Price Elasticities of Demand for Individual Commodities Imported into the United States

THE ESTIMATES of price elasticities in international trade which have so far been published have been derived mostly by applying correlation techniques. The application of these techniques is subject to a number of disadvantages.1 An alternative method of approach, which may be of particular significance, is to determine elasticities from the long-run effects to be expected from tariff changes, based on a study of the characteristics of demand and supply in the markets of individual commodities.

Abstract

THE ESTIMATES of price elasticities in international trade which have so far been published have been derived mostly by applying correlation techniques. The application of these techniques is subject to a number of disadvantages.1 An alternative method of approach, which may be of particular significance, is to determine elasticities from the long-run effects to be expected from tariff changes, based on a study of the characteristics of demand and supply in the markets of individual commodities.

THE ESTIMATES of price elasticities in international trade which have so far been published have been derived mostly by applying correlation techniques. The application of these techniques is subject to a number of disadvantages.1 An alternative method of approach, which may be of particular significance, is to determine elasticities from the long-run effects to be expected from tariff changes, based on a study of the characteristics of demand and supply in the markets of individual commodities.

The estimates prepared in 1945 by the U.S. Tariff Commission,2 of the effects of a 50 per cent reduction and of a 50 per cent increase in the 1939 U.S. tariff rates on the postwar volume and value of U.S. imports of individual commodities, provide a large volume of material for calculating estimates of the price elasticities of demand for the most important dutiable commodities imported into the United States. The reliability of the estimates of elasticity is, of course, completely dependent upon the reasonableness of the Tariff Commission’s estimates. The elasticity estimates are, in effect, a translation of the Tariff Commission estimates into a different language, and no independent validity can be claimed for them. While the Tariff Commission’s estimates were made in 1945 and were based on the expected long-run effects under conditions expected to prevail during 1951-55, their reasonableness cannot be fairly judged by comparing the estimates for values of imports with the figures actually recorded in these years. Both income and prices rose by far more than the Tariff Commission assumed, and the 1939 tariff was itself changed, in a manner different from that assumed in the Tariff Commission study. Furthermore, even if prices, income, and the tariff had been as assumed by the Tariff Commission, the actual figures would not test the reliability of the estimates, since changes have also occurred in many other factors, which have affected the demand for imports.

The estimates of the price elasticity of demand for 176 individual commodities imported into the United States, derived from the Tariff Commission study by the method described below, varied greatly for the different commodities. The average of these elasticities was approximately 2.5, which is significantly higher than the estimates made by several writers who have used correlation techniques. The average elasticity of demand for manufactured and semimanufactured commodities imported into the United States from a number of industrial countries tends to be higher than the average of approximately 2.5 for all the 176 commodities considered in this paper; while the elasticities for a number of raw material imports are, in general, below this average. The magnitude of the price elasticity of import demand for a commodity appears also to be inversely related to the percentage share of total U.S. consumption of the commodity which is supplied by imports.

Method of Derivation

In 1945 the U.S. Tariff Commission was asked to estimate for the long-run postwar period the effects on the quantity and value of U.S. imports which might be expected to follow a 50 per cent reduction or a 50 per cent increase in the duties imposed on some 450 commodities, the 1939 or expected postwar imports of each of which exceeded $100,000. The Tariff Commission assigned each commodity or each group of related commodities to an expert familiar with the characteristics of its demand and supply. The estimates prepared by these experts were made under the assumption that normal conditions would be returning during 1951-55, and that the per capita money income of the United States would then be 75 per cent higher than in 1939.3 The U.S. prices for the commodities selected were in most cases assumed to be approximately 13 per cent higher than in 1939, although in certain cases a deviation from this assumption was accepted as necessary. The relations between general price and cost levels in the different countries of the world during 1951-55 were assumed to be about the same as in 1939. If, however, technical, industrial, or other changes were known to have affected materially the competitive positions of particular foreign and domestic commodities, the changes were taken into account in the estimations.

Since, for the purpose of its study, the Tariff Commission assumed that the tariff changes would be universal and permanent, the estimates for each commodity were necessarily made after taking into account the effect upon that commodity of any changes in the prices of other commodities resulting from the universal changes in tariffs. For this reason, these estimates may be compared with estimates of the effects of a noncompetitive appreciation or depreciation against the dollar, which would similarly affect the prices of all imported commodities. A universal and equal proportionate change in tariffs, however, would not have exactly the same effects as a universal and uniform appreciation or depreciation against the dollar, since the existing U.S. tariff rates differ considerably for different commodities.

