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Immediate Effects of Devaluation on Prices of Raw Materials

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1950
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THE DEVALUATIONS of September 1949 stand in sharp contrast to those of the thirties in that nearly all of them took place within a short period of time and were not, as in the thirties, carried through piecemeal.1 This makes it possible to construct a simple theoretical model by means of which the impact of devaluation on the prices of raw materials may be studied. A formula may be derived for the estimation of this effect and, under certain conditions which can be regarded as normal, this formula depends only on the extent of the devaluation and the relative shares of the devaluing and non-devaluing areas in the total supply of and demand for the product under consideration. In theory, the effect also depends on the elasticities of demand and supply in the devaluing and non-devaluing areas. In fact, however, for commodities of which less than one fourth of the combined supplies of the two areas is traded between the areas, the influence of different elasticities on the effect of the devaluation is slight. Consequently, as long as less than one quarter of the total supply moves between the two areas, the simplified formula provides a satisfactory approximation.

In order to estimate changes in raw materials prices resulting from the devaluations of September 1949, it may be assumed, for simplicity, that the world is divided into two major groups of countries—those whose currencies have been devalued to approximately the same extent as sterling (the sterling market) and those whose currencies have maintained more or less their previous dollar parities (the dollar market). Supplies of raw materials, and likewise demand for raw materials, come from both groups of countries but not to the same extent for different commodities. Under the assumption that supply and demand in these two groups of countries are not isolated, i.e., that the markets are merged, the prices in the two markets must, costs of movement aside, be the same at any given rate of exchange. Devaluation must, therefore, raise the sterling prices of such commodities, except to the extent that dollar prices fall, until price equality has been restored at the new exchange rate.

The question of the effect of devaluation on prices may be put in quantitative terms by asking how much sterling prices may be expected to rise and dollar prices to fall for each commodity. The answer will depend on the extent to which supply and demand in each market respond to the change in price. As the sterling price rises, supply in the sterling market will expand, and as the dollar price falls supply in the dollar market will contract. Similarly, under the assumption that incomes in each market are not much affected by devaluation, the demand in the sterling market will contract as sterling prices rise, and the short-run demand in the dollar market will expand as dollar prices fall. To the extent that these commodities are used in one market to process goods for export to the other market, the effect on demand will be counteracted by the favorable or unfavorable effect of devaluation on the exports of such processed goods.

For many raw materials, the dollar and nondollar markets are not merged but are isolated from each other by obstacles and administrative controls. These hindrances prevent the free flow of goods and permit different prices and price movements in the two markets. Prices of commodities in this category behave differently from those which are formed by free market forces. A distinction should accordingly be made between commodity prices governed by the operation of free market forces in a world market and those in markets isolated from the prices quoted in other markets, either by exchange and import controls or by marketing arrangements including contractual agreements.

The immediate rise to be expected in the sterling price, and the associated fall in the dollar price as a result of the impact of devaluation, may be stated in simple terms for a commodity whose price is determined by economic forces and for which prices in dollar and sterling markets are so related that, costs of movement aside, they are equal at the official rate of exchange.2 In brief, the rise in sterling price must be such that the expansion of supply plus the contraction of demand in the sterling market induced by the rise in the sterling price is precisely equal to the contraction of supply plus the expansion of demand in the dollar market induced by the associated fall in the dollar price. The price changes in sterling and in dollars (in opposite directions) must equate the induced shifts in the inter-market trade in each commodity. This is the fundamental basis for determining the impact of devaluation on the prices of raw materials whose markets are not isolated.

According to the formula worked out below, the sterling price of a non-isolated commodity will rise more (and the dollar price will fall less), the less the share of the sterling market in total supply and total demand, and the more elastic the supply and demand in the dollar market and the less elastic the supply and demand in the sterling market. The common sense of this is readily apparent. In the first instance, the impact of sterling devaluation on the dollar price of a commodity cannot be large if the share of the sterling market in the total supply and the total demand is small. Under such conditions, the sterling market will simply follow the dollar market without affecting it very much. Given the share of the sterling market in total supply and total demand, then if a small fall in the dollar price brings a large expansion of demand and a large contraction of supply in the dollar market, the sterling price will be induced to rise considerably to meet the expanded demand and to replace the contracted supply of the dollar market. On the other hand, if the supply and demand are inelastic in the sterling market, supplies will not expand or be released for sale in dollar markets on a scale sufficient to induce a large fall in the dollar price.

