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A model of the labor surplus dualistic economy in the notions of J.C.H. Fei and G. Ranis Krumins, Juris Talivaldis 1967

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A MODEL OF THE LABOR SURPLUS DUALISTIC ECONOMY IN THE NOTIONS OF J.C.H. FEI AND G. RANIS b y JURIS TALIVALBIS KRUMINS B.Sc, Uni v e r s i t y of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT 0F THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department of ECONOMICS We accept t h i s t hesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July, 1967 In p re sen t i ng t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permiss ion f o r ex ten s i ve copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r ep r e s en t a t i v e s , It i s understood that copying o r p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be a l lowed wi thout my w r i t t e n pe rmi s s i on . Department of Economics  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada i i ABSTRACT The dynamic dual sector model of t h i s thesis i s constructed i n the notions of John CH. F e i and Gustav Ranis as expressed i n t h e i r book, Development of the Labor Surplus Economy.1 The construction takes the form of three stages of balanced economic growth which are demarcated by the value of the a g r i c u l t u r a l marginal product of labor; stage one i s concerned with the time period when th i s equals zero, stage two when i t l i e s between zero and the r e a l a g r i c u l t u r a l wage, and stage three, which i s omitted, when i t i s equal to the r e a l a g r i -c u l t u r a l wage. The model shows that i n the large labor surplus type of underdeveloped economy, successful development i s more a question of domestic p o l i c y , rather than foreign aid or trade. The d i s t i n c t i v e features of the type of economy analyzed are "disguised" unemployment and i n s t i t u t i o n a l wage i n the a g r i c u l t u r a l sector coupled with a small, growing i n d u s t r i a l sector. The s o l u t i o n f o r development l i e s i n the r e l o c a t i o n of t h i s surplus labor i n the a g r i c u l t u r a l sector to the i n d u s t r i a l sector, with a consequent increase i n p r o d u c t i v i t y per cap-i t a i n the a g r i c u l t u r a l sector, where a smaller percentage of the t o t a l labor force now provides the e n t i r e economy with food and basic inputs. This, then, i s accompanied by an increase i n the i n d u s t r i a l employment and development, the expansion of which depends on the two r e a l resource components, the a g r i c u l t u r a l "surplus" and a g r i c u l t u r a l labor force i i i which are provided by the agricultural sector. The essential feature of the industrial sector i s seen to be the absorption of surplus labor from the agricultural sector, which in turn results in the expansion of the industrial output and economic growth. i v TABLE OF CONTENTS Page ACKNOWLEDGEMENTS . . . . . v INTRODUCTION 1 Chapter I. A MODEL OF THE IABOR SURPLUS DUALISTIC ECONOMY — STAGE I 4 The A g r i c u l t u r a l Sector The I n d u s t r i a l Sector I n t e r s e c t o r a l Relations I I . A MODEL OF THE LABOR SURPLUS DUALISTIC ECONOMY — STAGE I I 22 CONCLUSION 28 FOOTNOTES 30 BIBLIOGRAPHY 32 Appendix I. THE MODEL — STAGES I AND I I 34 Assumptions (Stage I) The Model (Stage I) Assumptions (Stage II) The Model (Stage II) I I . INDUSTRIAL SECTOR ANALYSIS -.'41 I I I . MODEL AND ANALYSIS OF THE INDUSTRIAL SECTOR WITH CONSUMP-TION 50-Assumptions Model Analysis V ACKNOWLEDGEMENTS P h i l i p A. Neher, B.A., Ph.D. — T h e s i s Supervisor Roger P. Mendels, B. Com., M.A., Ph.D. — T h e s i s Advisor David J . Donaldson, B.A., M.A., Ph.D. — T h e s i s Advisor 1 INTRODUCTION The problem of economic development has, within the l a s t twenty-f i v e years, received a l o t of attention. The Harrod-Domar theory of economic growth i s generally considered to be one of the most important i n i t i a l contributions. More recently, the contributions of Duesenberry, Tobiri, 4 SoloW, 5 and Kaldor 5 have tackled the problem, but p r i m a r i l y with regard to the developed economy. Leibenstein i s an exception to t h i s r u l e , but does not d i f f e r from the above economists i n that the method of analysis i s p r i m a r i l y concerned with one output and, thus, a one SeC-cs tor economy. The one sector approach i s also adopted by Smithies, who r e l a t e s empirical research with n e o - c l a s s i c a l growth theory and, by the use of the Cobb-Douglas production function, analyzes the properties of a s i n g l e sector model. The r e s u l t s of t h i s analysis are consistent with the theory developed herein with regard to the i n d u s t r i a l sector. Jor-genson 9 tackles the problems of a dual sector closed economy — a n a g r i -c u l t u r a l and an i n d u s t r i a l sector — but omits the stage of analysis that pertains to a condition of redundant labor (marginal product of labor equals zero) and regards the rate of population increase as an endogenously determined parameter. F e i and Ranis, whose work was pre-ceded by that of L e w i s 1 0 and Nurske, 1 1 deal with t h i s problem at great length, and i t i s the purpose of t h i s paper to construct a dynamic model i n the notions of t h e i r text. Development of the Labor Surplus Economy.1 2 The equilibrium growth model i s constructed in three stages. Stage I, initiated at time t = 0, is concerned with the period of development when the marginal product of agricultural labor i s equal to zero. Stage II i s initiated at a time t = t' and is concerned with that period of development when the marginal product of agricultural labor i s greater than zero, but less than the real agricultural wage. Stage III i s initiated when the marginal product of agricultural labor i s equal to the real agricultural wage. This stage i s omitted because, in essence, the dual nature of the economy disappears and, for the purposes of a dynamic model, can be analyzed in terms of one sector. As stated above, this type of analysis has been adequately covered. CHAPTER I A MODEL OF THE LABOR SURPLUS DUALISTIC ECONOMY — STAGE I 4 The