The case for industrialization of an agricultural country

The Case for Industrialization of an Agricultural Country*

By

Md. Anisur Rahman, Dacca, Pak is tan

With 3 Figures

(Received August 25, 1965)

1. Introduction

One of the problems that confront planners in an underdeveloped country, predominantly agricultural and depending heavily on external trade for industrial goods, is whether a move towards industrialization would be wise in view of the fact that the country has been exporting agricultural goods for ages and as such possibly has a comparative advantage over the rest of the world in agriculture.

The present paper offers a rationalization for a planned move toward industrialization in such a country in terms of a simple planning mode] of a type whose utility lies mainly in fixing some general 'guidelines' for the direction of investment in the first stages of outlining a national economic plan. The study shows how, notwithstanding a possible comparative advantage in agriculture, industrialization may bring about a larger growth of the country's real national income out of given resources.

Real national income, as distinct from real national output, is defined as the volume of goods and services over which the country acquires command through the process of production and trade. This excludes exports, and includes instead the volume of imports earned by export 1. For an export-oriented country this gives a better approximation to its level of welfare than a measure of national output as such.

2. The Problem Stated

Imagine an agricultural country producing agricultural goods and exporting a significant part of it. Industrial goods are imported, with little or no domestic production. A central planning authority is to

* A preliminary and explorative version of this work appeared in the Pakistan Development Review, Summer 1964 [5].

1 See D e r k s e n [2] and T i n h e r g e n [6], p. 94. Pakistan [1] and Palestine [3] are two countries which explicitly follow this concept of real nationM income.

Md. A. Rahman: The Case for Industrializatio~ 481

allocate estimated investible resources of the country between the two sectors so as to maximize

Z-~X-~Y-~-(P--I) .E , (l) subject

E s = aX-~-bY~-ciP~-h (supply of exports), (2)

E d-~ c~ P-~ q (demand for exports), (3)

E s -~ E a (balance requirement), (4)

k ( X - - X o ) ~ - ( Y - - Y o ) - ~ S ; X ~ X o , Y • Y o (5) (production-possibility function)

where

Z = real national income at the end of a stipulated plan-period;

X, Y = indexes of agricultural and industrial production respectively, at end of the plan-period, appropriately scaled so that the "social rate of substitution" between the two commodities equals unity;

E = index of the volume of exports (of agricultural goods) at end of the plan-period;

P = expected terms of trade between agricultural and industrial goods at end of the plan-period: defined as the amount of industrial goods that exchanges for a unit of agricultural good (industrial good is chosen as the numeraire) ;

E s, E d = supply and demand respectively for exports at end of the plan-period;

S ~ volume of investible resources available to the country during the plan-period;

X0, Yo = indexes of pre-plan agricultural and industrial production respectively; a, b, cl, %, h, g, and k are constants.

The objective function (1) and relations (2), (3) and (4) are self- explanatory. Relation (5) assumes that all investment made during the plan-period mature immediately as the plan-period ends, not earlier and not later. This enables, first, the volume of resources 'S' available for investment s during the plan-period to be known (estimated) independently of other variables in the model, and secondly, the result of plan-period investment to be expressed independently of the time-distribution of different investment projects during the plan-period. This overlooks the possibility of projects, made during the plan-period, maturing well be- fore the period ends so as to generate additional income and hence saving during the plan-period itself, and also those which may not mature until well after the plan-period ends.

2 I. e., domestic saving plus foreign aid, if any. The latter is nowadays largely a matter of negotiations at the government level and may reasonably be regarded as exogenously given.

482 Md. A. Rahman:

An explicit treatment of the effect of time-priorities of different investment projects on saving and income in view of respective gestation lags would be the most satisfactory procedure theoretically. But in the first stages of drawing a national plan when relative time-priorities of different investment projects and possibly the projects themselves are yet to be worked out, there is pragmatic merit in proceeding with a simpler model as a first approximation.

Let

3. Solution

x ~ - X - - X o , Y = Y - - Y o , p ~ - P - - P o ; (6)

and z = Z - Zo, where Po = pre-plan terms of trade, and

Z0 = X0 ~ Yo (P0 - - 1). Eo -~ pre-plan real national income.

Then (1) may be written as

Z = x - ~ y + p . B - ~ Zo = z -~ Zo.

With Zo independent of the planning-decision to be made, Z will be maximized when z ~ x + y ~- p . E is maximized.

