Terms of Trade: The Price of What You Sell Against What You Buy

The terms of trade is the price of what a country sells against the price of what it buys, set out as an index. A rise means each unit exported now buys more imports, so the same effort brings back more. The measure takes in prices and never volumes. A country can therefore watch its terms improve while it trades less.

Two ideas stand behind the terms of trade, and each has been set out separately. The first is how an index works: a number set to 100 in a chosen period and read afterwards only as a movement away from that 100. Index arithmetic was set out where inflation was measured and carries over unaltered. The second is the terms on which two countries actually swap goods. The swap came earlier as a plain ratio of one good against another, built out of comparative costThe comparison of what each country gives up to make a thing, rather than of how much of it each can make. It decides the direction of a trade and was worked through earlier. with no money anywhere in the illustration. The new part is the version a statistician publishes: the same swap read off price movements, compressed into one number, and watched as that number travels. And one arithmetic fact comes with it that catches almost every reader on first meeting. The number does not travel the same distance up as it does down.

Where these numbers come from: the Republic of Sankhya and its partner Marut are inventions, and so is every rupee amount below. Onions sit at Rs 2,000/- a quintal and machines at Rs 50,000/- each for one reason only. The pair makes a ten per cent move easy to follow by hand and puts the ratio between them on a whole number. Rupee amounts are held whole and every index reading is carried as a whole count of hundredths of a point, so a figure gets rounded once when it is printed and never a second time.

What is the price of a machine when Sankhya pays for it in onions?

Start at a tea stall. The whole idea is visible there before any country walks into it. A vendor sells tea at Rs 10/- a cup and buys a gas cylinder at Rs 1,100/-. To pay for one refill he has to sell 110 cups. Nothing else about his working life needs to be known for that number to mean something to him. Now let the tea price go to Rs 11/- a cup while the cylinder price stays exactly where it was. The refill now takes 100 cups. Same stove, same cylinder, same hours, and it costs him ten cups less than it did last month. The terms of trade in its plainest form is this: how much of the thing being sold it takes to get one unit of the thing being bought.

A country asks the identical question and gets its answer in two quite different ways, and keeping those two ways apart is the first real skill the measure demands. The first way counts goods. In the Sankhya illustration already met, one machine costs 25 quintalsThe weight unit that grain, oilseed and vegetable trade is usually quoted in across India. One of them is a hundred kilograms. of onions, and any terms running from 10 up to 50 quintals a machine leave each of Sankhya and Marut ahead of building the thing at home. The figure of 25 came out of opportunity costWhat was given up in order to do a thing, counted as the next best use of the same time, land or labour rather than as money paid out. in a setting with no money in it anywhere. The goods ratio is the real terms of trade, and it is stated in onions.

The second way counts money. Sankhya sells its onions abroad at Rs 2,000/- a quintal and buys machines from Marut at Rs 50,000/- each, both invented figures. The division those two prices invite is the one to do. Rs 50,000/- over Rs 2,000/- is 25 quintals to the machine, the identical number the goods reading gave in the paragraph above, reached from a completely different direction with no opportunity cost anywhere in it. A price ratio between two goods is the terms of trade said in rupees instead of in onions, so the goods reading and the money prices agree exactly, and they have to. Because the two sentences are one sentence, Sankhya would walk away from money prices implying anything outside the band of 10 to 50 quintals a machine, in precisely the way it would walk away from goods terms outside that band.

So why does anybody build an index at all, rather than simply publishing the ratio? Because the ratio survives only while there is one thing on each side. Here Sankhya sells onions and Marut sells machines, and 25 quintals a machine is a sentence anyone can carry around. A real economy sells several thousand different things and buys several thousand more, and at that point there is no single quintal and no single machine left to divide into each other. Movement is what survives the collapse. Each of the several thousand prices can still be measured against its own past, and the two bundles of movement can still be set against each other. The index is what the price ratio turns into once there is no longer one ratio to take. The index therefore reports how far the ratio has travelled rather than what the ratio currently stands at. The absence of a single ratio is also why the index carries no unit, why it begins at 100, and why the two readings in the figure below never disagree and still cannot be converted into each other.

How do two price movements become one number that moves?

Take the export price first and give it its own index. Whatever Sankhya's onions fetched in the base period, call that 100. If the price later rises from Rs 2,000/- to Rs 2,200/- a quintal, that export price index reads 110. Now do the same for the import price. Whatever a Marut machine cost in the base period, call that 100 as well. If it later rises from Rs 50,000/- to Rs 55,000/-, that import price index also reads 110. Two prices, two separate movements, each measured only against its own past and never against the other.

