FOR MICHAEL SMITH ONLY

Primary Products and Economic Growth: An Empirical Measurement Author(s): Edward J. Chambers and Donald F. Gordon Source: Journal of Political Economy, Vol. 74, No. 4 (Aug., 1966), pp. 315-332 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/1829150 Accessed: 09-03-2017 03:54 UTC

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THE JOURNAL OF

POLITICAL ECONOMY

Volume LXXIV AUGUST 1966 Number 4

PRIMARY PRODUCTS AND ECONOMIC GROWTH

AN EMPIRICAL MEASUREMENT*

EDWARD J. CHAMBERS AND DONALD F. GORDON

University of Washington and University of Rochester

NE of the major issues in devel- opment economics is whether

dependence on the export of one or a few primary products-a charac-

teristic of less developed economies-

tends to promote or retard the economic

development of these countries (cf. Bald-

win, 1956, 1963; Caves and Holton, 1959, pp. 41-47 and chap. iv; Seers, 1959; Levin, 1960; North, 1961, esp. chap. i;

Swerling, 1961; Cairncross, 1962, pp. 214-28; Watkins, 1963). It is alleged on the one hand that through various

multipliers, linkages, demonstration, and leakage effects, such primary-product exports act positively; and it is argued, on the contrary, that through insta-

bilities associated with fluctuations in

* The authors wish to express their thanks for financial support received from a grant by the Ford Foundation to the Institute for Economic Research at the University of Washington. Earlier versions of this paper were discussed at conferences on quanti- tative research in economic history at Purdue Uni- versity and the University of Toronto. We are in- debted to the participants at those conferences and to our colleagues at the University of Washington for many helpful comments. Harry G. Johnson con- tributed improvements in presentation and clarity.

primary-product prices and because perhaps, of some inherent inferiority al- legedly associated with primary produc-

tion, concentration on such production retards development. The predominant attitude in the less developed countries, judging by the economic policies they pursue, is one of distrust of dependence on primary production. This skeptical view is supported by reference to such exam- ples as rice in the case of Burma and tin in the case of Bolivia. On the other hand, a number of economists have stressed the importance of primary-product ex- ports such as wool in the case of Aus- tralia, beef in the case of Argentina, cot- ton and grain in the case of the United States, and wheat in the case of Canada, in stimulating rapid general economic growth in the countries concerned dur- ing critical periods of their histories.

Canadian economists and economic historians, in particular, have long held that their country's experience is strong evidence of the positive effects of "sta- ple" exports-as primary-product ex- ports have been termed in the Cana-

315

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316 E. J. CHAMBERS AND D. F. GORDON

dian context-on economic development.

While it is true that the staple theory of Canadian development is somewhat am-

biguous, inasmuch as earlier Canadian

writers on the staple theory did not dis-

tinguish mere population growth re- gardless of per capita income changes from growth in the sense of increases in

per capita income, it is reasonable to think that they believed that successful staple exports were crucial to growth in both senses.' More recently some writers have explicitly mentioned the effects of

staples on per capita income.2 Despite the popularity of the staple

theory in Canada, and the importance of the Canadian case in the debate over the effects of primary production for ex- port on the presently less developed countries, there has been, so far as we are aware, no serious attempt to quantify the contribution of staple exports to Ca- nadian economic growth. In this paper we set up a model indicating a possible method of measuring the effects of staple production upon per capita income, and apply that model to make the indicated measurements for a classic staple period, that of the wheat boom on the Canadian prairies between 1901 and 1911.3 Our finding is that, even under the most gen- erous interpretation of "wheat boom" and the most favorable assumptions

1 Cf. Mackintosh (1939, p. 102), who mentions the effects of exports on "rates of economic and population growth." Since population growth is explicitly mentioned, then presumably "economic" refers to the growth in per capita income.

2 Cf. Watkins (1963) and Caves and Holton (1959). Bertram (1963), by linking the staple theory to general theories of economic growth, implies some- thing about the effects of staples on per capita in- come.

3The period 1900-1915 is impressed upon every Canadian student as a golden age in the economic growth of Canada, inextricably linked with wheat exports from the prairies. We use the period 1901-11 because of the availability of census data for those years.

about the magnitude of its effect, that effect could have amounted to no more than 8.40 per cent of the total increase in per capita income during the period; under a less favorable, but more reason- able, set of assumptions the effect was only some 5.20 per cent of the rise in per capita income.

If our findings are even reasonably correct, they have two important im- plications for development economics. In the first place the findings suggest that policy-makers for presently under- developed countries have no good reason from this case to expect much in the way

of rising per capita income from an ex- pansion of primary-product production of the order of magnitude in this Cana- dian example. In the Canadian case the expansion in one industry alone amount- ed in a decade to over a fifth of the GNP at the beginning. This yielded under our "reasonable" assumptions an increase of per capita income of less than 1.5 per cent of the original figure. In the second place they suggest that the wide appar- ent divergences among various countries in the effects of primary exports upon per capita income, on which the debate referred to above is based, may be il- lusory, and that in those cases where per capita incomes rose appreciably, the explanation may lie elsewhere than in exports-despite their concurrent ex- pansion.

I. THE SIMPLEST MODEL

Although the period 1901-11 in Cana- da is referred to as one of wheat export boom, we measure the contribution to the growth in per capita income of the increase in all prairie agricultural output. First, despite the fact that the export market was by far the most important, there is, of course, no magic that assigns a greater social significance to a dollar's

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 317

increase in exports than to a dollar's increase in domestic output. Second, wheat was produced in substitution with other field crops and livestock and the net effect of the "wheat boom" is there- fore more reliably measured by its effect on total output than on wheat output alone. Third, only about two-fifths of the gross proceeds from farm production on the prairies in 1911 was accounted for by all wheat production, and it is impos- sible to separate the contribution of wheat from that of other farm pro- duction without introducing quite arbi- trary assumptions in the allocation of costs.