Agricultural Sector I n i t i a l l y , the economy i s assumed to be overpopulated to the degree that redundant labor exists; put another way, the marginal pro-duct of labor i s equal to zero. Thus, before development, population growth, combined with the fact that the amount of land is assumed to be fixed, results in more and more intensive cultivation, with the conse-quent increase i n the effect of diminishing returns. Before development of the closed economy is initiated, there i s no reason to suppose that, in the long-run, total agricultural output (Y) increases. At a time t = 0, the developmental process is assumed to begin, and the application of new techniques makes i t possible for agricultural output to increase in the long-run. The cost of the imple-mentation of these techniques i s , for the purposes of this analysis, assumed to be negligible and is thus ignored. This is not unreasonable in light of the fact that the economy considered i s underdeveloped and has at i t s disposal the whole "spectrum of techniques" evolved by the more developed economies, which can be adopted at virtu a l l y no cost. It may reasonably be assumed that the rate of technological change (y) can be adjusted and, i n fact, used as an exogenous policy variable to maintain balanced growth for the purposes of this model. The magnitude of y for balanced growth conditions to pertain i s quite specific (see p. 16). It might, however, be argued —what are 5 the advantages of balanced growth i f i t forgoes a g r i c u l t u r a l output which could be obtained at no extra cost? Recalling that balanced growth i n the context of t h i s model r e f e r s to a process of i n d u s t r i a l i -zation, i t follows that i f there i s no upper l i m i t to y, obviously there i s no incentive to i n d u s t r i a l i z e . Assuming that underdeveloped economies do have the incentive to i n d u s t r i a l i z e , then there must e x i s t constraints l i m i t i n g the magnitude of y. Whether t h i s l i m i t i s l a r g e l y determined by the cost of innovation or the time required f o r i t s imple-mentation i s debatable. For the purposes of t h i s model, the l a t t e r i s regarded as the major determinant. In other words, the " l i m i t " to y i s given by time dependent v a r i a b l e s , such as education and crop maturation periods (rather than c o s t ) , and because of t h i s l i m i t , the concept of balanced growth can u s e f u l l y be applied. Thus, the term "exogenous p o l i c y v a r i a b l e " applied to y i s taken as being adjustable at no cost within the range (regarded as s u f f i c i e n t ) determined by the l i m i t . Assuming that land and labor are the only a g r i c u l t u r a l production inputs, then, because the amount of land i s f i x e d and the marginal pro-duct of labor i s zero under conditions of labor surplus, the a g r i c u l t u r a l production function can be written as: Y = f ( Y ( Q ) , t, Y ) or e x p l i c i t l y : ( 1 ) 6 Because a redundant a g r i c u l t u r a l work force e x i s t s , the notion of a competetive labor market can be ruled out. Thus, i t can be f a i r l y assumed that the r e a l a g r i c u l t u r a l wage (W ), measured i n terms of a g r i -a c u l t u r a l goods, i s determined i n s t i t u t i o n a l l y and remains constant. This wage, by d e f i n i t i o n , i s the t o t a l a g r i c u l t u r a l output at time t = 0 d i -vided by the t o t a l labor force (P) at time t = 0, and need not n e c e s s a r i l y be regarded as a " p h y s i o l o g i c a l minimum" wage. • C O ) A l t e r n a t i v e l y , t h i s can be written as: (0) a _ N ' = — = constant (3) P(0) P a where the a g r i c u l t u r a l money wage (w ) divided by t h e r p r i c e index of a g r i c u l t u r a l goods (p ) i s equal to a constant. At the time t = 0, an i n d u s t r i a l sector i s established and the redundant workers of the a g r i c u l t u r a l sector are relocated to t h i s sec-to r . As t h i s r e a l l o c a t i o n proceeds, the a g r i c u l t u r a l output becomes more than enough to cover the wages of the workers within the sector and a surplus i s produced which F e i and Ranis r e f e r to as the t o t a l a g r i c u l -t u r a l surplus (TAS). 1 3 This surplus i s used to pay the wages of the workers i n the i n d u s t r i a l sector, the whole output of which i s then re i n -vested. I t i s assumed that the i n d u s t r i a l entrepreneur does not consume and that the workers i n both sectors do not save. These assumptions 7 become more r e a l i s t i c i f the concept of the "dual" landlord, as envi-sioned by F e i and Ranis, i s accepted. The dual landlord ( i n i t i a l l y the r u r a l landlord) who, by assumption, receives exactly the same wage for the same work as the a g r i c u l t u r a l worker, i s regarded i n t h i s analysis to play the entrepreneurial r o l e i n both sectors. C o l l e c t i v e l y , these landlords are responsible for the establishment of the i n d u s t r i a l sec-tor and ensuring the r e a l l o c a t i o n of a g r i c u l t u r a l labor (A) to the i n d u s t r i a l sector at a rate that i s compatible with the concept of b a l -anced growth. (Balanced growth can be interpreted as keeping the average a g r i c u l t u r a l surplus (AAS), which i s defined as the t o t a l a g r i c u l t u r a l surplus divided by the number of i n d u s t r i a l workers (M), constant and equal to the r e a l a g r i c u l t u r a l wage.) The regulating body of d u a l i s t i c landlords can be termed the "government", as long as i t i s c l e a r l y under-stood what, for the purposes of t h i s a n a l y s i s , the r o l e of government i s . The t o t a l a g r i c u l t u r a l surplus (TAS) i s defined as: T o t a l A g r i c u l -t u r a l Output minus To t a l A g r i c u l t u r a l Wage B i l l , or: TAS = Y (0) W A (4) a The I n d u s t r i a l Sector On establishment of the i n d u s t r i a l sector, the r e a l l o c a t i o n of the redundant a g r i c u l t u r a l workers (assume at no cost) i s as rapid as possible i n order that the growth of the TAS be as rapid as possible. I t i s t h i s 8 TAS that " f u e l s " the