The terms of trade index is the first of those divided by the second, multiplied by 100. The division is worth reading slowly, and it is the only formula the terms of trade needs. Export price index over import price index, times 100. In the base period both indices read 100, they divide to 1, and the terms of trade index reads 100.00 by construction rather than by measurement. Three questions the construction never asks are worth marking. The construction never asks how large a machine is next to a quintal of onions, never asks how many rupees one is worth against the other, and never asks how many of either changed hands. The one question it does ask is which of the two prices has moved further from where it started.

The level of a terms of trade index carries no information at all on its own, and only the change carries any. A reading of 100.00 does not mean fair, balanced or normal. A reading of 100.00 means the base period and nothing else. Because the two numbers are measured against two different base periods and two different sets of goods, a reading of 250 in one country against 80 in another says nothing whatever about which of them trades on better terms. The only sentence that can safely be built out of a terms of trade index is a sentence about movement: it was 100.00, it is now something else, and here is what that difference does. How a base period gets chosen, and what happens to a series when the base is moved, is index arithmetic that was set out where inflation was measured and behaves here exactly as it behaves there.

What does a rise in the terms of trade actually hand a country?

Let the onion price rise ten per cent while the machine price stays exactly where it was, so the export price index reads 110, the import price index reads 100, and the terms of trade index reads 110.00. What has Sankhya got out of that? Hold the export volume fixed at 50 lakh quintals of onions, precisely the same onions grown by precisely the same farmers. The same onions now bring home ten per cent more imported machinery than they did in the base period. Not ten per cent more money, though the nominalMeasured in the money of the day, with no adjustment for how prices have moved. A nominal figure and a physical quantity can point in opposite directions in the same period. earnings do rise too. Ten per cent more machinery, physically, on the docks.

Sit for a moment with everything that did not happen there. Not one extra onion was grown. No worker worked a longer day. No machine got better. The only thing that changed anywhere in the story is a price, and the country brings home a tenth more equipment for the identical effort. An improvement in the terms of trade means exactly that, and the gain is real rather than a bookkeeping one. The extra machinery physically arrives.

Now count that same gain in onions. Onions are where the gain stops being an index reading and starts being cargo. At the base a machine costs Rs 50,000/- and a quintal fetches Rs 2,000/-, so a machine costs 25 quintals. Let the onion price go to Rs 2,200/- and leave the machine price untouched. The machine now costs Rs 50,000/- over Rs 2,200/-, or 22.73 quintals to two decimals. Two and a quarter quintals less for every machine, on every machine, all year. Watch how tightly that tracks the index: 25 divided by 1.10 is 22.73, precisely what a reading of 110.00 is claiming. Put the ten per cent on the machine price instead and a machine costs 25 times 1.10, or 27.50 quintals, against an index of 90.91. An index at 110.00 and a machine costing 22.73 quintals instead of 25 are one event described twice, so the index can never say anything the goods will not confirm.

The household version keeps it honest. A house that sells milk and buys diesel watches the same ratio without ever naming it. If the milk price rises while diesel holds, the same herd fills the same tank and something is left over at the end of it. The something left over is not an accounting entry. The money pays school fees.

Why does the same ten per cent not move the index the same distance both ways?

Here is the arithmetic that catches nearly everybody, and it is worth producing yourself before reading the explanation underneath it. A ten per cent rise in the export price took the index from 100.00 to 110.00. Go back to the base, leave the export price alone, and put the same ten per cent on the import price instead. Now the export price index reads 100 and the import price index reads 110. The terms of trade index does not fall to 90.00. The index falls to 90.91.

The reason is that the two indices do not sit in the same place in the sum. The export price index sits on top and the import price index sits underneath. Putting 110 on top gives 110 over 100, or 1.10, and the terms read 110.00. Putting 110 underneath gives 100 over 110, or 0.9090 and so on, and the terms read 90.91. The reciprocal of 1.10 is not 0.90. The nine hundredths of a point that seem to have gone missing are not a rounding artefact, and no amount of care with decimals will recover them. A number on top and a number underneath do not shift a ratio by the same distance, so a reader who expects the index to fall as far as it rose will misread every single move it ever makes.