Using (6) rewrite (2), (3) and (5) as (2):

E" = a x -~ b y -~ cl p @ ( a X 1 '~- b Y1 -~- cl Po + h )

= a x -~ b y -J- cl p -]- C, where C = a Xo -~ b Yo -~ Cl Po -~ h,

a known magnitude for the problem; (3):

E d--~ c u p -~ (c~ Po @ q) ---- c~ p -~- D, where D = c~ P0 -~ q,

a known magnitude; (5): k x ~ y = S .

Then we have to maximize

z = x + y ~ p . E , (7) subject to.

a x - ~ by--~-clp--F-C -~ c~p-~- D, (8) and

k x - ~ y = S. (9) From (8) we have

ax Tby - i -C- D

and hence c2(ax + b y + C--D)

E s = E d = c~ p -{- D = (c~ - cl) ~- D.

The Case for Industrialization of an Agricultural Country 483

Hence

p . E -- c2 (ax + b Y-}- C-- -- c~) ~ ~ D (ax + b y + C-- 2 -- c~)

Thus

z : x ÷ y ÷ p . E

c~ (ax-t-by + C - D) ~ _~ = x q - y = (c, - cO ~

D ( a x + b y + C - D ) ( c ~ - c O

Putting y - ~ S - - k x as given in (9), we get

z = ( l - k ) z ÷ s ÷

~_ c 2 [ ( a - k b ) x + b S - k C - D ] ~ D [ ( a - k b ) x + b S + C - D ] (ca - cO ~ + (c~ - cO

This is a function of the second degree in x and will reach its maximum, giving the solution to our planning problem and subject to the constraints imposed therein, a.t either of the following positions:

(i) d z / d x : O ; (ii) x : S / k , y : 0 ; (iii) x : 0 , y : S .

4. A n a l y s i s of t h e S o l u t i o n

Which of the three positions the solution will take depends on values of the various eonstaxits of the model. In what follows a discussion of some possibilities of a more practical interest is presented.

Case 1: ce = co. The country can export any amount of agricultural good at a terms of trade exogeneously given. For example, the planners may expect the pre-plan terms of trade to continue.

Since both

D c 2 1 ( c 2 - c 0 ' and (c2-c02

are 0 when c e ---- c~, we have

c2 + c ? _ 2 c2 ci

z = (1 - -k ) x + Z .

Then the nature of the solution depends entirely on a comparison between k, the production-opportunity cost of agricultural good in terms of industrial good, and 1, the social rate of substitution between the two. All investment will be required to be concentrated in one direction: in agriculture if k ~ 1, and in idustry if k ~ 1.

In practice social rates of substitution -- relative weights attached to outputs in measuring, and planning in terms of, national income are based oi1 actual market prices of some chosen "base period". Abstract-

Zeitschr. L National~konomie, XXVI. Bd., Heft 4 32

484 Md. A. Rahman:

ing from difference between internal and external terms of trade between agriculture and industry, and assuming the base-period terms of trade to continue, the country may be said to have comparative advantage in agriculture if k < 1; for the production-opportunity cost of agricultural good in terms of industrial good in the rest of the world must be no- less-than-unity to sustain the terms of trade at unity. This gives the situation where because of comparative advantage in agriculture a planned move towards industrialization would not be wise a. In line with the classical theory of complete specialization under constant costs we may refer to this as the "classical case".

Case 2: c 2 = o. Perfectly inelastic demand for exports. In this case

and

whence

C 2

(c~ - c l ) ~ - O,

z = (1 --k) x-~-S - D . [(a--kb) x-~-bS-[-C--D],

dz/dx= 1--[k-~ D (a--k b)].

In this case either of the two "corner solutions" would occur, depending on whether d z/dx is positive or negative. The latter depends not on the production-opportunity cost k of agricultural good alone, but also on c 1, a and b. ci, the rate of change in the amount of exports supplied with respect to change in terms of trade, would in general be positive, and so would 'a', the marginal export-propensity with respect to change in production of agriculture, the export-good. On the other hand 'b', the marginal export -- propensity with respect to change in domestic production of import good, would in general be negative 4. Thus in general (a--kb) also would be positive. This means with k > 1, and dz/dx<~o, concentration of all investment in the industrial sector would be dictated. With k < 1, concentration of all investment in agriculture would be warranted if D, the fixed amount of exports demanded, is relatively small; but D can be large enough so as to make dz/dx < o and hence to require expansion of industry alone irrespective of the value of k 5.

a For a "one-period" plan as postulated here. See section 5. 4 Which means part of rise in real income consequent to a rise in industrial

output would be "spent" on agricultural good so that export of agricultural good would fall. Exceptions axe not inconceivable, for example when agricultural good is an 'inferior' commodity; but it has to be 'strongly inferior' to mal~e (a--kb) a negative quantity.