It can further be shown that differences between the elasticities of supply and demand in the dollar and sterling markets may be neglected, provided the inter-area trade is less than 25 per cent of the total production of the two areas. The estimated effect of devaluation on price can then be determined exclusively by reference to the shares of the dollar and sterling markets in total supply and total demand. On the basis of these assumptions, estimates have been made of the changes in price that might be expected, as a result of sterling devaluation, for various raw materials.

Raw Materials Sold in Non-Isolated Markets

Derivation of simplified formula

The market for internationally traded raw materials is assumed to be divided into two areas. The currencies in area 2, the sterling area, are devalued against those of area 1, the dollar area. A raw material is assumed to be homogeneous as between the two areas, e.g., the tin or copper produced in one area is perfectly substitutable for the tin or copper produced in the other area.

The following notations are used for each raw material; subscripts refer to the areas.

S1 = initial production of the raw material in area 1

D1 = initial demand for the raw material in area 1

P1 = price of the raw material in area 1 in terms of the currency of area 1

r = rate of exchange expressed as dollars per pound sterling

eS1 = elasticity of supply of the raw material in area 1

eD1 = elasticity of demand for the raw material in area 13

When the markets for raw materials are in equilibrium before devaluation, the total supply of the two areas equals the total demand in the two areas, so that

Change in the dollar and the sterling prices of raw materials will affect supply and demand in the two areas. If the supply in area 1 changes by ΔS1 and similarly the demand by ΔD1, then the market will be in equilibrium after the devaluation if

The increments ΔS1 and ΔD1 can be expressed in terms of the elasticities, the quantities supplied and demanded before the devaluation, and the relative change in prices. Since, for instance,

the following substitution can be made in equation (1.2):

and similarly for the other increments.

By subtracting (1.1) from (1.2) and substituting for the increments, it follows that

If the markets in area 1 and 2 are merged and the raw material is homogeneous as between the two areas, there is only one price for the raw material, i.e.,

or

from which it follows that

where j is the relative change in the dollar equivalent of sterling, i.e.,

By substituting (1.4) in (1.3), and solving for ΔP2P2

This formula gives an expression for the relative rise in the sterling price of a commodity. It yields the familiar result, that the sterling price will rise more, the more elastic the supply and demand in the dollar area and the less elastic the demand and supply in the sterling area. It is also apparent from (1.5) that the relative share of an area in the total demand or supply of a commodity is important in determining the relative rise in the sterling price. If it is assumed that

equation (1.5) then becomes

where c is the difference between 1 and the ratio of the elasticities of demand and supply, or

and KS is the relative share of the dollar area in the total production of the commodity, i.e.,

and similarly

If the elasticity of supply equals that of demand, i.e., c = 0, formula (1.8) can be further simplified to

where

Two simplifying assumptions about the elasticities of demand and supply are used in the derivation of formula (1.9). First, the elasticities of total demand in each area, and also the supply elasticities, are taken to be equal (1.6 and 1.7). This assumption may be reasonable during a period so short that the total output in each area of the commodity under consideration cannot be expected to respond to the rise in sterling prices and the associated fall in dollar prices. Given time, however, production in the sterling market will respond to the higher sterling prices, and production in the dollar market to the lower dollar prices. The technical conditions of production will determine the length of the period required for a response of production to the changes in prices; and the response to the inducement to expand production in the sterling market may be greater than the response to the inducement to contract production in the dollar market. Any such difference in the elasticities of supply in the two markets will tend to be greater, the larger and more specialized the investment involved. The difference is likely to disappear over a longer period, after adequate time has elapsed for the adjustment of investment and output to the new price structure. The assumption of equal supply elasticities will then usually be valid, since most commodities are produced under similar conditions in the two areas.4

The second assumption is that the elasticity of supply, es, equals the elasticity of demand, eD. For this assumption there is no economic justification. If the two elasticities are different, the rise in the sterling prices following from the effect of devaluation may be estimated from formula (1.8). The error in assuming the elasticities to be equal can then be determined by computing the difference between (1.8) and (1.9) for various values of c, i.e., the difference between 1 and the ratio of eD and eS, and of KS and KD, i.e., the shares of the dollar area in total supply and in total demand. This difference is zero if KS = KD, regardless of the value of c, i.e., regardless of the values of eS and eD. For practically all major world trade commodities, –¼<KSKD<¼. For values of KS and KD that satisfy this condition, the difference between (1.8) and (1.9) is so small that the simplified formula (1.9) may be accepted as a reasonable approximation of (1.8).