Since the tariff changes under consideration were assumed to be permanent, the Tariff Commission’s estimates allow for both shifts in sources of supply and adjustments on the demand side resulting from changes in price differentials. The elasticities implicit in the Tariff Commission’s estimates are, therefore, long-run elasticities.

It was generally assumed that the share of total U.S. consumption supplied from abroad would remain constant with a rise in per capita income. This assumption was examined separately for each commodity, however, and allowance was made for the behavior of luxuries, the effect of a simultaneous rise in incomes abroad, and the effects of the wartime depletion of certain U.S. resources and of the development of new domestic industries.

From the data in the Tariff Commission study, three points on the demand schedule for U.S. imports that is implicit in the Tariff Commission’s estimates can be determined for each commodity. The method of derivation is indicated in Chart 1 below and explained in detail in the Appendix. In Chart 1, Dd is the (unknown) import demand schedule of U.S. consumers for a certain commodity at a certain per capita money income level, say 75 per cent above that of 1939. D0 is the same demand schedule as it appears to the foreign seller who receives for his goods the price paid by the U.S. consumer minus the duty imposed under the 1939 tariff. A particular reduction in the tariff shifts D0 upward by a known percentage to D1 between D0 and Dd, and an increase in the tariff shifts D0 downward to D2. The schedules Dd, D0, D1 D2 are not known, and the problem is to derive certain points on the curve D0 from the estimates given by the Tariff Commission. The Tariff Commission study gives estimates for the points C, B, and A for each commodity, that is to say, estimates of both quantity and price for each of the commodities that would be imported under the 1939 tariff, under a tariff 50 per cent lower, and under a tariff 50 per cent higher. The three points are located on the same supply schedule. From the known relationships between the unknown curves D1 and D0, and D2 and D0, one can derive from the point A on D1 a point A’ through which D0 has to pass; and from B, which must be on D2, a second point B’ through which D0 must also pass. B’, C, and A’ are then three points on D0, the demand curve as it appears to the foreign seller, i.e., after allowing for the 1939 tariff, which is implied by the Tariff Commission’s estimates. From these points the elasticities of a curve of constant elasticity either through B’ and C or through C and A’ can be determined. For each commodity considered here, two elasticities have been computed, one based on the estimated effect of a 50 per cent tariff reduction, i.e., derived from the points C and A’, the other based on the estimated effect of a 50 per cent tariff increase, i.e., derived from the points B’ and C.

In certain cases the Tariff Commission study gave estimates for a group of closely related commodities rather than for a single commodity. Such groups consist of items of various qualities, and a tariff reduction even of ad valorem duties might have a greater effect on the lower priced than on the more expensive items. The estimates of price before and after the tariff reduction (or increase) are in these cases averages of the prices of the commodities in the group, weighted by their volumes of imports. If a tariff reduction were to affect the volume of imports of the cheaper commodities more than those of the more expensive ones, the foreign price as estimated by the Tariff Commission after the tariff reduction will be lower than the price before the reduction. Account has been taken of this price effect in deriving the estimates of the elasticities of the demand schedules for the group.

Price Elasticities of U.S. Imports

This method of deriving price elasticities from the Tariff Commission’s estimates has been applied to 176 commodities, of which the foreign value of imports into the United States in 1939 amounted in most cases to more than $500,000. The results are summarized in Table 1. The total value of the imports of these 176 commodities in 1939 amounted to $668.7 million, or 29.4 per cent of the total value ($2,276 million) of U.S. imports in 1939, and 67.3 per cent of the value of imports of all dutiable commodities studied by the Tariff Commission ($994 million).

Table 1.

Price Elasticities of Demand for Major U.S. Imports1

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In this table, the following symbols are used: a dash (—) indicates “nil”; n.a. indicates that data are not available.

If the tariff is mixed or specific, these percentages will be lower if computed on the basis of a higher estimated postwar price.