Although higher the export-demand, greater will be the terms of trade and hence p. E ( ~ p . D if % ~ o) with a given export-supply curve; the fall in p. E resulting from a given positive shift in the latter will be greater with a greater demand for exports and c2 ~ o.


Case 3: c 2 ~ o . Negative slope of the export-demand function. In this case

d z / d x = - l - - k ~ 2 c 2 ( a - k b ) [ ( a - k b ) x - ~ b S - ~ C - D ] D ( a - k b ) (c~ - c~) ~ ~ (c~ - cl)

: 1 - - R, where R ---- d ( y : S -- k x) ~ d (p. E) dx dx [given y : S - - kx]

D ( a - - k b ) 2 c ~ ( a - - k b ) [ ( a - k b ) x - ~ b S - ~ C - D ] =-k-

C 2 - - C 1 (C2 - - C i ) ~

The expression R m a y be called the marginal real opportunity cost of agricultural good. This gives the amount of real income foregone by moving along the production-possibi l i ty function k z ~ -y - - - -S to produce an extra unit of industr ial good. I t is a combination of the production- opportunity cost, k and the loss of real income through a change in the country's terms of trade resulting from a unit expansion of agricultural output by shifting resources from industry to agriculture.

Maximization of z occurs at a position where 1 -- R = o, equalizing the social rate of substi tut ion between the two goods with the marginal real oppor tuni ty cost of agricultural good, if this equali ty occurs within bounds of the non-negativi ty constraints on x and y. The sign of the second derivative

2 c~ (a - k b) 2 d ~ z/d x 9" = - - d R/d x --

(c~ - c~) ~

is negative, thus ensuring that this really gives the maximum.

Alternatively, a corner solution may occur at either x -~ o, y -~ S; or at x = S/k, y -~ o.

The three possibilities are i l lustrated diagrammatical ly in figures (1), (2) and (3), nothing that the slope of R (x), given by

-2c~ (a--kb) ~ d R / d x -- ~_=~)2 ~ O .

Z?

J /¢ /,I ~t

A ~

Fig. 1. Solution: x = OM; y ~ M N . k

3 2 *

486 Md. A. Rahman:

Note tha t any of the above poss ibi l i t ies may occur whatever be the value of k. Thus, however smal l k may be, the value of R at x ~ S / k ,

R ~

o At x

Fig. 2. Solution: x ~ O N ~ S / k ; y ~ o

y - ~ 0 may exceed un i ty so tha t s i tuat ion (1) o.r (3) occurs, requi r ing a depar ture from complete special izat ion in agriculture.

I t is poss ible to trace the effect of a change in any of the constants on R and hence on the solution. Perhaps the most interest ing is the effect

R ~

o 2/ .~

Fig. 3. Solution: x ~ O; y ~ O N . k -~ S

of a change in size of p lanned investment S. Note that the value of R at x ~ S / k , y - - - - 0 is given b y

R ( x = S / k ) ~ - k D ( a - k b ) 2 c 2 ( a - k b ) [ _ ~ _ ] c~ - cl (c~ - cl) 2 " Jr" C - - D ,

whence

0 R (x = S / k ) - - 2 c 2 (a - k b) a 0 S (c~ - cl) ~ "-~"


This, in general, would be a positive expression, on the basis of argu- ment already given 6. This means irrespective of the magnitude of k, the size of planned investment S cart be sufficiently large so as to make R (x -~ S/k) ~ 1 and hence require a move away from complete speciali= zation in agriculture. Further, the slope of R (x) being a given constant, S can be large enough to bring about the situation pictured in figure 3 requiring all investment to be concentrated in industry.

5. Multiperiod Planning

The problem analyzed above is for a "one-period plan" as conceived and explained in section 2. In such a plan sectoral differences in saving rates in the economy would not affect the solution, as domestic saving available for plan-period investment is taken as a given datum. This does not hold however if a one-period (short-term) plan is regarded as part of a multiperiod (longterm, 'perspective') plan aiming at maximizing real national income at end of say n 'periods' each conceived as above. In particular, a move towards industrialization may be called for even if in a "one=period plan" such a move were not warranted. This possibility opens up if the rate of saving in the industrial sector, as the proportion of real income saved, is expected to be higher than that in the agricultural sector.