Run all four corners and the pattern stops being arguable. Push the export price up ten per cent and the index reads 110.00, ten points up. Pull the export price down ten per cent and the index reads 90.00, ten points down. The top of the ratio behaves itself in both directions. Now the bottom. Push the import price up ten per cent and the index reads 90.91, down 9.09 points. Pull the import price down ten per cent and the index reads 111.11, up 11.11 points. The same ten per cent, applied four times, gives two clean answers and two that are not clean at all.

For the index to land on exactly 90.00 by moving the import price, the import price index has to reach 111.11 rather than 110, a rise of 11.11 per cent instead of ten. The size of the effect is stated there as plainly as it can be put, and it is quite large enough to matter in any sentence comparing one year's move with another's.

If the terms of trade improve, is Sankhya better off?

Two roads reach an improvement and they do not feel remotely the same from the ground. On the first road, buyers abroad want more Sankhya onions and the export price rises ten per cent from Rs 2,000/- to Rs 2,200/- a quintal. Sankhya ships the same 50 lakh quintals it shipped last year, so its export volume index holds at 100. The terms of trade index reads 110.00, export earnings rise from Rs 1,000 croreAn Indian unit of counting. One crore is one hundred lakh, which is ten million. Rs 1,000 crore is therefore Rs 10,00,00,00,000/-. to Rs 1,100 crore, and the same onions bring home ten per cent more imported machinery.

On the second road nothing good happens to Sankhya at any point. Machine building abroad falls into a slump and the machine price drops ten per cent from Rs 50,000/- to Rs 45,000/-, so the import price index falls to 90 and the terms of trade index reads 111.11, a slightly larger improvement than the first road produced. But the slump that cheapened the machines is a slump in the same economies that buy Sankhya's onions, and Sankhya's export volume falls by 30 per cent, taking its export volume index from 100 to 70. Multiply the terms of trade index by the export volume index and divide by 100, and what the country's exports actually bring home reads 77.78 against a base of 100. The terms of trade improved by 11.11 points and what came home fell by 22.22.

The index cannot say why it moved, and why it moved is what decides whether the move is welcome. Two readings of nearly the same size, one arriving because somebody abroad wants what the country sells and one arriving because the world has largely stopped buying, and the number has the same shape in both. The blindness is not a defect in the measure. The measure is doing precisely what it says on the label: it is a price ratio and it reports prices. Everything about welcome or unwelcome has to be carried in from outside it, usually from the volume figures and from whatever is known about the cause.

What moves this measure, and what leaves it completely alone?

Prices move it. Quantities do not touch it. Not the export volume, not the import volume, not the gap between the two, not one of them anywhere. Double Sankhya's onion shipments from 50 lakh quintals to a full crore of quintals at unchanged prices, and both price indices still read 100, so the terms of trade index still reads 100.00. Halve the shipments and it still reads 100.00. There is no quantity term anywhere in the construction, and the missing term is the plain reason no quantity can move the output.

The absence is deliberate rather than an oversight, and it is the source of the commonest confusion about the whole measure. The terms of trade and the volume of trade are two separate questions, and this index answers only the first of them: what each unit exported brings back, never how many units there were. The two questions can move in opposite directions in the same year without either number being wrong about anything.

Quantity does move a different index sitting alongside this one, and that index is worth naming so the two never get confused again. The terms of trade index multiplied by the export volume index and divided by 100 gives what a country's exports actually bring home, sometimes described as the purchasing power of its exports. Doubling the volume leaves the terms at 100.00 and takes that second reading to 200.00, and Sankhya is straightforwardly better off. The index simply did not report it. Reporting it was never the job the index was built for. Onions here are a primary commodityA raw or lightly processed good such as grain, ore or oilseed, sold mainly on price rather than on brand, and typically priced the same wherever it is bought., and for an economy selling one of those the price series and the volume series routinely tell two different stories in the same year.

If the prices ask 25 quintals a machine, how many did Sankhya hand over?

Here is the one place where the price ratio and the quantities have to be put in the same room, and it is worth doing carefully because it is the sharpest check available on everything above. Over the period, Sankhya shipped 50 lakh quintals of onions and took delivery of 2,50,000 Marut machines, both invented figures and both belonging to this single product pair rather than to the whole of Sankhya's trade with the world. Divide one by the other. Fifty lakh quintals against 2,50,000 machines is 20 quintals a machine actually handed over. The prices asked 25. Sankhya gave up five quintals fewer for every machine than the prices it agreed to were asking, and five quintals a machine is not a small discrepancy to leave lying around unexplained.