To measure the effect of the wheat boom we must pose a counter-factual alternative. Let us imagine, for example, what would have happened if all the land that was brought under cultivation between 1901 and 1911 had been impene- trable rock. The labor and capital that developed the prairies would have been somewhere else. If they had been in Can- ada they presumably would have been working in other industries. Their physi- cal and value productivities would de- pend upon the production and demand functions in those industries. And if their value productivities had been less, they would have demanded a smaller quantity of goods and services from other industries or from abroad. Moreover, whether these factors of production would have been located in Canada at all, or located in some other countries, could only be determined by reference to knowledge of the supply functions of these factors to Canada. Little can be said about the effects of staples without at least a crude general equilibrium mod- el and without implying something about the nature of the relevant func- tions. In this paper we use such models, albeit very crude ones. Nevertheless,

we believe they enable us to arrive at rough estimates of the effects of the wheat boom which, though not precise, still give a more accurate picture than is suggested in traditional writings.4

Consider the simplest model of the results of a boom in staple production.

Let the Canadian economy circa 1900

be represented by two competitive in- dustries: a "wheat" industry which is a staple export; and a domestic manu- facturing industry producing, say, gadg-

ets. The two production functions are:

w = w(Lw(1)

g = g(LV) , (2)

where w, g, LW, and Lo are wheat, gadg- ets, and labor in wheat and gadgets, respectively. For the moment we will abstract from capital and other factors.

We will suppose that the prices of both products, pw and pg, are exogenous- ly determined, pw, = p the world price of wheat, and pa-pa, the world price of gadgets plus transportation cost and the Canadian tariff.5 For both products

4 The confusion that can arise through a failure to pose counter factual questions is well illustrated by a segment of the recent work of Caves and Holton (1959, chap. iv). They develop a short-run econ- ometric model of the Canadian economy based on annual observations and find exports to be a reliable predictor of changes in aggregate income lagged one year. This is in accord with the widely held belief that, if an autonomous sector of aggregate demand changes, then an induced sector of aggregate demand will move in the same direction. Given the long-run allocation of resources to staple production, such a model may be a test of the short-run sensitivity of income to changes in export demand. It is not, how- ever, a test of the staple theory of economic de- velopment for it gives no clue as to how much higher per capital income is as a result of this allocation rather than the next best alternative. Without care- ful interpretation, such a test will exaggerate the economy's dependence on a single export for its real income.

I To avoid complications introduced by ex- change rates, gold flows, and the like, we can imagine a universal world paper currency.

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318 E. T. CHAMBERS AND D. F. GORDON

Canada is presumed to supply too little to affect the world price. The maximiz- ing conditions in the two industries will be

PL=P w(LW), (3)

PL = j g'(Lu), (4)

where w'(L,.) and g'(L,) are marginal physical products.

The supply conditions in the labor market will be

L = f(PL), (5)

L = L9 + LW, (6)

WAGE la MVP lb MVP lc

D B

H E F s ' \ D SW M d

W~~~~~ -S a ;dg y R Cd a X T V G

LABOR LABOR IN WHEAT LABOR IN GADGETS FIG. 1

where PL is the wage and L is the total supply of labor. Thus our model consists of the four equations (3) - (6) which determine the equilibrium values of the

four variables PL, L, LW, and L,. The slope of the marginal physical

product in wheat, w", will be considered negative, indicating diminishing returns to the factor land, unspecified in equa- tion (1). Since only a small fraction of the ultimately settled acreage was under cul- tivation in 1901, one might well ask: Why would diminishing returns prevail? Following Ricardo we can envisage a wide and continuous variation in quality of all prairie land. With the technology in use in 1900 only a limited upper range would be settled, and within this range the variation in quality would account for diminishing marginal physical pro-

ductivity.6 On the other hand g(L,) will be considered to specify fully the gadget production function, that is, there is no

(or a negligible amount of) land or any

other scarce factor required; g(L,) will be linear and homogeneous, and g' equals average product, a constant.7

Now let technological change (Red Fife Wheat, the chilled steel plow, etc.) shift the production function for wheat such that marginal physical product rises by a constant amount for each quantity of labor. The resulting equi- librium in the labor market is simple

enough to be illustrated diagrammatical- ly in Figure 1. Figure la depicts the sup-

6 Of course on the intramarginal land diminish- ing marginal productivity would also obtain.

7 We find it convenient to follow the convention that all production functions are linear and homo- geneous if all factors are specified and all are divis- ible. When in fact a production function exhibits increasing or decreasing returns, it will be because of some indivisibility or because some factor is not in- cluded. This is a matter of classification only; the empirical substance is discussed later.

Here and elsewhere we are assuming that entre- preneurship, not specific to any industry, comes with each laborer in fixed proportions, so that it may be ignored in the analysis. Each laborer may be con- sidered to be his own entrepreneur, or more plausibly, for every n laborers there is one entre- preneur. It is not necessary that the entrepreneurs be of uniform quality, but if not, then the number in existence of the highest quality, though not the number in use, must be large enough to reduce their return as entrepreneurs to zero (Friedman, 1962, p. 140).

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 319

ply curve of labor, S (or f-t(L)). By adopting the convention of measuring

wheat and gadgets in units such that each has a price of unity, the ordinates in Figure lb and 1c measure simultane- ously goods and money. In Figure lb,

dw is the original marginal product of labor in wheat in both physical and value

terms, and in Figure 1c, s, is the original supply of labor to gadgets. This supply curve is the horizontal distance for each possible wage level between the total supply of labor in la and the demand for labor (= the value of the marginal phys- ical product) in the wheat industry.

The demand curve for labor in gadg- ets (the value of the marginal product) is infinitely elastic at OM in the original

equilibrium. This follows from the infi- nite elasticity of gadget demand (p0 = pa) and the constant marginal product

(see eq. [4]). When technological changes shift the

demand for labor in the wheat industry from da, to d', the supply curve of labor in the gadget industry moves an equal

horizontal distance, from s, to s,. Labor transfers from gadgets to wheat (PJ = XT), new settlement occurs, and culti- vation is extended until rent at the mar- gin is again zero. However, there is no increased supply of labor to the country

or increase in real or money wages, so long as any labor remains in the gadget industry at wage OM. The increase in total income is the increased rent of wheat land, ABCD, and presuming pop- ulation and labor force are equal, the in- crease in per capita income is ABCD/Y.