Formula (1.5) can be extended further by deriving the demand for raw materials from the demand and supply conditions of the final commodities in the production of which the raw materials are used. Account is thus taken of the effects of devaluation in reducing processing costs in the sterling area relative to the dollar area. For most of the major world trade commodities, the K’s do not differ by more than one quarter. For these values of the K’s, the simplified expression (1.9) given above yields a reasonable approximation to formula (2.12), given in the Appendix, which is based on the assumption of derived demand.

It has been assumed that the raw materials under consideration are homogeneous, or at least that the elasticity of substitution for any commodity, as between the sterling area and the dollar area, is infinite. A formula has been derived for the case of imperfect substitutability and has been applied to cotton. (See Appendix, formula 2.14.)

Computed and actual price changes

Formula (1.9) is applicable only to the prices of raw materials whose markets are not isolated. The assumptions on which it is based are appropriate only to commodities which are exported from the sterling market to the dollar market. The indicated effects of devaluation, computed on the basis of the simplified formula (1.9), together with the actual price changes as of a post-devaluation date for five such commodities, are shown in Table 1.

Table 1.Estimated Effects of Devaluation on Sterling Prices, Compared with Actual Price Changes, for Five Primary Commodities Supplied by the Sterling Area to the Dollar Area on Net Balance(Percentage increases over August 1949 prices1)
Actual Changes
Aug. 1949 to Oct. 19491Aug. 1949 to Dec. 19493Nondollar Area Where Price Is Quoted
CommodityEstimated Effects 2United States 4Nondollar areaUnited States 4Nondollar area
Wool141391818U.K
Tin15343265U.K.
Rubber2141275240Singapore
Cocoa133126536Gold Coast
Tea 5220442919Ceylon

Or closest available date.

These estimates, computed from the simplified formula (see text), are based on 1948 figures, compiled by the Statistics Division, Research Department, of the Fund. In the computation, the Western Hemisphere and the Belgian Congo were included in the dollar area; production of Japan, U.S.S.R., and China-Manchuria was not included in total production; and the assumption was made that the nondollar area devalued by 30.5 per cent. Of course, some nondollar countries devalued by less, but the principal suppliers and the most important nondollar consumers of these commodities in world trade did devalue by 30.5 per cent, so that the discrepancy introduced by the assumption of uniform devaluation is probably not significant.

For wool, rubber, and tea, the dates compared are August and December averages; for tin, August and January averages; for cocoa, August average and December 20.

The changes shown here are percentage changes in the sterling equivalent of reported dollar prices.

Tea price movements in Ceylon and the United States were dissimilar until shortly before devaluation when the prices approached equality.

Or closest available date.

These estimates, computed from the simplified formula (see text), are based on 1948 figures, compiled by the Statistics Division, Research Department, of the Fund. In the computation, the Western Hemisphere and the Belgian Congo were included in the dollar area; production of Japan, U.S.S.R., and China-Manchuria was not included in total production; and the assumption was made that the nondollar area devalued by 30.5 per cent. Of course, some nondollar countries devalued by less, but the principal suppliers and the most important nondollar consumers of these commodities in world trade did devalue by 30.5 per cent, so that the discrepancy introduced by the assumption of uniform devaluation is probably not significant.

For wool, rubber, and tea, the dates compared are August and December averages; for tin, August and January averages; for cocoa, August average and December 20.

The changes shown here are percentage changes in the sterling equivalent of reported dollar prices.

Tea price movements in Ceylon and the United States were dissimilar until shortly before devaluation when the prices approached equality.

