Personally I think it is more a case of the dollar being weak in general, than the pound in particular being strong against it - take a look here and view how it has fared against the Euro, Yen etc over the past 12 months: http://newsvote.bbc.co.uk/1/shared/fds/hi/business/market_data/currency/12/13/twelve_month.stm
What this means is that even if we are importing in Dollars, it won't help us if the currency of the country of origin has strengthened against the Dollar also. IMO it is more important to look at the relative currency value between ourselves and the source than specifically against the Dollar, because even if we suddenly got 4 dollars for every pound, this wouldn't necessarily help matters in terms of good imported from elsewhere, if their currency also appreciated to the same extent relative to the dollar. In the modern day the currency markets are reasonably fluid and interlinked.
But regardless of the current status quo, lowering interest rates still further is likely to (slightly) devalue sterling. So compared to today, the cost of imports will rise, all else being equal.
What this means is that even if we are importing in Dollars, it won't help us if the currency of the country of origin has strengthened against the Dollar also. IMO it is more important to look at the relative currency value between ourselves and the source than specifically against the Dollar, because even if we suddenly got 4 dollars for every pound, this wouldn't necessarily help matters in terms of good imported from elsewhere, if their currency also appreciated to the same extent relative to the dollar. In the modern day the currency markets are reasonably fluid and interlinked.
But regardless of the current status quo, lowering interest rates still further is likely to (slightly) devalue sterling. So compared to today, the cost of imports will rise, all else being equal.
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