i n d u s t r i a l sector, and the more " f u e l , " the l e s s i s the time required to reach the desirable goal of non-redundancy i n the a g r i c u l t u r a l sector. The t o t a l output of the i n d u s t r i a l sector (X) i s given by the l i n e a r and homogeneous Cobb-Douglas production function, which in c o r -porates two inputs, c a p i t a l (K) and labor (M), and a rate of technolog-i c a l increase (A) which i s neutral i n the Harrod and Hicksian sense. Thus, f o r any point i n time t greater than zero, i t i s assumed that the production function i s subject to constant returns to scale. The above i s equivalent to s t a t i n g that i n d u s t r i a l output i s exhausted by factor payments to the i n d u s t r i a l entrepreneurs and workers. Thus write: X = e K M ( 5 ) where 0 < a < 1. The p a r t i a l d e r i v a t i v e of i n d u s t r i a l output with respect to indus-t r i a l labor determines the r e a l i n d u s t r i a l wage (^ x), which i s measured i n terms of i n d u s t r i a l goods. I t i s the t o t a l i n d u s t r i a l wage b i l l (or share of output accruing to labor) that i s traded f o r the TAS. Thus, i t follows that the i n d u s t r i a l workers do not consume or save i n d u s t r i a l goods, but consume i n d i v i d u a l l y the same "basket" of a g r i c u l t u r a l goods as t h e i r a g r i c u l t u r a l counterparts, or: Y W = W = = constant (6) 3 X F(0) 9 As long as the r e a l a g r i c u l t u r a l wage remains constant, the r e a l indus-t r i a l wage remains constant, because the supply of labor to the indus-t r i a l sector i s i n f i n i t e l y e l a s t i c as long as there e x i s t s a redundancy of a g r i c u l t u r a l labor ( i . e . , marginal product equals zero). The whole process can best be v i s u a l i z e d i n terms of the " d u a l i s t i c " landlord sending a worker from h i s community to b u i l d a road rather than putting him to work i n the f i e l d s , the worker receiving the same return for h i s labor. The equilibrium r e a l wage Wx f o r the manufacturing sector can thus be given by: w | f = ( l - c r ) f = W = (7) 6M M x p r a where w denotes the money wage and p , the p r i c e index of a g r i c u l t u r a l x a goods. The r e a l wage f o r the a g r i c u l t u r a l sector i s given by: w W = — = constant ( r e c a l l equations #2 and #3) a p r a where w i s the a g r i c u l t u r a l money wage. Thus, when the labor market i s 3. i n equilibrium: w w ~r = zr •  • (8) P a P a i . e . , the money wage i s equal i n both sectors. The r e a l i n d u s t r i a l wage i n terms of i n d u s t r i a l goods i s defined as: 10 w W = — .. (9) x p x where p x i s the p r i c e index of i n d u s t r i a l goods. The equilibrium con-d i t i o n being that the r e a l wages of both sectors be equal, i t follows that: i . e . , the terms of trade remain constant under conditions of equilibrium growth. The share of manufacturing output that accrues to c a p i t a l i s assumed to be invested. Thus, r e c a l l i n g that the TAS i s traded f o r the output accruing to labor and the r u r a l (or dual) landlord receives the share to c a p i t a l , a further assumption i s made that both these shares are invested. In other words, gross investment i s assumed to be equal to the t o t a l out-put of the i n d u s t r i a l sector, e.g., lathes are used to produce lathes which, i n turn, are used to produce more lathes. (This l a s t assumption i s dropped i n Appendix I I I without serious consequences to the an a l y s i s , the net r e s u l t being that c a p i t a l accumulation i s decreased and the process of development slowed down.) Net c a p i t a l accumulation (K) i s defined as gross investment (I) l e s s depreciation, where depreciation (calculated by the dec l i n i n g balance method) i s a constant (n) of c a p i t a l stock (K). Thus write: 11 and I = X (12) Equations #5, #7, #11, and #12 are solved i n Appendix II to give the timepaths and rates of increase f o r the variables —- c a p i t a l stock, manufacturing labor force, and manufacturing output — i n terms of the parameters, a and A, and the constants, y^Q) and P ^ . I t i s determined that: K = K(0)e"*e where: W x 1-a (be - nt q-1 o (13){A2.15} ( 0 ) R e c a l l equation #6: W = W = -p - = constant X A P ( 0 ) I t can be seen that unless an i n i t i a l amount of c a p i t a l ( K ^ ) , no matter how small, i s made a v a i l a b l e , the amount of c a p i t a l stock remains zero through a l l time. This can presumably be procured by forced savings or an i n i t i a l endowment of for e i g n a i d . The dominating term of the equation A_ i s governed by the p o s i t i v e constant a; thus, the greater the degree of te c h n i c a l progress (A), the more rapid i s the growth of c a p i t a l . The de-p r e c i a t i o n constant (n) acts as a brake on the growth of c a p i t a l and becomes r e l a t i v e l y l e s s important with time. R e c a l l i n g equation #7, i t can be seen that the greater the value of a, the smaller i s the demand for labor, and consequently, the growth of c a p i t a l i s l e s s rapid. (Put another way, the greater the share accruing to c a p i t a l , the lower the 12 rate of labor absorption — s e e equation #18.) The time path of i n d u s t r i a l labor force i s given by: -1 a . .