The estimated effects of devaluation are not intended to include the influence of other market forces operating during the period considered. The actual price changes, however, show the effect not only of depreciation but also of changed business conditions and expectations, independent changes in supply and demand, exchange and trade controls, marketing and trade agreements, etc. For some commodities, these other factors are not of great importance in the short period, but for many commodities they are very important and they affect both the immediate impact of devaluation on prices and the future course of prices, production, and trade. There is no simple way of segregating the effects of forces other than those directly related to the devaluation, such as the effects of changed expectations in business which have been especially large because sterling was devalued just when the contraction of industrial production in the United States was coming to a halt.

The anticipation of devaluation also exerted an influence on the pre-devaluation prices of a number of commodities. For example, in the several months prior to the devaluation, holders of sterling may have purchased sterling commodities, thus pushing up sterling prices; or dollar area buyers of sterling commodities may have postponed payments in dollars. No attempt is made here to evaluate the impact of anticipation for each commodity, but the influence of anticipated devaluation should be sharply distinguished from the influence of other forces which might have affected commodity prices simultaneously.

Effects of devaluation on administered prices and in isolated markets

For many of the commodities of which there is a net import by the depreciating countries, market forces are not permitted to operate freely in the sterling market, mainly because of the dollar shortage. Even in the dollar market, many commodities are subject to administrative control by either governments or business enterprises. When administrative controls in either area prevent the free operation of market forces on prices, the price effects of devaluation will differ from those that might be predicted on the assumption of free markets.

One aspect of the dollar shortage is that many goods, of which there is a net import into nondollar markets, are in short supply there. For these goods, the home demand is only partly satisfied and various types of allocation and rationing are applied. Therefore, a rise in the sterling prices of these commodities need not reduce consumption in the sterling market, unless allocations or rations are cut. Furthermore, the fact that these commodities are being imported into the sterling market at a time when all possible encouragement is being given to local sup-pliers of dollar-saving goods implies that in the short run the supply in the sterling market is highly inelastic. As a result of shortages in the sterling market and the inelastic supply there, the early effects of sterling devaluation on dollar prices in the dollar market for these commodities should be close to zero.

A decline in dollar prices of commodities that are in short supply in the sterling market can be expected as a result of devaluation only for those commodities whose imports into the sterling market would tend to be reduced if, as a result of devaluation, the old dollar prices were maintained. Such reductions might result either from administrative decisions by the governments of nondollar countries or from a rise in sterling prices so great as to reduce the sterling market demand to the point where the commodities are no longer in short supply in the sterling market.

For some commodities, principally foodstuffs, not only was demand restricted in the nondollar market, but there were also major price discrepancies between the two markets prior to devaluation. These discrepancies were not all in the same direction. Where, for some commodities in short supply in the sterling market, the sterling price was already higher than the dollar price, an increase of sterling prices by less than 44 per cent would be required to equate the two. However, for those commodities whose sterling prices were kept lower than dollar prices, devaluation has either widened the gap or left it virtually unchanged. No generalization is possible concerning the price changes to be expected in the future for these commodities, because the actual movements will depend largely on changes in administrative controls, in both the sterling market and the dollar market.

Meanwhile, many important agricultural products and metals, which were in short supply in the dollar market as well as in the sterling market for much of the postwar period, are becoming more and more freely available in the dollar market at lower dollar prices so that the actual rise in their sterling prices will be limited by the independent effect of expanding supplies. A very moderate rise in sterling prices may then be sufficient to eliminate the pre-devaluation discrepancy between sterling and dollar prices.

In brief, for the purposes of the present enquiry, three important categories may be distinguished:

(1) Commodities which on net balance are supplied by the sterling market to the dollar market. Their prices tend to be formed in non-isolated markets. They have been discussed in the previous section, and the actual changes in their prices are shown in Table 1.

(2) Commodities supplied on net balance by the dollar to the non-dollar market, whose prices since devaluation have been substantially equal, or have moved parallel, in the two areas. The dollar and non-dollar markets for these commodities have not, in general, been merged, but there has apparently been some linkage between the price movements. The prices of nonferrous metals provide an important illustration. For some commodities in this category, it is of interest to compare the actual post-devaluation price changes with the estimates of the effects of devaluation on prices, based on the assumption of non-isolated markets (see Table 2).