But history does not perform con- trolled experiments. During the period in which we wish to measure the effects of the wheat boom other exogenous param- eters were also shifting. Suppose, for example, there was an independent in- crease in productivity in the manufac-

ture of gadgets which raised the constant value of marginal product in that indus-

try from OM to ON. In that case the new equilibrium wage would rise by a similar amount. Rent in the wheat industry would amount to AHIF in 1911 rather than A RD and the increase in rent would now be AHF-BRC rather than ABCD as before. But if we are interested in isolating the effects of the wheat boom,

we should not measure the increase in rent from 1901 to 1911 but rather the

difference between the rent as it was in 1911 and as it would have been in 1911 had the wheat boom not occurred. If

there was no wheat expansion, rent would have been reduced in the wheat industry to BHE by reason of the higher

wages. Thus a true estimate of the in- crease in income due to the wheat boom can be found by subtracting from actual rent of land in 1911, not the observed rent in 1901, but a hypothetical 1911 rent. This latter is the observed rent of 1901 (BRC) adjusted to allow for the higher wage level of 1911, that is, adjust-

ed to BHE. Subtracting BHE from the actual 1911 rent, AHF, leaves the area A BEF as the increase in income due to the wheat boom.

Under the above assumptions the pop- ulation would increase by YZ (= PQ + TV). But this growth is due solely to the autonomous shift in productivity in

the gadget industry which, given the world price of the two commodities, estab- lishes the real wage for the whole econo- my. The population would have been at

Z in 1911 whether or not the wheat boom had occurred. Thus the increase in per capita income due to the wheat boom is ABEF/Z. (However, we later introduce changes in the model to allow for insti- tutional forces that permit population growth to depend upon the agricultural expansion.)

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320 E. J. CHAMBERS AND D. F. GORDON

We have estimated the area ABEF for the period 1901-11 at $40.4 million. The censuses for 1901 and 1911 list by province the average rental paid per acre on all farms under lease.8 Leased acreage amounted to 11 per cent and to 8 per cent of total occupied acreage for the years 1911 and 1901, respectively, and we assumed these rents to be representa- tive for their respective provinces. We thus multiplied these average rents by the total acreage in each province and summed over all three prairie provinces for each year. This resulted in total rent figures of $9.2 million for 1901 (BRC in Fig. lb) and $45.8 million for 1911 (AHF). We made the adjustment to the 1901 rent (HRCE in Fig. lb) by assuming (1) that wage costs were the same pro- portion of total farm output in 1901 as they were in 1911 (46 per cent) and (2) that wage rates increased 2 per cent per year in agriculture over the decade, as they did in the economy as a whole. This reduces the observed 1901 rent of $9.2 million to the hypothetical 1911 rent of $5.4 million which, subtracted from the actual 1911 rent of $45.8 mil- lion, leaves $40.4 million as the estimate of ABEF.9

This figure is 1.94 per cent of national income for 1911.10 Using this model, there- fore, we conclude that in the absence of the "wheat boom" over the previous

8 Cf. 1911 Census, IV, pp. lviii and xiv, and p. 422, "Instructions Relating to Schedule No. 7."

9 Further details of this calculation are given in Appendix A together with sources of potential bias.

10 Our estimate of current dollar national income for 1911, of $2,081 million is obtained by (1) calcu- lating 1910 national income in current dollars by subtracting indirect taxes and capital consumption allowances from Firestone's adjusted gross national product (Firestone, 1958, pp. 65, 74); (2) applying the aggregate increase in real output between 1910 and 1911 to our 1910 national income estimate (Fire- stone, 1958, p. 276); (3) applying to the resulting figure the increase in prices between 1910 and 1911 as reported in Canada, Dominion of (1915, II, 240).

decade, per capita income would have been in 1911 some $5.61 below its actual figure of $288.75. Since per capita output grew at the rate of 2.1 per cent per an- num over the period 1901-11 or 23 per cent for the decade, our figure is just under one-twelfth or 8.40 per cent of the total growth. This contrasts sharply with the conclusions of Canadian staple theo- rists insofar as they argue that staples are responsible for rising per capita income. If our results are roughly accurate, the importance of staple expansion to the growth in per capita income must be questioned, and the contrast apparent to policy-makers in underdeveloped areas between successful and unsuccessful ex- port economies may be a false one. "Suc- cessful" export economies may be suc- cessful, as was Canada, for reasons inde- pendent of their primary-product export expansion. It is of considerable interest, therefore, to inquire if any peculiarity of this highly simplified model accounts for these results.

II. THE MORE COMPLICATED MODEL

A. CAPITAL

So far we have abstracted from capital (and other factors). The introduction of capital in the most general way compli- cates the model considerably by re- quiring a supply curve of capital and a consideration of elasticities of substitu- tion of labor for capital in both indus- tries and for land in wheat production. The number of equations becomes larger and the results more complicated, al- though not essentially different.

However, in a plausible special case the results can be seen intuitively. Since capital is highly mobile and Canada a relatively small country in the world economy, it seems reasonable to assume that the supply of capital to Canada is perfectly elastic. In this case the demand for labor in gadgets is still perfectly

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 321

elastic. This follows from the fixed prices of the co-operating factor and the final product, and the constancy of returns to

scale. So long as the demand curve for labor in gadgets is perfectly elastic, the effects of the wheat boom will merely be to transfer labor without any rise in

wages or population, and the effects upon national income can be measured by ABEF as before.

The same results would follow if we expand our model to include any other factors, such as fuel or raw materials, used by either industry, provided these factors are available to the two indus-

tries (from Canada or from abroad) at fixed world prices, or at prices fixed by the world market plus transportation and/or tariff.11

B. OTHER INDUSTRIES

We now wish to consider whether

the introduction of industries with dif-

"1 See mathematical note in Appendix B. If we introduce any other factor such as capital the mean- ing of the two demand curves in Fig. lb and ic changes. Instead of representing the marginal physi- cal products given the quantity of other factors, they become demand curves for labor given the price of the other factor. Of course at each price of labor the marginal physical product equals that price, but it is a marginal physical product for a quantity of labor combined with a varying amount of capital.

