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Price Parity

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Price Parity Theory

If there was only one commodity traded across the two economies, i.e. in the world market, and no transport costs then the exchange rate would be determined so that the price for that commodity would be about the same in both economies.
  • If rice was £4 per Kg in one economy and $3 per Kg in the other then £4 would equal $3.
  • If sugar was £7 per Kg in one economy and $6 per Kg in the other then £7 would equal $6.
What would happen to the exchange rates if both commodities were traded? (In reality many valuables are traded across many economic borders and so are on the world market.)

If rice was 95% of the value of cross border trade then still the exchange rate would be determined largely by the price of rice in the two economies. But what about the other 5%, say that was sugar and sugar sells for £7 and $6 per Kg respectively. Given that £4=$3 that makes sugar cheaper in the £ economy than the $ economy and the result will be an increased flow of sugar from the £ economy to the $ economy until the world market prices balance. (Again we assume insignificant transport costs, and no speculative purchases!) Thus the prices of sugar may rise in the £ economy and fall in the $ economy.

Since the sugar exporters must be paid in £ but the importers have $ the slight increase in demand for the £ currency may slightly raise the price of £ in $.

What if one year the £ economy has a bumper crop of rice so that rice drops from £4 to £2 per Kg but is still $3 in the other economy? There will be added demand to buy the £ currency and use it to buy the £ economies rice, leading to some increase in the £ rice price and in the price of £ in $ until again the prices are the same in both economies. So lets say rice ends up at £2.50 and at $2.50.

The effect on sugar would be drastic! Sugar would now be cheaper in the $ economy and would start to flow the other way until again the market price in both economies was the same.

Well this makes sense £ had a bumper crop of rice, shared it with $ and $ had to give something back. It looks great until you consider that the sugar industry had to grow in one country and shrink in the other because of a rice harvest! When you consider the cost of these changes, does it make sense? If there had been a single currency the sugar industry would not have been effected so directly by rice.

As the extra rice came onto the market the price would drop, but still money would now go to buy rice that might have previously bought sugar so the price of sugar might also have to drop.

What really happens will be determined by the bids to buy and offers to sell for everything on the market. If there is more on the market, stuff gets cheaper.


Price Parity



Clearly the terms ΔQiαβ(t0,t1) includes all of the change in items of type i from all contracts.

ΔQiαβ(t0,t1) = ΔQiαβc(t0,t1)
                        ∀ c


How can the market be represented? The bids to buy and offers to sell. It is all about putting a set of possible transactions into the market place.

Diαc(t) means α is bidding for this quantity of item i and offering in exchange this quantity of item j Sjαc(t)
Arbitration of many bilateral propositions. What happens to prices?

The Market Matrix

Price is a direct indicator of bid/offer quantity ratios

So what happens with price in multilateral transactions.

FOREX is best example.

EURUSD * USDTWD * TWDEUR =1

And that is true for all paths around the network.


RCEUSD * USDGBP * GBPRCE =1

SGRUSD *  USDGBP * GBPSGR =1

Because flows will neutralise differences but economic momentum and transaction costs may slow arbitrage. Supply and demand will determine flows and prices.

If SGRUSD *  USDGBP * GBPSGR <1 then at least one term must increase. S costs more in US or less in GB or USD strengthens.

Say US S on market increases. SGRUSD decreases. will
USDGBP * GBPSGR increase?


Although we cannot say how a price will respond to increases or decreases in supply one can say how a price might respond to other prices as arbitrage takes effect.


Biαc(t)

Siαc(t)


α


Exchangeability and the open market optional bid system

Rubbish: In the foreign trade market in any period economy x sells stuff s to economy y and y sells to x in the currency of economy blah. Then currency can be bought or sold and such is the market.





© Tom de Havas 2011. The information under this section is my own work it may be reproduced without modification but must include this notice.







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