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Volume 3, ISSUE1/2012 - Review of Applied Socio-Economic ...

Volume 3, ISSUE1/2012 - Review of Applied Socio-Economic ...

ISSN: 2247-6172 ISSN-L:

ISSN: 2247-6172 ISSN-L: 2247-6172 Review of Applied Socio- Economic Research (Volume 3, Issue 1/ 2012 ), pp. xxx-xxx URL: http://www.reaser.eu e-mail: editors@reaser.eu labor required for this production is not available in region A. To attain points on the constraint L A L B other than P factor prices should differ. So a first observation is noticed relevant to the regional problem and this indicates national production at levels (point Q) below the maximum attainable as defined by the economy's production possibility frontier A X B Y (see also Fig. 2). Suppose production takes place at point Q along L A L B with A producing A 2 A 2 and B producing B 2 B 2 . Production at this point assumes that factor prices are free to vary so that markets could clear with the appropriate factor price differentials created automatically. If factor prices are decided at a national level, while the labor market is assumed to clear in the region of high production activity (that is producer A, employing all its region's available labor, can still produce at the A 2 A 2 level), producer B cannot remain anymore on the level of B 2 B 2 production. Using the rest of available capital he can only produce along the horizontal line through Q and at a point of tangency of an isoquant and an isocost line. This will be point S where the isocost at this point has the same slope with producer's A isocost at point Q, taken the slopes of isocosts to represent the marginal rates of technical substitution. Unemployment then of the amount QS in region B will be the result of national wage fixing while the national production will be reduced even further, as indicated by point S in the economy's output possibility plane of Fig. (2). So the two main features of the Y P R Q S O Figure 2: Labour immobility and output X regional problem derived from the above geometric analysis, and which are common to every economy with various regions with a differential degree of development, are indicated to be production below the economy's maximum possibilities and a persistent rate of unemployment in its less developed regions. 3. Fiscal policy and the regional problem Up to now no mention was made about factor price subsidization and more generally on the role of fiscal policy for regional development. This is the next task. Given that labor is assumed to be immobile, unemployment in a region has been suggested to be cured by subsidizing it. This will become clear by developing a powerful theoretical argument attributed to Leif Johansen [5]. He has further indicated the inappropriateness of fiscal policy in providing regionally discriminatory subsidies to capital, a factor that is considered, due to its mobility, to be common to all regions. 3

ISSN: 2247-6172 ISSN-L: 2247-6172 Review of Applied Socio- Economic Research (Volume 3, Issue 1/ 2012 ), pp. xxx-xxx URL: http://www.reaser.eu e-mail: editors@reaser.eu Johansen's argument is developed within a linear programming framework where he assumes the existence of two regions (A and B) each one involved in two production processes, and each one employing two regionally-specific but industrially mobile factors and another factor which is assumed to be common to both regions (that is a perfectly mobile factor). This is of course a more general case than the geometric formulation presented earlier. The notation is as follows: x 1, x 2 : the outputs of the two production processes in Region A. y 1, y 2 : the outputs of the two production processes in Region B. V 1 ,V2: the total amounts available of the two regionally specific factors in Region A. W 1 , W 2 : the total amounts available of the two regionally specific factors in Region B. F: the total amount available of the common factor (a factor that is not tied to any particular region). a ij : amount of the ith resource of Region A used in the jth production process in Region A. bij: amount of the ith resource of Region B used in the jth production process in Region B. g 1 , g 2 : amounts of the common factor F used in the two production processes in Region A. h 1 , h 2 : amounts of the common factor F used in the two production processes in Region B. In linear programming analysis x 1 , x 2 , y 1 , y 2 , are the choice variables of the programme and a ij , b ij , their corresponding coefficients. The given information on the availability of resources in each region introduces the following constraints: a 11 x 1 + a 12 x 2 ≤ V 1 a 21 x 1 + a 22 x 2 ≤ V 2 b 11 y 1 + b 22 y 2 ≤ W 1 (1) b 11 y 1 + b 22 y 2 ≤ W 2 g 1 x 1 + g 2 x 2 + h 1 y 1 + h 2 y 2 ≤ F while the set of nonegativity restrictions which rules out production of negative outputs is: x 1 , x 2 , y 1 , y 2 ≥ 0 (2) An essential ingredient of the linear programme is also the objective or policy function. This is taken to be the maximization of income derived from the various production processes, i.e., R = P 1 x 1 + P 2 x 2 + Q 1 x 1 + Q 2 x 2 (3) where the P’s and Q’s are the product prices. While the analysis is confined to only two regions and two production processes it can very well be extended to an arbitrary number of regions and processes (as well as resources) in which case the maximand will be the national income. The optimal solution to the above problem will indicate the amounts of output to be produced. To find the accounting (or shadow) prices (as are defined in linear programming) of the resources involved in an optimal solution one needs to consider the dual programme. If the choice variables of the dual are called r 1, r 2, s 1 , s 2 , u, and the rules of transformation are applied to the primal (1) to (3) the dual programme takes the form: Minimize R* = r 1 V 1 + r 2 V 2 +s 1 W 1 + s 2 W 2 + uF (4) Subject to r 1 a 11 + r 2 a 21 + ug 1 ≥ P 1 r 1 a 12 + r 2 a 22 + ug 2 ≥ P 2 s 1 b 11 + s 2 b 21 + uh 1 ≥ Q 1 (5) s 1 b 21 + s 2 b 22 + uh 2 ≥ Q 2 and r 1 , r 2 , s 1 , s 2 , u ≥ 0 (6) 4

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