The ability of export staples to attract capital and thereby improve productivity has been a re- curring theme in Canadian writings on the staple. There is no doubt that the production of primary products has this capacity, but the same is true of any economically worthwhile production. We must guard against the double counting that is involved in estimating the contribution of an export to an economy not alone in the value of the export but also in the attraction of the capital that contributed to its production. In fact it must be remembered that had it been possible to produce the wheat with less capital the gain in per capita income to the economy would have been obviously greater and not less. The same is true for labor. Despite some loose talk about the contribution of backward linkage to growth, it should be noted that, if the inputs to the primary product industry from backwardly linked industries were not required, then the rent, and therefore the gain, from the export industry would have been larger.

ferent demand and production condi- tions into our simple two-industry model would affect the accuracy of our meas- ure of the gain in per capita income attributed to the wheat boom. In the following we will imagine that the only shift in productivity occurs in the wheat industry; that is, the wage level in gadgets remains at OM and the gain is measured by ABCD. First let us sup- pose that we have a third industry which is wholly domestic. It is characterized by constant returns to its one factor, labor, and is protected from foreign competi- tion by prohibitive tariffs and/or trans- port charges. Let it be "haircuts." In these circumstances the additional rental income will produce an increased demand for haircuts. The price of haircuts and wages in the industry will tend to rise. But this tendency will be prevented by a transfer of labor from the gadget in- dustry, where the demand for labor is completely elastic. Thus so long as any labor is left in the gadget industry in the new equilibrium, wages will not rise in the economy as a whole, and popu- lation will therefore not expand. The contribution to aggregate and per capita income of the expansion of staples will be measured by the increased rent in wheat.

Next suppose we have a fourth in- dustry (cheese), domestic or export, which experiences diminishing returns from the application of labor to "land." Like wheat and gadgets it has a world price which Canadian demand and sup- ply cannot affect, but unlike wheat it experiences no shift in its production function. Given the constant real wage in the economy, there will be therefore no change in output or earnings in this industry. Our previous measures of the effect of the wheat boom will remain valid in this, now four-industry, model.

Our more complicated model can be

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322 E. J. CHAMBERS AND D. F. GORDON

illustrated in Figure 2, where the supply of labor to the country and the demands and supplies for labor in each of our four industries are shown. Because of the

shift in the production function for wheat, employment of labor expands in

wheat and haircuts, contracts by an equal amount in gadgets and remains constant in cheese. Since wages remain

constant, area I = II + III. Money in- come expands by the increased rent IV, and since all prices are constant, measured real income expands proportionately. The area above the demand curve for

Wl GE MVP MVP MVP MVP

S~~~~~~~~~~~S

D ~~~~~~~~~~~,-Sg -S ~~~~~fgSC

L~~~~ L t A L a t X C L X~~~~~~~~ifh dh LH LABOR LABOR LABOR LABOR LABOR IN

IN WHEAT IN GADGETS IN CHEESE HAIRCUTS

FIG. 2

labor in haircuts is not income since, un-

like the similar areas in wheat and cheese, there is no co-operating factor

that receives income in this industry. Area V therefore is not an increase in money or in real income. In this expand- ed model, productivity in gadgets and fixed world prices no longer determine both money and real wages, but only the former. Real wages can also be affected by the prices of the domestic goods which can move independently of world prices through productivity improvements.

C. POPULATION EFFECTS

For one basic reason the conclusion

so far reached-that the expansion of prairie agriculture contributed only 8.40

per cent to the total growth in per capita income-unquestionably exaggerates the

effects of the staple. This is because the model produces no growth in popu- lation due to the wheat boom, and this in turn is due, among other things, to

the assumption that population only migrates for wages. No part of the in- crease in rent would go to new immi- grants, but would be captured in its en- tirety by individuals previously resident in Canada.

Suppose, however, that homestead legislation disposes of the newly valuable lands, not at the market price, which would be the expected long-run capital

value, but at a reduced price; and simul- taneously restricts the participation in this expected windfall to those who mi- grate to the region. Migrants may come from both Canada and abroad. Consider

12 While some development theorists (and cer- tainly Canadian economic historians) have stressed the role of exports, it is of some interest to note that, as we would expect, it makes no difference to the effect upon per capita income whether an increase in productivity occurs in a domestic or export indus- try. Thus a shift in productivity in the cheese in- dustry would have the same effect as the shift in wheat. Given the emphasis placed on exports in much of Canadian economic history we were sur- prised to find (1911 census) that during the decade, agricultural production in Ontario increased abso- lutely as much as in Saskatchewan, while Quebec and Ontario increases were together fully 79 per cent of that in the entire prairie region.

The reader will note that in our expanded model we have not considered the possibilities of increas- ing or decreasing returns in industries like haircuts that are domestic. This will be done below.

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 323

a unit of labor in, say, the United States,

to the right, in Figure la, of the inter-

section of the supply function S, with the real wage. He would not ordinarily mi-

grate. But he may perceive that the sum

of his wages plus rents will be greater on the prairies than his supply price of labor alone at home. To the extent that foreign immigrants take up the home- stead land before Canadians, the effec- tive supply curve will have shifted to the right. (The additional labor in the coun- try will not lower the real wage which is set independently, as demonstrated above.

We have roughly estimated the num- ber of people who might be supposed to have migrated for this reason at 200,000.

Our procedure is (1) to estimate the total increase in numbers on newly settled

farms at 370,000;13 (2) to subtract one- third for those who come from Canada itself;'4 (3) to subtract another 10 per cent for those who, having once acquired clear title to a homestead, are in a position to enjoy its future income stream by sale

(or lease) and return to their previously higher wage in, say, the United States,"5

"This is calculated from the 147,881 newly occupied farms for the decade 1901-11 (1911 Census of Agriculture, p. xii) and the approximate number of persons per homestead, 2.5 (Annual Reports of the Department of the Interior, 1902-1912, as re- printed in the Dominion Sessional Papers).

14 This is a rough average of the 37.3 per cent which is the proportion of Canadians listed in the "general farmer" occupational group in the 1911 Census of Occupations, and 30 per cent, which is the approximate proportion of Canadians and aliens "previously resident in Canada" taking up home- steads year by year for this decade (Annual Reports of the Department of the Interior). We are also assuming the family size of Canadian settlers is equal to that of non-Canadian settlers.

15 The homesteader obtained patent on his 160 acres and could pre-empt an additional 160 acres at the nominal price of $3 per acre after meeting resi- dence requirements (6 months on the land for each of 3 years; building a habitable house; breaking 30 acres and having two-thirds of this in crop) (Martin, 1938, esp. chap. xii, pp. 495-545).

and (4) to subtract a further 10 per cent for those who, considering the huge mi- grant wave leaving Europe for North and South America and Oceania during this decade, would perhaps have migrat- ed without the opportunity to capture any rent. This latter represents an exog- enous shift in the supply curve S in Fig- ures 1 and 2.