Count the shortfall out in onions first. Onions are what physically failed to sail. To settle 2,50,000 machines at 25 quintals apiece, Sankhya needed to ship 62,50,000 quintals, or 62.5 lakh. Sankhya shipped 50 lakh. The difference is 12,50,000 quintals, or 12.5 lakh quintals of onions that the trade called for and that never left. Now put the export price back on them. Twelve and a half lakh quintals at Rs 2,000/- a quintal is Rs 250 crore. Then count the same period in rupees straight off the invoices: exports of Rs 1,000 crore against imports of Rs 1,250 crore, a gap of Rs 250 crore. The shortfall counted in onions and the shortfall counted in rupees are the same shortfall, to the rupee. No stronger evidence exists that the price strand and the goods strand describe one trade rather than two.

Be careful about what that gap does and does not say. The temptation is to conclude that the terms of trade were really 20 rather than 25. The terms of trade were not 20. The terms of trade is the rate at which the two goods exchange, and that rate is the price ratio, sitting at 25 and comfortably inside the band of 10 to 50 that leaves both countries ahead. The delivered ratio is a different quantity altogether: it divides what actually moved by what actually moved, so it carries the rate and whether the flows matched, tangled together in one number. The price ratio answers at what rate, the delivered ratio answers whether it balanced, and mistaking the second for the first turns an unsettled account into an imaginary change in the terms. An unbalanced period, whether a gap of this kind is a shortfall of anything at all, and what settles it, are the work of the trade balance and belong to its own treatment.

Why does a lender to an onion exporter watch this ratio?

A lender in Sankhya has an onion exporter on its books. The borrower's revenue arrives in one price and a solid part of its costs arrives in another. The graders, the cold store and the packing line are imported capital goodsMachinery, plant and equipment bought in order to produce other things, rather than to be consumed or resold. They are paid for once and used for years. bought at the machine price. Neither the acreage under onions nor the order book has to change for that borrower's position to change underneath it. The ratio between two prices moving is quite enough on its own.

Put a number on the thing so it stops being a worry and becomes a quantity. Assume that in the base period the borrower's imported equipment bill took 20.00 per cent of its export revenue, an assumption laid on top of the index rather than part of it, and hold the physical quantities and the working capitalThe money tied up in day to day operations, mainly in stock, in what customers still owe and in what the business still owes its suppliers. It has to be funded before any profit is seen. cycle completely still so nothing else can be blamed. If the export price index rises to 110 while the import price index holds at 100, that equipment bill falls to 18.18 per cent of revenue. If instead the import price index rises to 110 while the export price index holds at 100, it climbs to 22.00 per cent. A lender reads the terms of trade as the share of a borrower's revenue that is quietly claimed by prices it does not set, and two full points of margin can move without a single unit being bought or sold differently.

The two figures repay a second look. The asymmetry has followed the argument across and changed sides. Going from 20.00 per cent to 18.18 per cent is a fall of 9.09 per cent. Going from 20.00 to 22.00 is a rise of a clean ten. On the index, the export price gave the clean ten and the import price gave the 9.09. On the equipment share it is the other way about. The unevenness belongs to the ratio itself rather than to either price, and it always lands on whichever of the two has been put underneath. An analyst covering the same exporter and an investor reading its results are working the same ratio from different ends, and the household version is a house running on one salary where the rent is fixed and the grocery bill is not. Nothing about the salary changed. The reach of the salary changed, and the house feels it in the third week of every month.

What does a move do to what a whole year of exports brings home?

Everything above stays arithmetic until it is attached to something a country can count on a dock, so attach it. The measure that does the attaching is the one named a moment ago: the terms of trade index multiplied by the export volume index and divided by 100. The combined reading is the honest answer to what a reader usually means when asking whether trade went well, and it is a different number from the terms of trade in every year in which a volume moved.

Read the five settings in the table above through that lens and the division of labour becomes obvious. When the export price rose ten per cent with volumes flat, nothing but the price had changed, and both readings moved to 110.00 together. When volumes doubled with prices flat, the terms of trade stood perfectly still at 100.00 while what came home doubled to 200.00. And on the unwelcome road, the terms of trade climbed to 111.11 while what came home sank to 77.78. The terms of trade index and the export volume index each answer half the question, and only multiplying them together answers the whole of it.

The reason this matters beyond bookkeeping is that only one of the two halves usually makes the headline. A terms of trade reading is published, quotable and short. A volume series is longer, duller and revised more often. The half that travels is not the half that decides, and those are precisely the conditions under which a measure gets misread in public, year after year, by people who have quoted it correctly.