These columns record the movement along the demand curve (D0 in Chart 1) connected with a 50 per cent change in tariff. (For column 2, the movement is from P0toP0; for column 3, from P0toP0.) This movement is smaller if the supply curve has a finite elasticity than if supply is infinitely elastic. If a group of commodities is studied, a tariff reduction will decrease the average price of the group if the cheaper commodities have a larger elasticity of demand than the more expensive commodities; and similarly for a tariff increase. In such cases, the movement along the demand curve is larger than if all commodities in the group have the same elasticity of demand, and the percentage price change studied may exceed the percentage of the price change equivalent to the tariff reduction (e.g., cotton yarn, 105).

These percentages attempt to allow for structural shifts during the war, and are more relevant than actual prewar percentages.

Expressed as absolute values. These elasticities of demand were derived from the estimates based on the Tariff Commission’s assumption that the postwar per capita money income would exceed the 1939 income by 75 per cent.

The estimate e2 of the price elasticity of demand for wool waste is positive. In this case a rise in price leads to an increase in imports. Wool waste and other wool products are complementary goods and, according to the assumptions of the study, the price of other wool products would rise with that of wool waste.

The estimates of price elasticity thus obtained range from 0 to −21.1, and for many commodities there are also large differences between e1 the elasticity implicit in the estimate of the volume of imports following a 50 per cent reduction in the 1939 tariff, and e2, which is similarly related to a 50 per cent increase in the tariff. The averages of the elasticities, weighted by the values of the 1939 imports of the commodities into the United States, are ē1=2.23 and ē2=2.74.

The raw materials included in these calculations have elasticities which tend to be considerably lower than the average for all 176 commodities. The commodities studied include 27 raw materials.4 The weighted averages of the estimated elasticities for these raw material imports are ē1 = .80 and ē2=1.62.

The elasticities of demand for finished manufactures are on the average considerably higher than those for raw materials. This is illustrated by the average elasticities for the major imports from the United Kingdom. The imports from the United Kingdom of 21 of the commodities listed in Table 1 account for 52 per cent of total U.S. imports from the United Kingdom in 1939.5 The average elasticities for these commodities, weighted by their 1939 values of U.S. imports from the United Kingdom, are ē1=3.12 and ē2=2.43. These averages are affected considerably by the relatively low elasticity of whiskey, estimated at approximately 1, and the fact that the 1939 value of U.S. whiskey imports from the United Kingdom is 43 per cent of that of the selected group of 21 commodities. The unusually low elasticity of demand for whiskey is partly a consequence of the U.S. internal revenue tax, which is so high that even if a large reduction is made in the per unit foreign price of whiskey, the reduction in the final price to U.S. consumers is relatively much smaller. Roughly, a 20 per cent reduction in the foreign price produces only a 10 per cent reduction in the domestic price. For this reason, whiskey may be regarded as a special case. The average elasticities for the other commodities, excluding whiskey, weighted by the 1939 values of their U.S. imports from the United Kingdom, are ē1=4.80 and ē2=3.55.

Computation of the average elasticities for commodities which are imported by the United States from industrial countries other than the United Kingdom may be based on commodities, listed in Table 1, which are imported from the 13 Continental ERP countries. For this purpose, these imports have been classified in commodity groups, for which a number of the commodities listed in the table may be considered representative.6 The elasticities, e1 and e2, for such a group were estimated by taking the average of the elasticities of the representative commodities in the group, weighted by the 1939 values of the imports into the United States of each commodity. The average elasticities of U.S. demand for imports from the Continental ERP countries were then computed as the averages of the estimates for the commodity groups of which these imports were composed, weighted for each country by the value of the 1948 imports of these groups from the country concerned into the United States. The results are presented in Table 2. Belgium, Denmark, France, and Italy are the countries for which the percentage of imports covered is relatively high, and for which the estimates of the average elasticities exceed the weighted averages for all 176 commodities (ē1 = 2.23 and ē2=2.74); the estimated average elasticities were highest for the Netherlands, but the percentage of imports covered is relatively low.

Table 2.

Average Price Elasticities of Demand for U.S. Imports from 13 ERP Countries

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The elasticities of U.S. import demand for the products of individual countries computed by this method cannot reflect the effects of any change in the export price of one country relative to that of a competing exporter. The use of this method is based on the assumption that changes in the U.S. prices of imports in response to a tariff change are independent of their country of origin.