If we now suppose (1) that the labor force participation rate of this 200,000 is the same as that existing in the prairie population as a whole (41.4 per cent), and (2) that their wage earnings are equivalent to the estimated average an-

nual earnings in Canadian manufactur- ing of males 16 and over ($504 in 1911),16 then the increased population would con- tribute some $42 million to the income stream in the form of wages, quite apart from the increased rent of $40.4 million already calculated. The addition of $82, 400,000 income and 200,000 population to a country which in their absence to- taled 7,007,000 population and $1,999 million in income, increases per capita output by 1.20 per cent as compared with our original estimate of 1.94 per cent. Its contribution to the decade's growth would be 5.20 instead of 8.40 per cent."7 The fundamental reason for

16 The figure of $504 is derived as follows: average earnings of male persons in manufacturing in 1910 = $489 (1911 Census of Manufactures, p. vi) plus an adjustment of 2.9 per cent for the increase in average weekly earnings 1910-11 (Canada, Dominion of, 1915, II, 558) = $15.

17 Some critics have suggested that a more plausible assumption about population would have been a completely elastic supply curve of labor. Originally we did in fact approach the problem this way but abandoned it when we realized that it was incompatible with a gadget-type industry and stability (a horizontal supply curve and a horizontal demand curve for labor). For reasons outlined below in the text we feel that some sizable fraction of Canadian industry possessed the gadget properties in 1911. However, if we do reject the gadget indus- try and adapt the horizontal supply curve of labor,

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324 E. J. CHAMBERS AND D. F. GORDON

these results is that in the revised model the additional population has no effect upon the real wage, while the same in- crease in rental income is distributed over a larger number of people.

III. A NOTE ON GADGETS

A peculiarity of the above models which makes the area ABEF in Figure 1 a "true" measure of the change in in- come attributable to the change in staple production is the existence of a gadget industry with a completely elastic de- mand curve for labor. This elastic de- mand curve for labor is a consequence of (1) the fact that the price of gadgets is fixed in world markets, (2) that the sup- ply of other inputs is perfectly elastic to the industry (that is, there are no exter- nal pecuniary economies or diseconomies in the purchase of these inputs), and (3) that its production function is linear and homogeneous which implies no external technological economies or diseconomies.18

To fulfil the first condition in the Ca-

nadian case, the gadget industry will nor- mally be producing for the domestic market subject to substantial foreign competition.'9 Appendix C contains a set of industries meeting this latter condi-

the estimated increase in per capita income would be more limited and conceivably could be negative. This would be the case if the ratio of previous rental and other property income accruing to Canadians to previous wage income was higher than the incre- mental ratio of property income to wage income. The higher the marginal propensity to spend on domestic industries and hence the higher the popu- lation multiplier through immigration (given the wheat rent), the more likely is the negative result.

18 We can exclude internal economies and dis- economies, both technological and pecuniary. If pecuniary economies (diseconomies) are non- existent for the industry, they are likewise for the firm. Net technological economies cannot exist for the competitive firm in equilibrium, while techno- logical diseconomies, though they exist for the firm, do not affect the industry because of expansion or contraction in the number of firms.

tion. It was constructed by reconciling

industry classifications from the 1911

Census of Manufactures with commodity classifications from the foreign trade re- turns for the 1910-11 fiscal year. Accord- ing to the census, wage and salary em- ployment in Canada for these industries exceeded 125,000 in 1911, or 23 per cent of the labor force in manufacturing.

With respect to our second condition, the supply of non-labor inputs to gadgets

would not be perfectly elastic (a) if gadg- ets used a significant portion of a partic- ular type of (scarce) land in Canada, or (b) if an intermediate product to gadgets

uses a significant portion of a particular type of land in Canada, and if the price of the intermediate product is not fixed in world markets. While we cannot test the proposition that all inputs other than labor were available at a fixed price to our set of gadget industries, it is pos-

19 More generally the gadget industry could be either export or import. Of course, if it were an ex- port industry, then cheese and/or wheat must be import-competing in order to balance foreign trade. In general there is nothing in the logic of the model which dictates that any one of the three industries- wheat, cheese or gadgets-be either an export- or an import-competing industry. Indeed since the gadget "industry" is a group of industries, they may be simultaneously net import-competing and net ex- porting; for example the agricultural implements industry in 1911 was in the latter category. Some readers may see a similarity between our gadget industry and the largely self-sufficient subsistence sector in Lewis' (1955) well-known theory of growth, in that in both models the particular indus- try provides a completely elastic supply curve of labor to other industries. There are, however, im- portant differences. In our model the gadget indus- try is in no sense "backward" as opposed to "pro- gressive" other industries. In Lewis' subsistence sector real incomes appear to depend on productiv- ity within that sector. Since, however, the gadget industry is not self-sufficient, real wages depend not only upon productivity in gadgets but also upon world prices and productivity in the insulated do- mestic industry with its resulting price effect. Final- ly Lewis' subsistence sector is not an exporting industry while, as just noted, gadgets could be so in principle although they were generally not in the period under consideration.

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 325

sible to speculate about the existence of a subset of industries from those in Ap- pendix C. Take cotton textiles as an

example. Raw material and capital must

be obtained at the world price leaving labor as an input with domestic origin. In

the case of woolen textiles, while some producers used wool grown in Canada, the supply to the industry must have

been close to perfectly elastic. Or, take the very large iron and steel products group (including foundries) in which we may plausibly say that the supply of iron ore, coal, and other material inputs ap- proached perfect elasticity. We believe ourselves justified in concluding that within the set of industries found in Appendix C there exists a subset whose input prices, apart from labor, were fixed

and which account for well over half the total employment in the group.

This brings us to our third condition, the existence of external technological economies or diseconomies. Since so many of the ablest economists have la- bored so long to produce so little in the way of satisfactory concrete examples of these phenomena, it seems safe to con- clude that such economies or disecono- mies would not sensibly affect even a small fraction of the industries meeting our first two criteria (cf., for example, Scitovsky, 1954; Meade, 1952). Strictly all that we require for our argument is that some of them escape these influ- ences. (It should also be noted that so far as external economies, either pecuni- ary or technological, are concerned, their existence is incompatible with equilib- rium and a perfectly elastic demand curve for the industry.)