(14){A2.16} M = Ke W x 1-0 which can be interpreted., i n a s i m i l a r fashion noting the r e i n f o r c i n g e f f e c t of exponential e Writing equation #14 as: K M W x l-o ^ - ^ t a . e where W x 1-0 = constant (by equation #6), an important property of the model i s r e a d i l y observed — - t h e f a c t that the c a p i t a l per worker decreases exponentially as e of F e i and Ranis, who state: This i s consistent with the theory Under our assumption of the constancy of the r e a l wage, i t should be noted that the phenomenon of " c a p i t a l shallowing" — a reduction i n the c a p i t a l - l a b o r r a t i o — follows r i g o r o u s l y as long as innovations are not very labor saving. l t f This can be seen to apply to a neutral rate of technological increase as given by the Cobb-Douglas function. Having solved f o r the time paths of c a p i t a l stock and manufacturing labor force, the time path f o r manufacturing output can be determined by the use of the production function or by r e c a l l i n g equation #7 and sta t i n g that: X = M W x 1-a (15) 13 This demonstrates the property that the output per capita remains con-stant with respect to time. A l t e r n a t i v e l y , t h i s can be written as: X* = M* (16) dX 1 • „. dM 1 where: X dT ' X ' dt * M That i s , the rate of increase i n manufacturing output i s equal to the rate of increase i n the s i z e of the manufacturing labor force. Assuming a modest value of K* within the region of the i n i t i a l time period, say 0.01 per annum, and generally a c c e p t e d 1 5 values f o r X and a, i n the order of 0.02 and 0.35 per annum re s p e c t i v e l y , rates of t o t a l i n d u s t r i a l output increase and labor absorption of approximately 7% per annum i s obtained. Although the rate of c a p i t a l accumulation plays a r e l a t i v e l y small part i n the i n d u s t r i a l i z a t i o n process i n i t i a l l y , i t s exponential time dependence property (see equation .#17) ensures that i t gains i n importance, and, depending upon the time period involved, the rate of c a p i t a l accumulation can become the dominant fa c t o r governing the rate of i n d u s t r i a l i z a t i o n . This i s consistent with the "success case" (Japan) discussed by F e i and Ranis: We thus see, as our theory an t i c i p a t e d , that innovations can play an important r o l e i n the labor absorption process. In the early years they accounted f o r the l i o n ' s share (around 80 percent) of the t o t a l growth of the i n d u s t r i a l labor force i n Japan, with c a p i t a l accumulation playing a r e l a -t i v e l y minor r o l e (around 20 percent). Over time, •14 however, there i s i n evidence a d e f i n i t e tendency for the r e l a t i v e contributions of these two forces slowly to reverse themselves. 1 6 S i m i l a r l y , from equation #13, the rate of c a p i t a l stock accumula-t i o n (K*) can be determined: o-l : K* = e° x l-o a - n (17) K* i s thus observed to be i n v e r s e l y governed by the same exponential term that applies to the rate of c a p i t a l shallowing. The r e l a t i o n of K* and M* (and thus to X*) i s given by equation #A2.19 i n Appendix I I . X* = M* = ~ + K* (18) {A2. or the rate of c a p i t a l accumulation i s equal to the rate of increase i n the i n d u s t r i a l labor force (or i n d u s t r i a l output) minus the constant term ^. Thus, the greater the rate of increase i n technology and the greater the demand for labor (see equation #7), the greater i s the rate of labor absorption, with respect to the rate of c a p i t a l accumulation, into the i n d u s t r i a l sector. R e c a l l i n g that the supply of labor i s i n f i n i t e l y e l a s t i c ( i t can be withdrawn without a f f e c t i n g the t o t a l a g r i c u l t u r a l output) and that new techniques can be adopted at no cost, i t might at f i r s t seem that there i s no l i m i t to the rate of i n d u s t r i a l output and population expan-sion. There i s a l i m i t , however, and t h i s l i m i t i s given by the i n t e r -s e c t o r a l r e l a t i o n s that hold f o r balanced growth. 15 Int e r s e c t o r a l Relations The t o t a l labor force (P) i s comprised of the i n d u s t r i a l labor force (M) and the a g r i c u l t u r a l labor force (A). P = A + M ...... (19) I t i s assumed that the growth rate of the t o t a l labor force i s given by the constant (a); thus, the time path i s given by: P = P ( 0 ) e a t ......(20) Having shown that W = W i s a condition of equilibrium or b a l -a x anced growth, i t remains to evaluate the exogenous p o l i c y v a r i a b l e (y) which determines the growth rate of the t o t a l a g r i c u l t u r a l output. Recalling that a l l the i n d u s t r i a l output.is invested, i t follows that the wages of both sectors are provided f o r by the t o t a l a g r i c u l t u r a l output: Y = W A + W M .. (21) a x R e c a l l equation #6: W = W = constant x a 16 — = W = constant P a (22) R e c a l l equations #1 and #20: (#1) Y = Y (0) (#20) P = P (0) at e Thus, the rate of a g r i c u l t u r a l technological increase has to equal the rate of increase i n the t o t a l labor force i n order that the equilibrium (or balanced) growth path i s maintained. Re c a l l i n g that, by assumption, any value of y can be adopted at no cost to the domestic economy, the d u a l i s t i c landlords or government can f r e e l y adjust y to ensure stable and balanced growth. F e i and Ranis define the concept of balanced growth as e s s e n t i a l l y dependent upon the constancy of the r e a l wage i n the l o n g - r u n ; 1 7 thus, t h e i r c r i t e r i o n of balanced growth i s i d e n t i c a l to that of the model. An i n t e r e s t i n g i n t e r s e c t o r a l r e l a t i o n s h i p that can be derived from the above i s that under conditions of balanced growth, the value of indus-t r i a l output accruing to the i n d u s t r i a l labor force has to equal the value of the t o t a l a g r i c u l t u r a l surplus. R e c a l l equation #21: Y = a (23) Y = W A + W M a x 17 Y - W A = W M a x Recall equation #15: M = X 1-g W x Recall equation #10: P = P r a rx Thus: p TAS = p (l-o)X ......(24) 3. X or: TAS* = X* ......(25) The rate of increase in the total agricultural surplus i s equal to the rate of increase in industrial output. Although agricultural labor i s plentiful and rates of technological increase of various magnitudes can be incorporated in the agricultural production function without cost (by assumption), there i s a ceiling to TAS* given by the balance condi-tion that y = a. It is this condition, then, that limits the rate of increase in industrial output and, thus, the rate of labor absorption. Successful development can be stated to prevail when the rate of increase in the total industrial output is greater than the rate of increase in the total agricultural output: 18 i . e • > X* > Y* Unless t h i s holds, a process of " i n d u s t r i a l i z a t i o n " i s bound to f a i l , r e c a l l i n g that X* = M* (equation #16) and that Y* = y = a (equations #1 and #23). The c r i t e r i o n of successful development thus can be seen to be given by the condition that: i . e . , the rate of increase i n the i n d u s t r i a l labor force must be greater than the rate of increase of the t o t a l labor force. This c r i t e r i o n i s i d e n t i c a l to that given by F e i and Ranis i n order that the "success case" f o r development be r e a l i z e d . 