269. J. E. Meade to Harrod , [November 1932] [a]

[Note attached to letter not found; answered by 270 ]

[November 1932] [1]

I must alter the type of analysis [2] slightly by telling of two countries x and y, (where one "country" may be the whole of the world except one other particular country), and by dividing commodities into those produced in x and only consumed in x, those produced in y and only consumed in y, those produced in x and exported to y and those produced in y and imported into x. (This is done, in distinction to the division into A, B & C goods, [3] because as I shall consider reductions or increases in expenditure on all commodities & in incomes in both countries, we cannot assume that the price level of A goods is given as far as one country is concerned, & cannot therefore assume that the amount that country produces for export is unaffected by a primary change of some other good in the trade balance.)

Let us assume that people can only spend income on goods or increase or decrease their money balances (i.e. there are no "capital transactions" [b] within either country or between the countries). Let = the income per day in country x and = the income per day in country y. (Income = receipt of money for sale of output of home produced goods, whether consumed at home or exported.) Let = proportion of income in x spent on imports from y, and = proportion of income in y spent on imports from x. Then we start from an equilibrium in which there are no gold movements or movement of short term funds between x and y, so that .

Let decrease to (e.g. because of a change in taste), so that country x spends mp less on imports from y. Our problem is to decide what it is that determines, whether so increases that there is no net decrease in expenditure by x on imports or whether so decreases that there is a decrease in y's expenditure on imports from x, equal in amount to , or what intermediate position is the result.

I wish now to assume that everyone in x & in y spends on day n what he received on day n-1, and that the proportions and remain constant, so that on day n country x spends on imports from y times the incomes of persons in x on day n - 1, and country y on day n spends on imports from x times the incomes of persons in y on day n - 1.

On day 1 less is spent on imports from y and the same amount more is spent on goods produced in x by members of x. Let  = A. Then on day 1 there is an increase A in expenditure on home produced and home consumed goods in x; there is no change in x's exports, so that x's incomes increase by A between day 0 and day 1. x's imports decrease by A, which means that y's exports decrease by A; y's expenditure on home-produced and home consumed goods remains unchanged between day 0 and day 1, so that y's incomes fall by A on day 1. On day 2 x spends more on home-produced and home consumed goods than on day 1, since x's incomes on day 1 are greater than incomes on day 0 by A; similarly x spends A more on imports on day 2 than on day 1. y however, since on day 1 her income is less than income on day 0 by A, spends A less on imports from x and less on home produced and home consumed goods. On day 2 incomes in x are greater than incomes on day 1, by (since that much more is spent on home produced goods in x) - A [c] (since this much less is received for sale of exports by A.) i.e. x's incomes rise between day 1 and day 2 by . Conversely y's incomes fall between day 1 and day 2 by , since less is spent on home produced and home consumed goods in y and A more is spent by x on imports from y. On day 3 x spends more on home produced and home consumed goods than on day 2, and more on imports from y than on day 2. On day 3 y spends less on home produced and home consumed goods, and less on imports from x than on day 2. On day 3 therefore x's incomes are greater on day 2 by --the increased expenditure on consumed goods-- --the decrease in expenditure on x's exports. i.e. there is a decrease in x's incomes between day 3 and day 2 of . Conversely y's incomes decrease between day 3 and day 2 by {=  }.

Thus incomes in x increase in all by the sum of the series to infinity: . Since and must both be < 1, must lie between 1 and -1, so that the series can be summed and is equal to . The decrease in incomes in y is equal to the same quantity . Thus in the new equilibrium x's exports will have decreased by , (i.e. the decrease in incomes in y multiplied by the fraction ). x's imports will have decreased by A (the primary decrease in import due to the change in to ) -  , (i.e. the secondary increase in x's imports due to the rise in x's incomes by ). This is equal to , so that the decrease in imports is equal to the decrease in exports. (It will only be equal to 0, if is equal to 0. That is to say, if country y is so great that it spends a negligible proportion of its income on imports.)

This result can also of course be obtained by summing directly the changes in x's imports and exports. x's imports decrease by

and x's exports decrease by

. [4]

This is of course all written on the assumption that in both countries persons spend on day n everything that they received on day n - 1. This may be modified for two main reasons:--(1.) Persons in x may spend on day 1, what they received on day 0, while persons in y may only spend on day n what they received on day 0 (i.e. the velocities of circulation may be different in the different countries). (2) There will have been some transfer of money (i.e. gold) from y to x, and incomes in y will have fallen and in x will have risen; but the proportions of incomes to money holdings may have altered in x and y, and this may lead to "dishoarding" or "hoarding" {cf. D. H. Robertson. [5] Induced Hoarding and Induced Dishoarding Persons, who have not hoarded or dishoarded, (i.e. have always spent on day n their income of day n - 1), may be induced to hoard or dishoard by the alteration in the income velocity of circulation of money.}.

However I don't think anything is served by putting these two last considerations into algebra--even if I can, which is v[ery] doubtful,--until I know whether you accept the main contention, that in this case as in the case of reducing wage rates, the velocity of circulation of money will determine what actually happens.

  1. 1. The note is undated; since it is also neither signed nor initialled, it would seem that it was attached to a letter not found.

    2. Meade's note refers to chapter VI of Harrod's International Economics ( 1933:10 ). Meade had a typescript of the book: see letter 272 , [jump to page] .

    3. Harrod defined A, B and C goods respectively as "the staple goods of homogeneous character and capable of entering into foreign trade"; inhomogeneous commodities, somewhat specialized in character, also capable of entering into international trade; and "goods and services [...] by their nature incapable of entering into international trade" ( 1933:10 , pp. 59-61). Meade's alternative analysis was not adopted in the published version.

    4. Meade omitted to indicate that the series continues to infinity on the left-hand side of the formula; the result on the right-hand side, however, accounts for this.

    5. Robertson, Banking Policy and the Price Level (1926), pp. 45-47.

    1. a. AN, ten pages on five numbered leaves, in HP IV-745-767/1.

      b. In the manuscript, at first Meade closed the inverted comma after the word "capital", but changed his mind and crossed it out without closing it elsewhere. It is not possible, therefore, to guess whether the solution proposed here respects Meade's intention, or whether he wanted to cross out the inverted commas altogether.

      c. In this sentence, in the manuscript Meade adopted the notation

    , and respectively to date the variables at day 1. This convention was dropped in the remainder of the manuscript, and has therefore been normalized here.

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