IV. SOME QUALIFICATIONS

Like all theoretical models, what we have presented represents a gross simpli- fication of reality. We wish now to con-

sider briefly some possibly significant qualifications.

i) Gross domestic versus gross national product.-One qualification to the model turns on the difference between national and domestic product. Our model as- sumed that the increased rental value of prairie land accrued solely to Canadian residents, that is, to gross national as

well as to gross domestic product. The possibility mentioned above, that set- tlers, having acquired title through homesteading, could leave and enjoy their rents (or their equivalent) from abroad, shows that this may not be so. Moreover, railway and other land com- pany sales of non-homestead land to set- tlers would further diminish the incre- ment to Canadians if rents thereby capi- talized and captured accrued to some foreign equity interest in these compa-

nies. To the extent that these factors were operative, our previous estimate of the contribution of wheat to per capita income is exaggerated.

ii) The effect of decreasing and increas- ing cost industries.-At least one writer has suggested that, by increasing in- come and population initially, exports may increase demand so that a secondary improvement in productivity results from economies of scale (cf. North, 1961, pp. 1-14). On the other hand it is in principle also necessary to consider dis- economies of scale resulting from in- creased income and population.

Consider first economies of scale. In our model all industries other than gadg- ets or haircuts are by hypothesis indus- tries of diminishing physical returns. We have already considered the question of increasing returns in gadgets. It is in haircut-type industries-insulated from world markets-where economies of scale, internal or external, may operate. Suppose, to take a fairly generous esti-

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326 E. J. CHAMBERS AND D. F. GORDON

mate, the average and marginal propen-

sities to consume haircuts are both one- half. Then total income in haircuts is approximately $1 billion in 1911 (with no wheat boom), while the increase in expenditures on haircuts from the initial increase in wheat income of $82,400,000 is approximately $42,000,000 or some 4

per cent of this. Suppose, second, that we tentatively use Denison's estimate that the coefficient of economies of scale is 10 per cent, i.e., a 1 per cent increase in

input results in a 1.1 per cent increase in output.20 In this case the increase in pro-

ductivity due to the transfer of factors from the gadget industry to the decreas-

ing-cost haircut industry is about 0.4 per

cent in haircuts, and for the economy as a whole about 0.2 per cent. This is spread

over 10 years. It is fairly clear that an estimate rather than the above hypothet- ical arithmetic would be unlikely to

change the order of magnitude of this result, and we shall therefore ignore it.21

Moreover the existence of increasing- cost haircut-type industries will work in the opposite direction. This will be the case if one such industry (say, lumber) uses a specific factor of production. When demand increases, the price of lumber and rents to landlords in lumber will both rise. The increase in rents to landlords represents only a transfer of income on

the previous level of output from con- sumers to the producers of lumber. How-

20 Denison (1962, p. 175). Denison divides ex- ternal economies into national and local. If the ex- pansion on the prairies had the effect of reducing the size of the typical Canadian community, or slowing its increase, the external effects would be negative on the local level.

21 Of course while 0.2 per cent is an insignificant fraction of the 23 per cent increase in per capita in- come for the decade, it is one-sixth or a not insig- nificant fraction of the 1.20 per cent that we have found to be the result of a decade of wheat expansion alone. It changes our 5.20 per cent to 6.05.

ever, since the increment of output is ob- tained only at higher real cost, the in- crease in the price paid by consumers is not entirely offset by larger landowner

22 income.

iii) The method of comparative statics. -Like so many attempts to measure economic forces we have employed the method of comparative statics, which presumes that we are observing points of equilibrium. In taking 1901 as the begin- ning of our period we may have a happy coincidence of empirical data and a rea- sonable approximation to an equilibrium. A question may be raised by some con- cerning the choice of 1911 as a terminal date for a comparative static analysis. Thus the shift in labor required by the parametric shift in the wheat industry may not have been approximated by 1911. If this were the case, the wage level in western agriculture would be ab- normally high due to the short-run scar- city of labor. It would follow that rents would be abnormally low, and the true gain to the economy would be properly measured not by land rents alone but by land rents plus the quasi-rent to labor.

But, in fact, there is no convincing evidence that wages were abnormally high on the prairies. Annual farm wages in Saskatchewan, for example, were

22 If increasing- or decreasing-cost haircut-type industries are not offsetting, there may be a further effect upon per capita income through population changes. Owners of labor and other factors may im- migrate (or fail to emigrate), for example, in re- sponse to net economies of scale since with given money earnings their real incomes will be raised by the lower average price of haircut-type products. (The former equivalence between real and money wages would be relaxed and the labor supply func- tion in Figs. 1 and 2 would shift to the right.) The opposite would be true if net diseconomies prevail. However, in either case, if these net migrants possess a factor stock equal to the average already in the country, this further effect on per capita income will be zero.

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 327

$402.50 in 1910 (Canada, Dominion of, 1914, p. 203), while the Coates Commis- sion (Canada, Dominion of, 1915, p. 653) reports hourly wages for unskilled labor in Toronto in 1911 at a level such that a

casual laborer working only 39 weeks a year (at 54 hours per week) could have earned $468 annually. Considering the very real hardships of the plains winters, and the scarcity of social amenities, this suggests a depressed imputed wage due to overoptimistic expectations of yields and prices. Of course, it is also suggestive of the normal discrepancy between agri- cultural and urban money incomes. On balance we find no particular reason to adjust our estimate.

V. SKETCH OF AN ALTERNATIVE

We conclude therefore that, if the staple theory of economic growth is in- terpreted as explaining a rising per capita income, then it fails for a period which has been considered an example, par excellence, of its operation. A natural question arises: If not wheat, what did produce the reasonably satisfactory growth rate of the wheat era? We shall not here attempt a theoretical explana- tion of the differences in the wealth of nations over time and space, but we will sketch an alternative way of looking at growth in small economies.

First, whatever the original impor- tance of natural resources, casual obser- vation of per capita incomes the world over suggests that resource endowment has very little connection with income levels-serving to confirm our closer look at a particular Canadian period. (There are, of course, exceptions such as Ku- wait.) Next, while domestic capital for- mation has been stressed in the literature on underdevelopment as a crucial vari-

able, more recent empirical analyses in

advanced countries have severely depre-

ciated the quantitative importance of net capital formation as a cause of growth (Massel, 1960; Solow, 1962). Moreover, for relatively small economies (that is, most of the world's economies) the sup- ply of capital from abroad is presumably highly elastic. And the experience of cer- tain countries such as Germany and Japan in the postwar world suggests that, if sufficiently high returns are avail- able, domestic capital formation is fairly responsive.

