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,
or (see Chart 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
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,
In this case the Tariff Commission study gives estimates for (P0, q0), (P0, q1), and (P0, q2). The desire is to determine
from (4) and (3) which can be written more generally:
The point elasticity at each point of a curve of constant elasticity passed through the points (P0, q0) and (
and similarly for the points (
If instead of an ad valorem tariff the duty is specific, formulae (6) and (8) become simply
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
if the tariff is ad valorem;
if the tariff is specific. The elasticities are expressed by (9a) with
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
If B is the cheaper commodity, so that Pb<Pa, then the tariff reduction would decrease the per unit foreign value (P1<P0), if
This will be so if the demand for B is more elastic than the demand for A.
According to (6) and (7),
ΔPa = Da0(qa1) - Da0(qa0) = (1 − δ)Pa − Pa = −δPa
ΔPb = −δPb
This reduces (17) to
which can be simplified to
qb1qa0 > qb0qa1
qb1qa0 + qb1qb0 > qb0qa1 + qb1qb0
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:
which is the same as (12). In the case of a specific duty t, this is simply
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.
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.
Post War Imports and Domestic Production of Major Commodities (79th Congress, First Session, 1945).
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.
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.
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).
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.
If the points C, A’, and B’ on the demand curve D0 in Chart 1 are indicated by the coordinates (p0,q0), (
from which it follows directly that
which expresses the hypothesis referred to in the text.
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).
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.