Without entering into a detailed analysis of this situation we can draw upon the result of an earlier work done by the author, to show that even when the case fo~ complete specialization in agriculture is at its strongest for a "one-period" plan, a move towards industrialization may still be warranted for a multi-period plan.

Suppose the pro-plan terms of trade is unity and the planners expect this to continue unchanged irrespective of the supply of its exports. Sup- pose also that k, assumed to be constant throughout the planning horizon, is less than unity so that the country may be said to have comparative advantage in agriculture. We then have the "classical case" as described in section 4 requiring concentration of all investment in agriculture in a one-period plan.

The multi-period plan problem, however, is identical mathematically with the problem of investment allocation examined by the author in [4] 7. As the solution is given therein, with s~ and s e representing the rates of saving in agriculture and industry respectively and se ~ sJk, and the planning horizon sufficiently large, concentration of all investment in industry would be required in an earlier phase of the plan to exploit the higher saving rate in industry, the programme to be switched in favour of agriculture only in a later phase.

6 See Case 2. 7 Except for the presence of tolerance limits to the distribution of income

as postulated in that study; the present problem is equivalent to the case where such tolerance limits are not binding.

488 Md. A. Rahman:

The case for a move towards industrialization in a multi-period plan must be stronger if demand for exports is less than perfectly elastic at the pre-plan terms of trade. If sectoral saving rates were identical, and the various constants in the model were to remain unchanged over time, a move towards industrialization would be required sooner or later in any case. This is because: (a) The multi-period optimum would be given by a succession of one-period optima; for the volmlae of saving in a second plan-period, say, would depend only on real income at end of the first plan-period so that maximization of the latter would maximize the former irrespective of sectoral composition of national output. Thus in the first period one of the three solutions pictured in figures 1, 2 and 3 would occur. (b) If no move towards industrialization is warranted in the first period, we have the situation pictured in figure 2. For the second period the same function R (x) holds if x is defined as increase in agricultural output not over the second plan-period, but since the pre-plan period. The line x ~ S/k (S also defined as cumulative saving since the pre-plan period) would now shift to the right. (c) This would go on as the planning horizon extends, and eventually the line x = S/k, appropriately defined, would be stationed to the right of the intersection point Q where R = 1 (figure 2).

With a sectoral saving rate higher in industry than in agriculture, a move toward industrialization might be required all the more earlier.

6. Conclusion

We may conclude as follows: 1. A comparative advantage in agriculture, if it exists, does not neces-

sarily warrant complete specialization in agriculture in the best interests of an expanding country. The technical rate of substitution between agricultural and Industrial products is only one among several considera- tions that should enter into a decision to keep on specializing in agriculture or to move towards industrialization.

2. The case for keeping on specializing in agriculture is strongest if the expected demand for exports of agricultural products from the country is perfectly elastic at a terms of trade favourable to agriculture. Even in this case, with a long-term multi-period plan, concentration of investment in agriculture throughout the plan-period is not necessarily the best policy if rate of saving in industry is higher than that in agriculture.

3. With a downward falling export demand function for agriculture, even in a short run one-period plan, a move towards industrialization may be warranted depending on the relative values of the 'constants' of the planning model. These values can even be such as to call for a halt to agricultural expansion altogether and concentration of all investment in industry.

4. With the export demand function falling downward the volume of resources planned for investment has a significant role in dictating the direction in which expansion should be planned. Greater the volume


of investment, i.e., faster the rate of growth of real national income planned, stronger is the case for industrialization in a one-period as well as in a multi-period plan. This inc identa l ly has interes t ing bear ing on flows of large foreign aid from advanced to underdeveloped countries.

R e f e r e n c e s

[1] Central Statistical Office, Pakistan, Pakistan Statistical Year Book, 1957, p. 201.

[2] J. B. D. D e r k s e n : International Comparisons of Real National In- come: an International Survey, Income and Wealth Series 1, Bowes and Bowes, Cambridge.

[3] P. J. L o f t u s : National Income of Palestine, 1945, Jerusalem 1948. [4] M. A. R a h m a n : Regional Investment Allocation, Quarterly Journal

of Economics, LXXVII (1963), pp. 26--39. [5] M. A. R a h m a n : The Operational Logic of Planning for Industriali-

zation, Pakistan Development Review, Summer 1964. [6] J. T i n b c r g e n and H. C. B o s : Mathematical Models of Economic

Growth, McGraw Hill 1962.

Address of author: Md. Anisur R a hm an, Reader in Economics, University of Dacca; Dacca-2, East Pakistan.

The case for industrialization of an agricultural country

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