1 8 In order to a s c e r t a i n that f u l f i l l m e n t of the conditions given by the model leads to successful development, r e c a l l equation #20: M* > a P = P at P* = a (26) R e c a l l equation #18: M* = - + K* a 19 where ( r e c a l l equation #17) K* = e a 6-1 W x 1-a - n If M* < P* i n i t i a l l y , the exponential term e ensures that eventually: M* > P* = a A l t e r n a t i v e l y : (M*)* = "~ > (P*)* = 0 F e i and Ranis, throughout t h e i r text ( p a r t i c u l a r l y Chapter 3 ) , lay great emphasis on "the achievement of s u b s t a n t i a l p r o d u c t i v i t y increases through innovation without much c a p i t a l accumulation." 1 9 This, they claim, provides "the key.to a successful development e f f o r t . " Thus, although they stress that labor-using (capital-saving) innovation i s one of the determinants of "successful economic development" 2 1 (as defined by t h e i r c r i t e r i o n M* > a), the model demonstrates that t h i s "successful development" can take place by employing neutral ( i n the Hicksian sense) innovation i n the pursuance of a balanced growth time path. Apart from the degree of labor-using bias of innovation that F e i and Ranis maintain i s important to the development e f f o r t , they also attach great emphasis to the i n t e n s i t y of i n n o v a t i o n 2 2 — t h i s , f or the 20 purposes of the model, i s given by the magnitude of A (the rate of increase i n industrial.technology). R e c a l l i n g that the rate of c a p i t a l accumulation i s governed by the exponential term e and that the rate of increase i n i n d u s t r i a l output i s d i r e c t l y dependent upon the rate of c a p i t a l accumulation, i t can be seen that the greater the magnitude of A, the greater the rate of expansion of the i n d u s t r i a l sector and the sooner i s the state of non-redundancy i n the a g r i c u l t u r a l labor force achieved. The smaller the value of a , the l e s s i s the e f f e c t of "diminishing  returns to labor" and, thus, the greater i s the rate of i n d u s t r i a l expansion. F e i and Ranis discuss the " C r i t i c a l Minimum E f f o r t C r i t e r i o n " and state: In other words, the rate of i n d u s t r i a l c a p i t a l accumulation must be large enough, the i n t e n s i t y of innovation high enough, the labor-using bias of innovation strong enough, and the law of diminishing returns to labor weak enough so that t h e i r combined e f f e c t on the demand f o r labor exceeds the population growth r a t e . 2 3 The above c r i t e r i a (with the exception of labor-using innovation), i n addition to t h e i r emphasis of the constant i n d u s t r i a l wage, 2 4 can f a i r l y be stated as the c r i t e r i a of the model thus f a r developed. CHAPTER II A MODEL OF THE LABOR SURPLUS DUALISTIC ECONOMY — STAGE I I 22 At the time t = t ' , the marginal product of the a g r i c u l t u r a l labor force i s no longer equal to zero, but i s s t i l l l e s s than the r e a l a g r i -c u l t u r a l wage. Put another way, the redundant a g r i c u l t u r a l labor force has been absorbed by the i n d u s t r i a l sector, but a condition of labor surplus e x i s t s . The a g r i c u l t u r a l production function must therefore be amended to incorporate a p o s i t i v e marginal product of labor and can be written i n the Cobb-Douglas form: Y = C 2 e Y , t A a (27) ( r e c a l l the quantity of land i s assumed to be fixed) which i s l i n e a r and homogeneous — 0 < a < 1; y' denotes the rate of technological increase. This then changes the form of the TAS function to: TAS = C 2 e Y , t A a - WaA (28) As a r e s u l t of the marginal product of the a g r i c u l t u r a l workers being p o s i t i v e , t h e i r absorption into.the i n d u s t r i a l sector r e s u l t s i n a decrease of t o t a l a g r i c u l t u r a l output. Therefore, although the TAS i s s t i l l increasing, the AAS i s d e c l i n i n g . This r e s u l t s i n a worsening of the terms of trade f o r the i n d u s t r i a l sector because of the r e l a t i v e 23 shortage of a g r i c u l t u r a l , as opposed to i n d u s t r i a l , goods. The e f f e c t of t h i s i s to force up the l e v e l of the r e a l i n d u s t r i a l wage and to v i o l a t e the condition f o r balanced growth. The average a g r i c u l t u r a l surplus continues to decline u n t i l a p h y s i o l o g i c a l minimum value i s reached. Below t h i s minimum value, i t i s impossible to e s t a b l i s h equi-l i b r i u m conditions at any set of r e l a t i v e p r i c e s because of the absolute shortage of f o o d . 2 5 The f i n a l and i n e v i t a b l e r e s u l t of t h i s i s the c o l -lapse of the development e f f o r t . This can, however, be averted i f the conditions f o r balanced growth as applied i n Stage I are enforced during Stage I I , i . e . , the r e a l i n d u s t r i a l wage and the terms of trade remain c o n s t a n t . 2 6 These balanced growth conditions can be preserved by the adjustment of the rate of a g r i c u l t u r a l technological increase (y')> which i s again r e -garded as an exogenous p o l i c y v a r i a b l e and i s subject to the same con-s t r a i n t s as Y« Thus, with the exceptions of the a g r i c u l t u r a l and TAS functions, the equations of the model f o r Stage I I are i d e n t i c a l to those of Stage I, the basic i n d u s t r i a l and i n t e r s e c t o r a l r e l a t i o n s being preserved under conditions of balanced growth. In other words, apart from the above q u a l i f i c a t i o n s , Stage I I , i n model form, i s essen-t i a l l y i d e n t i c a l to Stage I. F e i and Ranis denote the s t a r t of Stage I I by what they term a "shortage point" i n the supply of labor to the i n d u s t r i a l sector — i f . there i s no change i n the technological rate of increase, the supply curve f o r labor takes an upward turn at t h i s point, r e s u l t i n g i n an increase i n the r e a l i n d u s t r i a l wage as previously mentioned.. The 24 "commercialization point" i s reached when the marginal product of agri-cultural labor i s equal to the real agricultural wage. Fei and Ranis, who strongly advocate balanced growth, 2 7 write: Sooner or later, as agricultural productivity continues to increase, the shortage and commerciali-zation points w i l l coincide . . . and phase [stage] 2 i s eliminated. 