If natural resources and capital are not important, then is technology a sig- nificant factor? Clearly for the world as a whole technological advance has been a necessary condition for much of what- ever economic growth has taken place. But when we attempt to account for dif- ferences among countries at a point of

time, technology, almost tautologically, is of little use. The state of the arts can be considered virtually identical for all countries. Barring a few fairly trivial royalty payments for patents, all coun- tries have access to the same accumu- lated store of knowledge; it is the use of this technology which varies.

The causes of variation in the appli- cation of technology can perhaps be use- fully classified in two categories. On the one hand, there are the potentially broad institutional, cultural, psycholog- ical, or sociological factors; on the other, there are the more narrow skills, econom- ically productive education, or human capital. Given a certain institutional and cultural environment, the success of a small economy may be closely related to the level of technical training, encom- passing all of its aspects, that permits it to use the wide spectrum of "free" tech- nological advances occurring elsewhere. While no small country is likely to con-

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328 E. T. CHAMBERS AND D. F. GORDON

tribute a large proportion of the world's technical advances, its rate of growth, nevertheless, may vary significantly with its ability to apply them.23 Application, in turn, may be highly dependent upon its human capital, or economically rele- vant education in the broadest sense, covering everything from the techniques of electron microscopy to the layout of supermarkets. We therefore tentatively

suggest (with Schultz [19631 and others) that these may be the fundamental forces that have produced economic growth in Canada and other "successful" economies, and that they can be more confidently expected to produce growth in presently underdeveloped societies. One elementary point should be kept in mind. In the absence of peculiar changes in production functions, ordinary theory would predict that economic growth would produce export booms; but an ob- served ex post correlation does not neces-

sarily imply that exports were the causal factor.

VI. CONCLUDING SUMMARY

As a conclusion let us summarize the argument.

1. We have constructed a model in which the increase in income to the econ- omy by the expansion in primary-prod- uct exports can be measured by the rents paid to specialized natural re- sources critical for those exports.

2. We have argued that this model is applicable to the Canadian economy in

23 Staple theorists have stressed the dependence of Canada upon foreign technology but, given their preoccupation with primary-product exports, have emphasized only those which shift production func- tions in those industries. Surely in a simple arith- metic sense per capita output will grow more if, for a given rate of technical advance, these advances occur in those industries which make up most of the national product, regardless of whether they are primary product or otherwise.

the first decade of this century when per capita real income rose by 23 per cent.

3. On the basis of this model we have calculated that the spectacular expan- sion of all prairie agriculture contributed at the most only 8.40 per cent and, more realistically, 5.20 per cent of this in- crease. Put otherwise, per capita income was at the most 1.94 per cent and, more plausibly, 1.20 per cent higher at the end of the decade than it would other- wise have been.

4. These conclusions are not substan- tially altered in one direction or another either by reasonable qualifications to the model or by possible errors in the data.

5. We suggest that, when successful exporting economies simultaneously ex- perience a rise in per capita income, most of the latter may, as in the instance we have measured, be attributable to other factors.

On the other hand, to avoid a pos- sible misunderstanding, we would em- phasize certain things that we have not said. We have said nothing about the theory of international trade and in par- ticular about the proposition that free trade will "normally" raise per capita income subject to the well-known theo- retical qualifications. There is nothing in this paper that would constitute a new argument for protection. And further, we have not said anything about the con- tribution of international trade in gen- eral to per capita income, which for a small economy might be very great. Rather we have measured the contribu- tion to per capita income of an export- oriented primary-product sector whose expansion amounted to one-fifth of the initial GNP. In its absence an alterna- tive use of resources would have occurred and other exports would have been available.

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 329

APPENDIX A

SOME SOURCES OF BIAS IN THE ESTIMATE OF THE INCREASED INCOME

Despite the fact that our calculations suggest that only 5.20 per cent of the in- crease in per capita income over the decade was attributable to the changes in prairie agriculture, there are various detailed rea- sons for supposing that this is in fact an overestimate:

1. We ignored as insignificant the por- tion of the rent per acre figure that repre- sents the use of buildings on rented land, even though the buildings represented some 12.5 per cent of the total value of both and despite the fact that yearly payments for buildings should be a larger proportion of these assets as their payments represent depreciation as well as net earnings.

2. We have assumed the same level of market prices for agricultural products in 1911 as in 1901, which overestimates the contribution of the wheat boom. Actually hypothetical 1911 rents on 1901 acreage would have been higher and therefore the true gain was less than our estimates, be- cause (a) the price of wheat rose in this period, and (b) presumably it would have risen more had the increase in Canadian wheat production (in 1911 some 5 per cent of world output) not occurred. Similar cor- rections would have to be carried out on other agricultural products.

3. In applying rent per acre figures from

APPENDIX B

Some readers may prefer a slightly more formal presentation of the argument that in our model the expansion of the wheat industry does not raise the wage of labor, even where production functions are pre- sumed to use capital and/or other factors. Clearly it will not raise the wage if the de- mand for labor in the gadget industry is perfectly elastic, and the gadget industry is still in existence after the expansion.

To show that the demand for labor in gadgets is perfectly elastic, consider an ex-

an 11 per cent sample (1911) to all occupied land, there is some reason to believe that we are overstating imputed rents. Britnell (1941, pp. 45-46) thinks that for 1911-21 the tenancy rate was highest on the choicest land of well-established districts.

4. By 1911 some evidence on the "per- manent" yield in the sense of the long-run average yield per acre was available, so that year-to-year changes in rent per acre would presumably be a function of expected crop prices. If rental agreements for 1911- 12 were negotiated on the basis of projec- tion of prices of the recent crop years as typical, the estimated rent figure will have an upward bias. The average farm price of wheat in the prairie provinces declined from $0.79, $0.82, and $0.78, respectively, in the 1908-9, 1909-10, and 1910-11 crop years

to $0.61 in 1911-12. The price did not rise above $0.65 until the 1914-15 crop year.

