between A and M within the domestic enclave. We take agricultural product as the numeraire, its price being equal to unity.
1 Constant Elasticity of Substitution 2 Constant Returns to Scale Let be the amount of i th factor required to produce one unit of commodity j, be the level of j th commodity produced, * be the global price per unit of commodity j, be the share of expenditure on factor i to the total cost of producing one unit of commodity j, be the elasticity of substitution for commodity j, be the proportion of i th factor employed in j th sector, and, be the demand for commodity j, where, = , , , and = , , . Let w and stand for wage rates of unskilled and skilled labours respectively, while and stand for rental rates of domestic and foreign capital respectively. We take (. ) as the social welfare function, where, is the marginal social utility of commodity j. To describe the model, we have the following main equations: (Agricultural product is taken as the numeraire. Hence, * = 1) All these three equations imply the competitive zero-profit pricing system.
From the conditions of full-employment at all relevant factors' markets, we have the following four equations: In the present model, the endogenous variables to be determined are , , , , , , . * , * * are exogenously given world's prices and the assumption of small open economy implies that the country is a price-taker. We now describe how does the model work.
So, = [ ( )] with = , where > 0. Hence, the system is not decomposable. Now, equations 4 and 7 give: It is known that, = ( , ) and = ( , ). It is also known that, is a diminishing function of , and is an increasing function of . Hence, = ( ), > 0. This is because, a rise in rental rate of domestic capital implies a rise in rental rate of the foreign capital and a consequent decline in the wage rate of the skilled labour. Therefore, the foreign enclave has a tendency to substitute the foreign capital by skilled labour which causes a rise in labour-capital ratio in the foreign enclave.
On the other hand, we know, = ( , ). As is negatively related to , so, = ( ) with > 0. This can be explained in a way that, when the rental rate of domestic capital is increased, the wage rate of skilled labour declines, and hence, the domestic manufacturing sector has the tendency to substitute capital by labour. Equation 4.1 can be expressed then as: This equation shows a unique relationship between and , that maintains the equilibrium in the skilled labour market. The relationship is depicted by a negatively sloped SS curve ( Figure 1) with < 0 (see Appendix 1). The intuitive explanation behind this can be easily understood. Given skilled labour supply, a rise in the production of domestic manufacturing good will be followed by an excess demand situation for skilled labour. Consequently, there will be a rise in the wage rate of skilled labour reducing rental rate of domestic capital to maintain equilibrium condition. As a result, the manufacturers will be induced to substitute skilled labour by cheaper domestic capital. This process will be continued unless and until the equilibrium will be restored.
The expression of equation 5 gives, = , and substituting this value of in equation 6, one gets: So, this gives us two relationships, say, = ( , ) and = ( , ). Now, = ( ) ℎ < 0. So, = ( ), < 0. As rental rate is increased, the wage rate of unskilled labour falls. The producer has a tendency to substitute capital by unskilled labour in agriculture.
Therefore, the capital-labour ratio will decline. By analogous reason it follows that, = ( ), with < 0. Hence, from equation 6.1, ( ) + ( ) = (6.1.1) Equation (6.1.1) shows the one to one correspondence between rental rate of domestic capital and level of output of domestic manufacturing sector that keeps the domestic capital market in equilibrium. The relationship between the two is positive ( . , > 0) and is depicted by KK curve in Figure 1 (see Appendix 2). This can be explicated by following explanation. With constant supply of domestic capital, whenever there is an increase in the production of manufacturing goods, there will be a higher demand for capital. That will cause an excess demand situation in the domestic capital market leading to a rise in the rental rate of domestic capital. The equilibrium level of are determined by the intersection of KK and SS curves. Once these two unknowns are solved, one can solve the entire system.

Foreign-Capital Inflow and Skilled-Unskilled Wage Gap
As the entire F (foreign investment) is injected into sector T (foreign enclave), the demand for S (skilled labour) and so (skilled wage) will rise in this sector. As S is perfectly mobile within sectors M (domestic manufacturing) and T, hence, S will start to move from sector M to sector T. This process is continued unless and until the wage rate in sector M rises to match to that of in sector T. Due to this movement, the labour-capital ratio declines in sector M causing a decline in marginal productivity of K (domestic capital) followed by a decline in . In a similar manner, as K is perfectly mobile between two sectors, M and A (agriculture), the decline in will induce the owners of K to transfer their capital from sector M to sector A by inducing a decline in unskilled labour-capital ratio in sector A. This results in a decline in the marginal productivity of K in sector A. This movement of K is continued unless equality is attained in the rental rates of K in both the sectors. At the same time, the rise in K-L ratio causes a rise in the marginal productivity of L (unskilled labour) in sector A. It will be reflected through a rise in in sector A. Last, but not the least, the inflow of foreign capital causes an excess supply situation in the foreign capital market, thereby declining (rental rate of foreign capital). Therefore, we can see that foreign-capital inflow causes an increase in both and w. Hence, it can be concluded that partial investment liberalization makes the work force better off and the domestic capital owners worse off.
The impact of foreign-capital inflow on and can be derived from equations (4.1.1) and (6.1.1). By differentiating equation (4.1.1): 3 Equivalently, by differentiating 6.1.1: Here, we consider > 0 as foreign-investment liberalization causes a rise in inflow of foreign capital.
Let us see the impact of investment-liberalization on the gap between and .
We summarize the result in the form of the following proposition. This is followed by a transfer of domestic capital from sector M to sector A. Consequently, the marginal productivity of unskilled labour rises causing a rise in wage rate. This is the indirect effect of foreign investment which will be dominated by that of direct effect.