Table 2.Post-Devaluation Changes in Sterling Prices of Specified Categories of Commodities1(Percentage increases over August 1949 prices 2)
Actual Changes
Aug. 1949 to Oct. 19491Aug. 1949 to Dec. 19493Nondollar Area Where Price Is Quoted
CommodityEstimated Effects 2United States 4Nondollar areaUnited States 4Nondollar area
Category 2 1
Copper2944315143U.K.
Lead3130281512U.K.
Zinc2936294239U.K.
Cotton 52037254956Egypt
Copra35105422Straits
Petroleum44444444Iran
Category 3 1
Cotton 5371440India
Cordage fibers4586231British East Africa
Coconut oil200190Ceylon
Sugar460420U.K.
Wheat55355635U.K.
Bacon481271U.K.
Butter460450U.K.
Pig iron490450U.K.
Nitrate380360U.K.
Cocoa3127359Gold Coast
Rice200410U.K., India, Burma
Coffee804415144U.K.

For description of categories, see text.

Or closest available date.

For a description of the computation of these estimates, see Table 1, footnote 2. For cotton, a different estimate can be made if allowance is made for the non-homogeneity of the various kinds of cotton. See Appendix.

The changes shown here are percentage changes in the sterling equivalent of reported dollar prices.

The average price of Egyptian cotton apparently moved with that of U.S. cotton, while the price of Indian cotton remained fixed.

For description of categories, see text.

Or closest available date.

For a description of the computation of these estimates, see Table 1, footnote 2. For cotton, a different estimate can be made if allowance is made for the non-homogeneity of the various kinds of cotton. See Appendix.

The changes shown here are percentage changes in the sterling equivalent of reported dollar prices.

The average price of Egyptian cotton apparently moved with that of U.S. cotton, while the price of Indian cotton remained fixed.

(3) Commodities, principally agricultural, many of which are in short supply in the sterling market, whose sterling prices differ from dollar prices. The observed percentage increases in sterling prices of the primary commodities in categories 2 and 3 are given in Table 2. For many commodities in these categories, the observed price in the non-dollar area is neither an open-market price paid to the producer nor the price paid by an administrative agency, but it is a controlled or subsidized price at which the commodities are sold by designated agencies to qualified purchasers.

The sterling prices of commodities in category 2 might, by and large, be expected to rise by 44 per cent as a result of the devaluation, with the actual rise tempered or accelerated by changing conditions in the dollar markets and the extent to which prices in the sterling market differed from those in the dollar market before devaluation. Eventually they might be expected to fall as sterling supplies are increased in response to higher sterling prices.

Largely because of administrative controls, the prices of commodities in category 3 behave quite differently in the two areas. No generalization is possible with regard to these commodities, since the influence of changes in administrative arrangements and contracts and gradual changes in world supply will overshadow the effects of devaluation. The effects of devaluation are virtual rather than actual, since market forces are not permitted to exert their full influence on those prices.

Appendix

The demand for raw materials can also be treated as derived from the demand and supply conditions of the final commodities in the production of which the raw materials are used. Assume that the raw material is used in the production of one final good only, and that one unit of raw material and one unit of labor are used in the production of one unit of final good. Then if the only cost factors considered are raw materials and labor, it follows that:

where the p, p1, and w are the per unit cost in terms of dollars of the final good, raw material, and labor, respectively.

If in each area wages in terms of the currency of that area are Constant, the change in p due to devaluation is for the dollar area

and for the sterling area

The difference between (2.2) and (2.3) measures the advantage to the sterling area arising from the lower processing costs in terms of dollars after the devaluation. Formula (2.3) can be explained as follows. If w2 is the per unit labor cost in the sterling area, in terms of sterling, then this labor cost in terms of dollars is

from which it follows, since w2 is constant, that

Further, if ηS = elasticity of supply of final goods, and ηD = elasticity of demand for final goods (absolute value), it can be proved that

where the e’s, as previously defined, refer to the raw material and N is the number of dollars of raw material used per dollar of final commodity. Let the supply functions of the final good and the raw material be respectively

and

where qf and qr refer to quantities of finished goods and raw materials respectively. Since

because of the definition of the units, (2.4) can be proved by substituting (2.5) and (2.6) in (2.1), in which w is independent of q, and by taking the derivative with respect to q. The proof for the demand elasticities is similar.