5. In moving from the observed 1901 rent to the hypothetical 1911 rent by allow- ing for exogenous wage increases, we have assumed no substitution of other factors for labor. This exaggerates the increases in

costs, hence minimizes the hypothetical 1911 rent, and in turn overestimates the difference between the actual and hypo- thetical 1911 rents.

panded linear and homogeneous production function for gadgets, G(L,K). If, as our model presumes, the price of gadgets and the price of capital are fixed in world mar-

kets, fi, and fiK, the demand and supply conditions for labor in the gadget industry can be represented by

PK =fg GK(LU,KU),

PL = fi GL(Lv,Kv),

L4 =O (PL)+ a.

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330 E. J. CHAMBERS AND D. F. GORDON

The first two equations are the familiar marginal productivity conditions while the third is the supply of labor, derived from

the total supply of labor, f(PL), minus the demand for labor in the wheat industry. Here a is a shift parameter. Differentiating

all equations with respect to a, solving for bPL/ba, and using the fact that the Hessian vanishes, yields dPL/da = 0, that is, a shift

APPENDIX C

"GADGET"-TYPE INDUSTRIES: GROSS VALUE OF DOMESTIC PRODUCTION AND

VALUE OF IMPORTS ENTERED FOR CONSUMPTION, 1910

No. of Values

Salary GVP 1911 Enteredb Product Description of Decennial Census and Census for Con- PoutDsrpino

Classification of Industry Wage of Mfg. sumption Imported Articles Em- ($000)a ($000)

ployees

Liquors, malt .................... 3,062 12,648 695 Ale, beer, and porter Boots and shoes .................. 17,227 33,987 2,095 Boots and shoes of leather Brooms and brushes .............. 937 1,732 483 Brooms and brushes Buttons ......................... 457 407 638 Buttons Carpets ......................... 1,070 1,972 1 722 Wool manufactures-carpets (includ-

ing $101,000 in non-wool mats) Mats and rugs .88 113 530 Mats and rugs (30 sq. ft. or less) of wool Carriages and wagons ....... ...... 5,523 11,767 1,338 Carriages, ex. automobiles and parts Bicycles ......................... 53 72 147 Bicycles and tricycles Cement, Portland ................ 2,150 5,683 494 Portland cement Combs .......................... 175 187 218 Combs Cordage, rope, and twine .......... 1,055 3,624 5,529 Cordage and twine and manufactures

of Corsets and supplies ....... ....... 1,138 1,572 416 Corsets and supplies Cottons, textiles, dyeing and finish-

ing ........................... 13,136 24,901 14,388 Imports of cotton manufactures ex. raw cotton, yarn and thread, socks and stockings, bags, shirts, clothing nop, blouses, lace, shawls

Thread .......................... 456 1,096 1,947 Yarn and thread of cotton Woolen yarn ..................... 329 792 3,826 Woolen yarns Hosiery and knit goods, woolen goods 12,876 19,133 18,278 Stockings, cotton and wool; blankets;

cassimeres; cloths and doeskins; coat- ings and overcoatings; tweeds; felt cloth nop; flannels, plain; knitted goods, nop; shawls; bed comforters; wool fabrics; all fabrics composed wholly or partly of wool nop

Automobiles ..................... 2,438 6,252 4,757 Automobiles and motor vehicles of all kinds and parts thereof

Paints and varnishes .............. 1,198 8,041 1,756 Total paints and colors, and varnishes Electrical apparatus and supplies .. 6,345 15,022 5,130 Total electrical apparatus Fertilizers ....................... 227 644 422 Fertilizers compounded or manufac-

tured

a 1911-1912 .Sessional Paper, No. 1Oa. b 1911 Census of Manufactures.

in the supply curve of labor produces no change in its price, or alternatively, the demand is perfectly elastic. An exactly par- allel argument can be developed if we use a more general but still linear and homo-

geneous production function G(Ki ... K., L) where K2 ... K. are all inputs, other than capital and labor, available at a fixed price.

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PRIMARY PRODUCTS AND ECONOMIC GROWTH 331

"GADGET"-TYPE INDUSTRIES: GROSS VALUE OF DOMESTIC PRODUCTION AND VALUE OF IMPORTS ENTERED FOR CONSUMPTION, 1910-Continued

No. of Values Salary GyP 191 1 Enteredb PoutDsrpino

Decennial Census and Census forVal Product Description of Classification of Industry Wage of Mfg. gumption Imported Articles

Em- ($OOO)a ($000) ployees

Glass incl. mirrors and plate . 2,586 3,167 3,447 Glass ex. ornamental glass. Gloves and mittens .1,651 2,995 2,099 Gloves and mitts of all kinds Glue .264 585 263 Glue, glue stock and mucilage Explosives .482 2,168 1,217 Total gunpowder and explosives Rubber and elastic goods .1,315 5,849 2,210 Total gutta-percha and India rubber ex.

raw and scrap rubber imports Hairwork........................ 297 487 238 Manufactures of hair Hats, caps, and furs .............. 4,639 11,155 3,509 Total hats, caps, and bonnets ex. manu-

facturers' suppliers Liquors, distilled .844 12,064 3,396 Total spirits Liquors, vinous .86 363 1,142 Total wines, sparkling and non-spar-

kling Agricultural implements .9,560 20,723 4,516 Total agricultural implements Boilers and engines .5,864 11,874 1,423 Engines including boilers Cream separators .252 640 784 Cream separators Brass castings...............1,300 3,093 1,923 Total brass and manufactures of, ex.

brass bars and scrap brass Saws .486 879 113 Saws Scales .260 506 113 Scales Safes and vaults .449 460 194 Safes and vaults Sewing machines .769 974 504 Sewing machines and parts and attach-

ments Umbrellas .256 610 117 Umbrellas, parasols, etc. Shoddy .185 785 330 Shoddy Soap .917 5,221 882 Soap Wire and wire fencing .1,560 5,491 3,767 Wire and fencing Foundry and machine shop products 26,835 45,611 26,606 Iron and steel pipe, chains, fittings for

iron pipe, machinery, ex. sewing ma- chines, stoves

Iron and steel products .11,286 34,614 40,679 Bar iron or rolled steel nop, forgings, frogs and railway switches, hoops, billets, ingots, nuts and bolts, rolling mill products, nails, railway brass, screws, skates, bearings, sheet steel, tubing, ware, miscellaneous steel manufactures

Drugs including chemicals ......... 1,336 3,634 12,178 Drugs, dyes, and chemicals

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