Foreign-Capital Inflow and Expansion of Three Sectors
Now, we consider the effect of rise in F within different sectors. Equations 4.1.1 and 6.1.1 show that in determination of and the rental rate of capital in sector M, the amount of foreign capital plays a parametric role. In the SS curve (Figure 1), F plays the role of a parameter. If there is a change in demand for capital, the SS curve will shift. This is because, change in foreign capital causes a parametric change in demand for foreign capital. In fact, a rise in F is followed by a leftward shift of SS curve. The reason is that, increase in F calls for larger amount of skilled labour in sector T. The skilled labour then will be transferred from sector M to sector T and consequently, the volume will fall. This leads to, < 0. In other words, < 0 (see appendix 4). In figure 1, the increase in F is shown by a leftward shift of the SS curve and the equilibrium point moves leftward. But volume of increases, i.e., > 0 (see appendix 5). It has already been found that an increase in in sector T leads to a transfer of skilled labour from sector M to sector T. Therefore, sector M releases capital, which is transferred to sector A, and so, increases (i.e., > 0, or, > 0).
We summarize these results in the form of proposition 2 as follows.
Proposition 2: Foreign-capital inflow causes an expansion of the foreign enclave and the agricultural sector, though it reduces the output of domestic manufacturing sector.
The reasons behind this proposition can be given as follows. Investment liberalization causes a rise in the capital stock in sector T and transfer of some of the skilled labours from sector M to sector T.
Consequently, sector T expands and there is a transfer of domestic capital from sector M to sector A.
Hence, sector A also expands with a contraction in sector M.

Foreign-Capital Inflow and Welfare in Absence of Tariff
To find out the impact of foreign-capital inflow on the social welfare of the economy with imposition of no tariff, we take the social welfare function of the following form: Here, it can be noted that the manufacturing sector is relatively capital intensive than the agricultural sector. This implies that the ratio of domestic capital to skilled labour, required to produce one unit of manufacturing sector, is higher than the ratio of domestic capital to skilled labour. In other words, − < 0. Again, < 0, and so, − > 0. On the other hand, as, < 0, so, > 0, and finally, > 0.
The following proposition is immediately derived from the above result.
Proposition 3: Foreign-capital inflow in a small open economy makes it better off in terms of social welfare in the absence of tariff.

Concluding Remarks
The main objective of the present exercise is to develop a model to find out the impact of foreign-capital inflow on welfare of a small open economy, with agriculture, domestic manufacture and foreign enclave being the three sectors of the economy. Foreign capital is specific to only foreign enclave. The work finds that though the inflow of foreign capital increases the skilled-unskilled wage-gap and declines the rental rate of domestic capital, the entire labour force becomes better off in the absence of any type of 5 As the budget constraint of the economy, given that foreign capital is fully repatriated, gives: * + * + = * + * + − . Then by differentiating both sides: * + * + = * + * + − − .
6 * + * + = + + + ( s national product at market price is equal to the national product at factor cost). Hence, * + * + = + + + + . 7 It may be noted that the change in social welfare in terms of agricultural product is nothing but the change in net national product at factor cost (no change has taken place in the endowments of domestically owned factors of production). market distorting policies adopted by the state. It implies that, in a small open economy, foreign direct investment is beneficial when the market is allowed to work freely. This is a departure from the traditional model of Brecher-Alejandro (1977) which says that, in a free market system, the introduction of investment liberalization leaves the level of national welfare unchanged in the absence of tariff. Here, we see that, the instillation of the sector-specific foreign capital makes the country better off in the absence of tariff, whereas, the work of Beladi and Marjit (1992a) has shown that Brecher-Alejandro's (1977) proposition remains valid when sector-specific foreign capital is introduced. Our model shows that an economy, experiencing an expansion of export sector and a contraction of import-competing sector, in fact enjoys a welfare gain. The result is something new in the context of existing literature in this field. In vector matrix form we can write it as, Applying Cramer's rule (as Δ = 0) we find, As, , > 0, ℎ < 0, , < 0 ( ̂ < 0). Now, = − , so, < 0, or, ̂ < 0.