Relation between the Magnitude of the Elasticities and Other Factors

The difference between the two estimates, e1 and e2, of the price elasticities of demand for a commodity has an implication for the effect of a price decrease on the quantity sold. The hypothesis is sometimes accepted that the reaction of the quantity sold to a change in price is more intense the larger the price change.7 In particular, a percentage price decrease results in a percentage increase in the quantity sold, and the larger the percentage price decrease the larger, relative to this price decrease, is the increase in the quantity sold. It can easily be seen that this holds true if e1>e2. In this connection it should be borne in mind that these price elasticities are long-run elasticities, i.e., derived from a demand curve which reflects the quantities demanded, at the prices in the relevant range, after the long-run adjustments made subsequent to the change in tariff are assumed to have taken place. Therefore, if the average elasticities are such that ē1>ē2, it follows that the above hypothesis holds true for a majority of the imports. Although e1 exceeds e2 for some commodities,8 the opposite is true for most commodities. The difference between ē1=2.23 and ē2=2.74 is statistically significant,9 so that on the basis of the estimates which have been calculated it appears that ē1<ē2. Therefore, it seems reasonable to say that whether or not the above hypothesis (i.e., that the reaction of the quantity sold to a change in price is more intense the larger the price increase) holds depends on the type of commodity, and that for a substantial number of commodities imported into the United States, it is false.

For most of the 176 commodities, the Tariff Commission estimated the postwar percentage share of total consumption which was supplied by imports. These shares, recorded in column 4 of Table 1, allowed for the structural shifts which had taken place since the prewar years. The average of the shares, weighted by the 1939 value of imports of the commodities, is 27 per cent. The calculations are in some cases based on arbitrary definitions of “commodity” and “market,” since the commodity classification used by the Tariff Commission follows that of the tariff law. Despite this fact, it is economically meaningful to make a broad distinction between the commodities for which this percentage is less than the average, 27, and those for which it exceeds the average. The weighted averages of the elasticities for the commodities in the former group are ē1=3.13 and ē2=3.64; for the latter they are ē1=1.77 and ē2=2.33. The differences between the two averages are in both cases statistically significant. Thus it appears that commodities whose imports supply a relatively large share of the U.S. market tend to have a relatively low elasticity of import demand; while commodities whose imports supply a relatively small share of the market have relatively high elasticities.

From these estimates, no clear relation emerges between the price elasticity of import demand for a commodity and the height of the tariff imposed on it. The weighted average of the 1939 tariff as a percentage of the 1939 prices of the commodities considered (see column 1 of Table 1) is 39. The weighted average of the elasticities derived from the estimated effects of a tariff reduction is 2.90 for commodities upon which the tariff was less than 39 per cent, and 2.42 for commodities upon which the tariff exceeded that level. The difference between these averages does not appear to be statistically significant. On the other hand, similar averages derived from the estimated effects of a tariff increase are 3.89 and 2.36, respectively; the difference between these two averages appears to be statistically significant. It seems therefore that on the basis of both groups of estimates no definite conclusion can be established regarding a relationship between the magnitudes of the elasticities and the tariffs on individual commodities.

Appendix: Method of Derivation

The commodities examined by the Tariff Commission may be divided into two categories: (1) those which have a perfectly elastic supply curve, and (2) those whose foreign price rises with the volume of imports. In each category some commodities are treated separately, and others are grouped with closely related items of various qualities, the weighted foreign price of which varies inversely with the volume of imports.

The simplest case of an infinitely elastic supply is depicted in Chart 2; the tariff is assumed to be ad valorem. The changes in U.S. demand for a certain commodity associated with variations of the duty paid price in the relevant range are represented by Dd; the schedule Dd is not known. From Dd a schedule D0 can be derived giving the changes in quantities demanded when the per unit foreign value varies and the 1939 ad valorem tariff rate is τ. We have, for each quantity,

D0(q)[1+τ]=Dd(q)(1)

or (see Chart 2)

P0[1+τ]=Pd(2)

Similarly, D1 and D2 can be derived from Dd when the tariff rate is 50 per cent lower and higher respectively than τ, so that in Chart 2

P0[1+τ]=P1[1+12τ]=P2[1+32τ]=Pd(3)

If the foreign supply price (f.o.b.) is P0, a 50 per cent tariff reduction will shift the quantity demanded to q1; a 50 per cent tariff increase will affect a shift from q0 to q2. Since the supply is infinitely elastic,

D0(q0)=D1(q1)=D2(q2)=P0(4)

In this case the Tariff Commission study gives estimates for (P0, q0), (P0, q1), and (P0, q2). The desire is to determine