2 8 To determine the value of the exogenous variable y'> i t is neces-sary to re c a l l the balance growth conditions given by equation #22: (Y/P) = W = constant a Y* = P* Recall equations #27 and #20: (#27) Y = Czey,tAa; .'. Y* = y' +.aA* (#20) P = P ( 0 ) e a t ; . \ P* = a Thus: y' + aA* = a ......(29) It can thus be seen that the turning point at time t = t' from Stage I to II is marked entirely by the agricultural rate of technical progress having to change from the rate y to y' in order that balanced growth conditions be maintained. Unless A* is negative (and this hypothesis can be rejected i f the Cobb-Douglas function i s ruled appli-cable) , that i s , i f the manufacturing sector i s absorbing labor to the 25 degree that the absolute size of the agricultural working force i s being reduced, then the rate of increase in agricultural technology i s less for Stage II than Stage I. Fei and Ranis imply that in order for balanced'growth to be pre-served, the transition from Stage I to II must be marked by a greater rate of increase in agricultural technology: Agricultural productivityvchange may be mainly related to the success in insuring mass participa-tion in the search for indigenous technological change — with relatively l i t t l e need for new capital formation. 2 9 A characteristic feature of this stage of development is that there exists a positive rate of increase in the marginal product of agri-cultural labor (mpp ) —r otherwise, Stage III could never be realized. Recall equation #27: Y - C ^ V 6Y _ y't.a-1 mpPa = = a C 2 e A ••(30) mpp * = (a-l)A* + y 1 cl Recall equation #29: a = Y' + aA* Substituting: mpp * = a - A* ..(31) EL 26 Recalling that P* = a, then i f M* > a, i t follows that A* < a and that mpp * i s p o s i t i v e . In other words, i f the rate of labor absorption i s 3. greater than the rate of increase i n the t o t a l labor force, then the marginal product of a g r i c u l t u r a l labor has a p o s i t i v e rate of increase. (It should be noted that mpp * cannot be negative i f the Cobb-Douglas a Y 11 a function, Y = C 2e A , i s considered applicable.) R e c a l l equation #18: M* = - + K* a From the above, the greater the value of M*, the greater i s the value of mpp * and, thus, the shorter the time required to reach Stage I I I . K* and M* were analyzed f o r Stage I of the model (p. 14), and t h i s analysis i s equally applicable to Stage I I . Thus, depending on the value of M*, mpp * can be stated to be: 3. 0 < mpp^* < a The rate of expansion of the i n d u s t r i a l sector f o r Stage II i s thus seen to be subject to a c e i l i n g given only by the population para-meter a. F e i and Ranis, i t can be r e c a l l e d , discuss the success, stagna-t i o n , or f a i l u r e cases i n terms of whether M* i s greater than, equal to, or l e s s than P* = a . 3 0 I f M* and P* equal a, i t follows that A* = a. Applying the rate of marginal p r o d u c t i v i t y increase as a c r i t e r i o n , i f 27 A* = a, then mpp * i s equal to zero, i . e . , there.is no rate of increase i n the marginal product and "stagnation" r e s u l t s . I t seems rather curious that using the same c r i t e r i o n , the model shows that the rate of increase i n a g r i c u l t u r a l technology i s l e s s f or Stage II than I, whereas F e i and Ranis imply i t should be greater. To conclude t h i s discussion of Stage I I , i t i s s u f f i c i e n t to say that the t r a n s i t i o n from Stage I to II i s marked by a change i n the exogenous p o l i c y v a r i a b l e y t o Y 1 i n order that balanced growth condi-tions be maintained. The time paths f o r the v a r i a b l e s , as solved for i n Stage I, are equally applicable to Stage I I — the e s s e n t i a l l i n k being that the average a g r i c u l t u r a l surplus remains constant throughout. 28 CONCLUSION The t r a n s i t i o n to Stage I I I occurs when the marginal product of labor i s equal to i t s r e a l wage; i n other words, a l l the disguised un-employed labor of the a g r i c u l t u r a l sector has been absorbed by the i n d u s t r i a l sector. In t h i s stage, the workers of both sectors receive t h e i r r e a l wages, which are no longer constant and are equal to the marginal product of the labor force. In essence, the dual nature of the economy disappears and, for the purposes of a dynamic model, can be analyzed i n terms of one t o t a l output function. This i s expressed more p o e t i c a l l y by F e i and Ranis, who write: A f t e r the turning point the a g r i c u l t u r a l sector has f u l f i l l e d i t s c r u c i a l h i s t o r i c a l mission, and the s p o t l i g h t s h i f t s to the i n d u s t r i a l sector. The c h a r a c t e r i s t i c s of development i n the mature economy can thus be most a p t l y discussed i n terms of the growth process of a one-sector i n d u s t r i a l economy. 3 1 As stated i n the Introduction, t h i s paper omits the model and analysis of Stage I I I . The model was constructed to express i n a dynamic mathematical form the notions expressed i n the text e n t i t l e d , Development of the  Labor Surplus Economy. 3 2 The authors, F e i and Ranis, attach great importance to the concept of balanced growth and analyze e m p i r i c a l l y the economic growth of Japan and India with the resultant conclusion: 29 This analysis of the contrasting cases of success [japan] and failure [India] leads us more or less inevitably to the specification of a bal-anced growth pattern as optimal for the achieve-ment of a satisfactory labor reallocation and growth performance in the dualistic economy on a sustained b a s i s . 