If it is assumed that the two markets for final commodities are isolated from each other, then for the dollar area before devaluation

or

After devaluation the supply and demand curves are assumed to have the same elasticities but to shift by factors ζi and εi respectively, in the i-th area, so that for the dollar area

where the primes denote the value of the variable after devaluation. The dollar area’s demand curve does not shift at all, so that ζ1 = 0, but the supply curve is shifted by

because (2.2) implies that for any quantity supplied the corresponding price will be reduced by the reduction of the price for the raw material component of the finished good. It follows that

If (2.4) is used and derivatives of the second order and higher are neglected, it follows that

For the sterling area it follows, similarly, that

and

where now

and

from (2.3) and (1.4)

so that

From the definition of the units of quantities of raw materials and final goods, it follows that

The assumption is made that the markets for raw materials are not isolated, and that the equilibrium condition for these markets, following from (1.1) and (1.2), is

Then, as in the derivation of the formula (1.9) above, the left-hand member of this equation can be written

If (2.7), (2.8), and (2.9) are substituted for the right-hand member, then

Thus treating the demand for raw materials as a derived demand leads to an expression similar to (1.3) except that the factor eSeDeS+eD occurs instead of eD in the right hand member of the equilibrium condition.

When (2.10) is solved for Δp2p2 in a manner similar to that followed for formula (1.9), then

which corresponds to (1.8).

When c = 0, (2.11) reduces to

which corresponds to the simplified formula (1.9).

It can be seen that (1.9) is a reasonable approximation of (2.11) and (2.12) for values of KS and KD satisfying –¼<KSKD<¼.

Finally, the possibility may be taken into account that, contrary to the previous assumption, the elasticity of substitution for some raw materials as between the sterling area and the dollar area may be finite. In that case, the model can be changed as follows:

Let

Pi.k = price of raw material produced in area i and consumed in area k in terms of the currency of area k;

Di = total demand for raw material produced in area i;

p= elasticity of substitution.

The definition of the elasticity of substitution implies that

The equilibrium conditions are

The supply equations are

The markets for each kind of raw material are not assumed to be isolated so that

If the demand for raw materials produced in the dollar and sterling areas, taken together, is fixed, then

From these equations it can be shown that

or if eS2 = eS1 = eS

This formula expresses the relative rise in sterling prices of raw materials produced in the sterling area if the elasticity of substitution is finite. This is most clearly the case with cotton, where substitution is limited by differences in length of staple. The elasticity of substitution between Indian and U.S. cotton has been estimated at –2.9 and that between Egyptian and Indian cotton at –1.1.1

If it is assumed in (2.14) that the ratio of the supply and substitution elasticities, eSp, equals 14 and 18, then the computed price changes are 19 and 21 per cent, respectively, as against the observed change of 25 per cent in the sterling price.

December 1949

Mr. B. A. de Vries, economist in the Trade and Payments Division, Exchange Restrictions Department, was educated at the University of Utrecht and the University of Chicago, and was formerly a member of the staff of the Cowles Commission,

This study benefited considerably from the advice of Messrs. J. J. Polak and Sidney S. Alexander of the Research Department of the Fund.

The sterling and dollar prices before devaluation are presumed to be equivalent, at the rate of $4.03; after the rise in the sterling price and the fall in the dollar price, the prices are again presumed to be equivalent at $2.80. Under these conditions, the fall in dollar price associated with any given rise in sterling price is one that equates the prices of a commodity in the two currencies at the new rate of exchange. Thus, a 30.5 per cent devaluation of sterling implies that a 44 per cent rise of the sterling price would be associated with an unchanged dollar price; a 22 per cent rise in the sterling price with an 18 per cent fall in the dollar market; and a 30 per cent rise in the sterling price with a 10 per cent fall in the dollar price (1.44 × 1.00 = 1.22 × 1.18 = 1.30 × 1.10 = 1.44).

Defined to be positive if, at the reduced price, more is demanded than at the higher price.

An important exception might be rubber. In the computation of the effect of devaluation on the price of rubber (Table 1), synthetic rubber is included for the dollar area; synthetic rubber is produced under conditions which differ from those under which natural rubber is produced. On the demand side, commodities for which there are altogether different tastes in the two areas provide another exception.

J. Tinbergen, “Some Measurements of Elasticities of Substitution,” Review of Economics and Statistics, August, 1946.

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