P0=D0(q1)

and

P0=D0(q2)

from (4) and (3) which can be written more generally:

D0(q)D1(q)=1+12τ1+τ(5a)
D0(q)D2(q)=1+32τ1+τ(5b)

Thus

P0=D0(q1)=1+12τ1+τD1(q1)=(1δ)P0(6)

where

δ=12τ1+τ(7)

and similarly

P0=D0(q2)=1+32τ1+τD1(q2)=(1+δ)P0(8)

The point elasticity at each point of a curve of constant elasticity passed through the points (P0, q0) and (P0,q1) on D0 is

ε1=logq1logq0logP0logP0(9a)

and similarly for the points (P0,q2) and (P0, q0) on D0

ε2=logq2logq0logP0logP0(9b)

If instead of an ad valorem tariff the duty is specific, formulae (6) and (8) become simply

P0=P012t(10)
P0=P0+12t(11)

where t is the duty per unit of quantity levied before the tariff change.

It is not necessary that the supply curve be perfectly elastic in order to have a case in which a tariff change does not affect the foreign price. A very elastic demand for the commodity in third countries may cause the change in foreign price due to the tariff change to be negligible.

In general, a tariff change will cause a larger change in the foreign price the less elastic are the supply and demand abroad. Thus a tariff reduction of 50 per cent may lead to an increase of the foreign price to P1 and of the quantity demanded to q1 (see Chart 1). In such cases the Tariff Commission Study gives the estimates Pt, qi(i=0, 1, 2). Formulae (6) and (8) then become

P0=(1δ)P1(12)
P0=(1+δ)P2(13)

if the tariff is ad valorem;

and

P0=P112t(14)
P0=P2+12t(15)

if the tariff is specific. The elasticities are expressed by (9a) with P0 substituted from (12) or (14), and by (9b) with P0 substituted from (13) or (15).

Commodities subject to a duty, partly specific and partly ad valorem, were treated as if the duty were ad valorem. The τ used was the ad valorem equivalent of the duty in terms of the per unit foreign value, which was determined by the Tariff Commission for the actual 1939 values. If in the Tariff Commission estimates the foreign price was different from that in 1939, τ was adjusted accordingly.

This adjustment assumes that the tariff is specific and that the composition of a heterogeneous commodity group would not change, so that a higher foreign price implies a proportionally lower percentage ad valorem equivalent. Since the tariff is in fact mixed, there will be a slight upward bias in the estimated elasticities of demand for commodities subject to it.

A second upward bias seems likely to be more important. When a mixed tariff is treated as ad valorem with τ as the percentage of P0, the price decrease connected with a 50 per cent tariff reduction is underestimated and the elasticity which is thus derived is correspondingly overestimated. This bias may partly explain why the averages of the elasticities for commodities subject to mixed tariffs are higher than those for other commodities. In judging the significance of this bias for the average of the elasticities of all commodities, allowance should be made for the fact that the 1939 values of imports into the United States of the selected commodities with mixed tariffs represent only 11 per cent of the total imports of all 176 commodities.

In many cases a tariff reduction will lead to a decrease instead of an increase of the per unit foreign value. After a tariff reduction, demand may be increased more for the cheaper qualities in a group of related commodities than for the more expensive ones. This is often so if the duty is specific.

Suppose, for instance, that each of two commodities, A and B, has a horizontal supply schedule Sa and Sb. In Chart 3, Da0, Da1 Db0, and Db1 correspond to D0 and D1 in Chart 1; the first was the demand schedule before, and the second the schedule after, the tariff cut. In this case the Tariff Commission study would give (see Chart 3)

qa0 + qb0 = q0

qa1 + qb1 = q1

and the weighted prices

Paqa0+Pbqb0q0=P0

and

Paqa1+Pbqb1q1=P1

If B is the cheaper commodity, so that Pb<Pa, then the tariff reduction would decrease the per unit foreign value (P1<P0), if

qb1q1>qb0q0(16)

This will be so if the demand for B is more elastic than the demand for A.

Let

ΔqbqbPbΔPb<ΔqaqaPaΔPa(17)

According to (6) and (7),

ΔPa = Da0(qa1) - Da0(qa0) = (1 − δ)PaPa = −δPa

and similarly

ΔPb = −δPb

so that

PbΔPb=PaΔPa=1δ

This reduces (17) to

qb1qb012(qb1+qb0)>qa1qa012(qa1+qa0)

which can be simplified to

qb1qa0 > qb0qa1

or

qb1qa0 + qb1qb0 > qb0qa1 + qb1qb0

or

qb1q0 > qb0q1

which is the same as (16).