3 3 Apart from the i n i t i a l amount of capital required, which might be obtained by means of foreign aid, the model, which i s stated in a more rigorous fashion in Appendix I, serves to demonstrate that the underdeveloped economy can cure i t s i l l s domestically by the judicious allocation of i t s resources, this task to be accomplished by the dualistic landlord, or, more r e a l i s t i c a l l y , by proper f i s c a l measures of the domestic government. 30 FOOTNOTES ij.C.H. F e i , and G. Ranis, Development of the Labor Surplus Economy (Homewood, I l l i n o i s : Irwin, 1964). 2R.F. Harrod, "An Essay i n Dynamic Theory," Economic Journal, 49:14-33 (1939); Towards a Dynamic Economics (London: Macmillan, 1948); E.D. Domar, " C a p i t a l Expansion, Rate of Growth and Employment," Econometrica, 14:137-147 (1946). 3J.S. Duesenberry, Business Cycles and Economic Growth (New York: McGraw-Hill, 1958). \ j . Tobin, "A Dynamic Aggregative Model," Journal of P o l i t i c a l Economy,. 63:103-115 (1955). 5R.M. Solow, "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economics, 70:65-94 (1956). 6N. Kaldor, "A Model of Economic Growth," Economic Journal, 67:591-624 (1957). 7H. Leibenstein, Economic Backwardness and Economic Growth (New York: Wiley, 1957); A Theory of Economic-Demographic Development (Princeton: Princeton U n i v e r s i t y Press, 1954). 8A. Smithies, "Pr o d u c t i v i t y , Real Wages, and Economic Growth," Quarterly Journal of Economics, 74:189-205 (1960). 9D.W. Jorgenson, "The Development of a Dual Economy," The Economic  Journal, 71:309-334 (1961). 10W.A. Lewis, "Development with Unlimited Supplies of Labor," The  Manchester School of Economic, and Social:Studies, 22:139-191 (1954). HR. Nurske, Problems, of C a p i t a l Formation i n Underdeveloped Areas (New York: Oxford U n i v e r s i t y Press, 1953). 1 2 F e i and Ranis, op. c i t . 1 3 J b i d . , p. 23. i f I b i d . , p. 97... 1 5 S m i t h i e s , op. c i t . , p. 204. 1 6 F e i and Ranis, op. c i t . , p. 131. 1 7 I b i d . , p. 188. 1 8 I b i d . , p. 112. 1 9 I b i d . , p. 63. 2 0 I b i d . 2 1 I b i d . , p. 97. 2 2 I b i d . 2 3 I b i d . , p. 122.. 2 t tIbid.. p. 124. 2 5 I b i d . , p. 159. 2 6 lb i d . , p. 218. 2 7 I b i d . , p. 185. 2 8 I b i d . , p.. 214. 2 9 I b i d . , p. 217. 3 0 I b i d . , p. 112.. 3 1 Ibid. , p. -267. 3 2 I b i d . , p. 1-287. 3 3 I b i d . , p. 185. 32 BIBLIOGRAPHY Domar, E.D. "C a p i t a l Expansion, Rate of Growth and Employment,11  Econometrica, 14:137-147 (1946). Duesenberry, J.S. : Business Cycles and Economic Growth. New York: McGraw-Hill, 1958. F e i , J.C.H., and Ranis, G. Development of the Labor Surplus Economy. Homewood, I l l i n o i s : Irwin, 1964. Harrod, R.F. "An Essay i n Dynamic Theory," Economic Journal49:14-33 (1939); Towards a Dynamic Economics. London: Macmillan, 1948. Jorgenson, D.W. "The Development of a Dual Economy," Economic Journal, 71:309-334 (1961). Kaldor, N. "A Model of Economic Growth," Economic:Journal,67 :591-624 (1957). Leibenstein, H. Economic Backwardness and Economic Growth. New York: Wiley, 1957; A Theory of Economic-Demographic Development. Princeton: Princeton U n i v e r s i t y Press, 1954. Lewis, W.A. "Development with Unlimited Supplies of Labor," The Manchester School of Economic and -Social Studies, 22:139-191 (1954). Meade, J.E. A Neo-Classical Theory of Economic Growth. New York: Oxford Un i v e r s i t y Press, 1961. Nurske, R. Problems of C a p i t a l Formation i n Underdeveloped Areas. New York: Oxford Un i v e r s i t y Press, 1953. 01gaard, A. Growth, P r o d u c t i v i t y and Relative P r i c e s . Copenhagen: G.E.C. Forlag, 1966. Phelps, E.S. Golden Rules of Economic -Growth. New York: Norton, 1966. Smithies, A. "Productivity, Real Wages, and Economic Growth," Quarterly Journal of.Economics, 74:189-205 (1960). Solow, R.M. "A Contribution to the Theory of Economic Growth," Quarterly Journal of Economicsy. 70:65-94 (1956). Tobin, J . "A Dynamic Aggregative Model," Journal of P o l i t i c a l Economy, 63:103-115 (1955). APPENDIX I THE MODEL —.STAGES I AND II Assumptions (Stage I) The Agricultural Sector 1. There exists a redundant labor force, i.e., the marginal product of agricultural labor (mpp ) equals zero. 2. The real wage paid to the agricultural worker (W ) is institutionally determined and is measured in terms of agricultural goods. 3. The agricultural entrepreneur plays a "dual" role (i.e., also controls the manufacturing sector) and his behavior is characterized by profit maximization. 4. A l l technological change takes place at a rate (y) which is treated as an exogenous policy variable to maintain the constancy of the average agricultural surplus (AAS). 5. Agricultural workers do not save. 6. At time t = 0, the process of development begins and the agricultural output (Y) becomes a function of the rate 35 of technological change and Y ^ . 7. There are only two inputs: land, which i s f i x e d , and labor engaged i n a g r i c u l t u r e (A). 8. The rate of growth of the t o t a l labor force (P) (= A + M) i s a constant (a). The I n d u s t r i a l Sector 9. There are constant returns to scale —- t h i s i s equivalent to s t a t i n g that manufacturing output (X) i s exhausted by f a c t o r payments to labor and to the owners of c a p i t a l (the "dual" a g r i c u l t u r a l entrepreneur). 10. There are diminishing returns to i n d u s t r i a l labor (M) and c a p i t a l (K). 11. A l l t e c h n i c a l change i s neutral i n the Harrod and Hicksian sense and takes place at a constant rate (A). 12. No i n d u s t r i a l output i s possible without some i n i t i a l c a p i t a l stock ( K , ^ ) , however small t h i s may be. 36 13. I n d u s t r i a l workers do not save. 14. The i n d u s t r i a l entrepreneur's (or the " d u a l i s t i c " land-lord's) behavior i s characterized by p r o f i t maximization. 15. Property owners within the i n d u s t r i a l sector do not consume.* 16. The t o t a l a g r i c u l t u r a l surplus (TAS) i s used by the r u r a l ("dual") landlords for the exchange and investment of the share of i n d u s t r i a l output that accrues to the workers i n the i n d u s t r i a l sector.