In measuring the elasticity of demand in this case, the supply of each commodity is assumed to be perfectly elastic and the effect of a relative increase in demand for cheaper commodities in the group is taken into account. If the duty is ad valorem, the foreign value of imports, after a 50 per cent reduction in the tariff (see 7), would be

(1 − δ)Paqa1 + (1 − δ)Pbqb1;

if this is divided by q1, the weighted per unit foreign value is obtained:

P0=(1δ)Paqa1+(1δ)Pbqb1q1=P1(1δ)(18)

which is the same as (12). In the case of a specific duty t, this is simply

P0=(Pa12t)qa1+(Pb12t)qb1q1=P112t(19)

which is the same as (14). Similar formulae can be derived for tariff increases.

Formulae (9a) and (9b) again give the elasticities; the prices used are those defined in (18) and (19).

*

Mr. de Vries, economist in the Trade and Payments Division, was educated at the University of Utrecht, the University of Chicago, and the Massachusetts Institute of Technology. He was formerly a member of the staff of the Cowles Commission.

1

For a discussion of these disadvantages, see Guy H. Orcutt, “Measurement of Price Elasticities in International Trade,” The Review of Economics and Statistics, May 1950 (Vol. XXXII, No. 2). Methods of computation, other than by linear correlation, have also been discussed by Arnold C. Harberger, Empirical Determination of the Elasticity of Demand for Imports, Cowles Commission Discussion Paper, Economics 267, July 20, 1949.

2

Post War Imports and Domestic Production of Major Commodities (79th Congress, First Session, 1945).

3

The Tariff Commission also prepared separate estimates under the assumption that the per capita income during the long-run postwar period would be equal to that in 1939. In this paper no elasticities computed from estimates based on this assumption are presented, since it has proved to be more unrealistic than that of a 75 per cent higher per capita income.

4

The list of these commodities is as follows (the number in Table 1 is indicated in parentheses): monosodium glutamate (1); tonka beans (16); paraffin wax (17); fats and oils (18); manganese ore and tungsten (30-32); lead, zinc, and copper (46, 47, 49); unstemmed cigarette leaf and tobacco for cigar fillers (56, 57); rice (70); by-product feeds (71); dates (72); coconuts (80); beans (84); cocoa (93); raw cotton, long staple (97); hard fiber rope (117); burlap (118); jute bags and bagging (124, 125); raw wool (130); rayon yarn (144); furs (161); and sponges (174). The main countries of origin of these imports are: Argentina, Australia, Bolivia, Brazil, Chile, China, Cuba, Egypt, Greece, India, Indonesia, Japan, Mexico, Peru, Philippines, South Africa, and Turkey.

5

These 21 commodities are the following (their numbers in Table 1 are indicated in parentheses): kaolin (21); pottery, tableware (23); mustard, prepared (96); whiskey (100); cotton yarn (105); cotton cloth (107); flax yarns (116); coarse linens (119); towels (120); miscellaneous flax fabrics and manufactures (121); plain linen handkerchiefs (123); wool waste (131); wool rags and shoddy (132); woolens and worsteds (135); wool hosiery (136); wool knit outerwear (137); wool wearing apparel (138); rayon staple fiber (145); books (156); lace (165); and leather (169).

6

For certain commodity groups, no representative commodities can be found among those listed in Table 1. The proportion of total imports from the ERP countries, which is accounted for by the groups for which there are representative commodities, is indicated in Table 2, column 3.

7

If the points C, A’, and B’ on the demand curve D0 in Chart 1 are indicated by the coordinates (p0,q0), (P0,q1), and (P0,q2), respectively, then e1 > e2means that

logq1logq0logp0logp0>logq0logq2logp0logp0

from which it follows directly that

logq1logq2logp0logp0>logq1logq0logp0logp0

which expresses the hypothesis referred to in the text.

8

Among the commodities for which e1 > e2 are pottery, tableware (23), sugar candy (55), woolens and worsteds (135), wool knit outerwear (137), and silk wearing apparel (143).

9

To test the statistical significance of the difference between these averages, and of those subsequently defined, a t-test was designed with 98 per cent probability.