* The Model (Stage I) A g r i c u l t u r a l Sector Y = Y ( 0 ) e Y t . . . . ( A l . l ) ( A g r i c u l t u r a l Production Function) W a Y ( 0 ) p a P ( 0 ) a = W_ = constant ....(A1.2) (Real A g r i c u l t u r a l Wage) TAS = Y / n N e Y t - W A (A1.3) (0) a (Total A g r i c u l t u r a l Surplus) * A l l the manufacturing output i s reinvested by assumptions #15 and #16. -37 Industrial Sector X = e K M ....(Al.4) (Cobb-Douglas Production Function) w % = .'(l-a)J = W = — ....(A1.5) 6M M x p rx (Demand for Labor) W — real industrial wage measured i n terms of indus-t r i a l goods wx — industrial money wage p — price index of industrial goods w — = W ....(A1.6) P a X (Supply of Labor) p — price index of agricultural goods K = I -• nK (A1..7) (Only Industrialists Save) I — gross industrial investment n — constant rate of deprecia-tion of capital X = I (A1.8) (Gross Investment Relation) 38 Intersectoral Relations P = A + M (A1.9) (Total Labor Force) p = p e a t ...(ALIO) •(0)' (Growth of Total Labor Force) p . TAS = p (l-a)X ... ( A L U ) 3 X (Balanced Market Condition) w w a _ _x P P r a *x ...(Al.l2) (Balanced Real Wage Condition) w — agricultural money wage 3. #A1.2 and #A1.5 provide two equations each, thus giving a total of 14 equations — there are 14 unknowns, respectively: X, K, M, I Y, A, P, TAS W , W x a w , w , p , p . x a' *x r a 39 Assumptions (Stage II) 19. The marginal product of the a g r i c u l t u r a l labor force i s no longer equal to zero, but because a condition of labor sur-plus e x i s t s , i t i s l e s s than the r e a l a g r i c u l t u r a l wage. Assumptions #2 through #16 as f o r Stage I. The Model (Stage II) A g r i c u l t u r a l Sector .Y't Aa Y = C 2e r A ...(A1.13) (Linear and Homogeneous Cobb-Douglas Function, 0 < a < 1, where y' i s an exogenous p o l i c y v a r i a b l e and plays the same r o l e as y i n Stage I) TAS = C 2 e Y , t A a - W A ...(A1.14) The other equations are as f o r Stage I. APPENDIX II INDUSTRIAL SECTOR ANALYSIS 41 State: X = e' (A2.1) (Cobb-Douglas Production Function) X — industrial output X — rate of technological i n -crease K — capital M — industrial population l-o — relative share of labor and x = — M Dividing X and K by M and representing output per man = x, capital per man = k: x • • • • (A. 2«- 2) The industrial real wage i s given by the usual marginal productivity condition: — = (l-a)x = W = constant SM x .(A2.3) 42 (1-a) = constant x = constant By equation #A2.2: At . a x = e k Thus: .(A2.4) (Ci — constant) i.e., capital per worker in the industrial sector decreases exponen- t i a l l y as e Net capital accumulation (K) is defined as gross investment (I) less depreciation, where depreciation (calculated by the declining balance or evaporation method) is a constant (n) of capital stock (K). Thus can write: K = I - nK (A2.5) Then, by assumptions #15 and #16, total industrial output i s equal to gross investment (i.e., the rural (dual) landlords invest the share accruing to labor). X = K + nK .(A2.6) 43 or: gross saving = gross investment ..(A2.7) Using the production function to eliminate X, obtain the relation: K + nK = e K M (A2.8) Recall equations #A2.2 and #A2.3: (#A2.2) (#A2.3) (l-a)x = W Xt , a x = e k e A t k° (1-a) = W (A2.9) w.r.t. equation #A2.8, required to find: -e^ *" K° 3 in terms not including M. We have: Xt T,a „,l-a Xt T ra e K M = e K r K , l - a (A2.10) eXt K° K 1' 0 Xt _ e K (A2.ll) From equation #A2.9: W , a x k = it-44 k = W x e (l-o) ...(A2.12) Recall k = — ; substitute equation //A2.11 into equation #A2.10: At 17o .„l-a At v e K M = e K W x . e (l-o) o-l o Substitute this into equation #A2.8: K + nK = e X t K W x At.. . e (l-o) o- l o ...(A2.13) Simplifying the above equation: o-l K + nK = e Xt K At o-l W x l-o 0-1 Let: C = W x l-o Thus can write: K + nK = K C g (A2.14) Equation #A2.14 is the fundamental differential equation for the develop-ment of the industrial sector of a dual sector economy under conditions of labor surplus. To solve equation #A2 .14: Integrating: j ^  = j (C . e° - n)dt K ' A log K = — . e . C - n t + constant Or: K = Ae C . r e - n t A — constant of integration At t = 0: = Ae Thus: Let: 6-1 W x 1-a Substituting: ...(A2. 46 Re c a l l equation #A2.12: M W e (1-a) W x 1-a a -^t a • e (A2.16) Rec a l l equation #A2.3: (l-a)x = W x X = W x 1-a M (A2.17) The time paths of the v a r i a b l e X, K, M can now be plotted f o r various values of the parameters. Re c a l l equation #A2.3: (l-a)x = W x W or: x = x 1-a 47 Taking natural logarithms: lnx = InW - l n ( l - a ) x x* = 0 u * dx 1 where x* = -r— . — dt x but: x* = X* - M* X* = M* ...(A2.18) R e c a l l equation #A2.2: Xt . a x = e k lnx = Xt + a(lnK-lnM) S i m i l a r l y : x* = X + aK* - aM* Or: X* - M* = X + aK* - aM* Re c a l l equation #A2.18: X* = M* 48 Substituting: aM* = X + oK* Or: X* = M* = - + K* a (A2.19) Recall equation #A2.14: K + nK = K C e a-1 where C = W x 1-a Recall: - = K* K Thus: .(A2.20) APPENDIX III MODEL AND ANALYSIS OF THE INDUSTRIAL SECTOR WITH CONSUMPTION 50 Assumptions Assumptions #1 to #14 are as before. Amend assumptions #15 and #16 to read: The TAS i s used for consumption by the r u r a l landlords of the i n d u s t r i a l output that accrues to workers i n the i n d u s t r i a l sector. Model By d e f i n i t i o n , t o t a l i n d u s t r i a l output i s equal to consumption plus gross investment: X = ( l - a ) X + K + nK Or: aX = K + nK i . e . , saving = investment Using the Cobb-Douglas Production Function to eliminate X, the following r e l a t i o n i s obtained: .51 K + TIK = ae At K M 1-a Comparing this to the previous model, the only difference i s a is on the right hand side. Solving for K, the same result is obtained as before: a-1 But now: <j) = -W X 1-a Analysis The effect of this change in <j> i s to decrease K at any t. Having established K, the relations between the variables are as before, the net result being that i t takes a longer time for the labor surplus to be exhausted. Similarly, one can explore a situation where part of the TAS i s invested and part is consumed. 

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