Exchange Rates

Yesterday I read my favourite economics blogger, Eric Crampton, and in particular his article on exchange rates.  He in turn linked to Matt Nolan, with the exchange rate as a price.

This led to me thinking about the exchange rate, and what it means.  Intuitively I feel that a high exchange rate is generally a reflection that a country is doing well relative to the rest of the world, and if you want a lower exchange rate that presumably also means you want to do less well.  But I’ve also usually assumed that there are some in society who are hurt by a high exchange rate, and I want to test that assumption today.

Let’s do a thought experiment.  We’re a country of one person.  This person makes butter and sells it on the international markets.  That’s all this person makes, and they don’t particularly like butter themselves (they’re just very good at making it), so they don’t eat any of their own butter.  Their butter is particularly salty, and the Americans won’t eat it, they export all their butter to Belgium.  Conversely, they really like Belgian chocolate, and that’s all they eat.  So all their production is exported to Belgium, and all their consumption is imported from Belgium.  Let’s call their country New Butterland, they use the NB Dollar as their currency.

So, what does the exchange rate mean for this person?  Let’s assume that they are making butter and selling it for NB$10 per kg.  They buy Belgian chocolate for €5 per 100g or €50 per kg.  Their exchange rate is $1:€1.  So, New Butterland needs to make 5kg of butter to buy 1kg of Belgian chocolate.

Imagine that New Butterland’s currency goes up, it’s now $0.8:€1.  So now for every 5kg of butter, you get €62.5, and can buy 1.25kg of Belgian chocolate.  New Butterland is wealthier than before, the Belgians now need to pay more for their New Butterland butter.  This assumes that Belgians like New Butterland butter so much that they buy as much of it as they can get, irrespective of price (and it makes you wonder why New Butterland doesn’t just put up the price of their butter).

Let’s extend our model though, let’s assume that New Butterland doesn’t set the price of their product.   The Belgians can also buy lard from Great Shortenia, who make lard out of the animal fats that are residue of their intensive factory farming industry.  They’ll therefore only pay €5 per kg for butter, at any price above that they will buy exclusively lard.  New Butterland is now a price taker instead of a price setter.  What changes for New Butterland v’s the base case?  Nothing.  The price in NB$ used to be $10 per kg.  It’s now $8 per kg.  But 5kg of butter still buys 1kg of chocolate.

So, what we can say is that where you are purely an importer/exporter, then a change in the exchange rate depends on your market power.  If you are a price setter, then an increase in your exchange rate makes you richer.  If you are a price taker, then an increase in your exchange rate makes no difference at all to your wealth in terms of what your money can buy, but the number of dollars that you have reduces.

OK, take it the next step and add someone who isn’t an exporter.  Our New Butterland butter manufacturer has a neighbour.  This neighbour eats butter, and makes bread.  Our butter manufacturer decides that man cannot live on Belgian chocolate alone, and starts eating bread slathered with Belgian chocolate, the neighbour eats the same, but with butter as well.  The neighbour doesn’t export, as bread goes stale whilst on the ship.

So, we have one person in New Butterland who is an exporter, and one who produces product for the domestic market.  Both eat a combination of local produce and imported produce.  Let’s assume the bread is sold for $5 per loaf.  Each day, New Butterland makes 10kg of butter, and 10 loaves of bread.  The trade is a bit more complicated, but at $1:€1, we get:

  • Neighbour makes 10 loaves of bread.  Sells 5 loaves to the butter maker for $25, and keeps the other 5 for personal consumption.  Buys 0.5kg of butter for $5, and buys 400g of chocolate for $20.  So the neighbour each day has 5 loaves, 0.5kg of butter, and 400g of chocolate.
  • The butter maker makes 10kg of butter, sells 0.5kg for $5 to the neighbour, buys 5 loaves of bread for $25.  Sells 9.5kg of butter to the Belgians for $95.  And buys 1.5kg of chocolate.  As in real life New Zealand, the dairy farmer is richer than the bread maker.

So, what happens when the exchange rate changes.  We’re now at $0.80:€1, and we assume Belgians again love New Butterland butter and buy all they can get irrespective of price (New Butterland is a price setter).  How does our production change?  The bread maker still sells his bread for the same price, but his dollars buy more chocolate since chocolate is now $40 per kg.  The butter maker’s bread costs the same price, but she can buy more chocolate than she used to0 as well.  The terms of trade have improved, New Butterland as a whole gets more chocolate per kg of butter exported.

  • The neighbour makes 10 loaves of bread.  Sells 5 loaves to the butter maker for $25, and keeps the other 5.  Buys 0.5kg of butter for $5, and buys 500g of chocolate for $20.  So the neighbour each day has 5 loaves, 0.5kg of butter, and 500g of chocolate, the neighbour is 100g of chocolate better off
  • The butter maker makes 10kg of butter, sells 0.5kg for $5 to the neighbour, buys 5 loaves of bread for $25.  Sells 9.5kg of butter to the Belgians for $95.  And buys 1.875kg of chocolate at $40 per kg.  Both parties are better off than they were before.

So, when as a country you are a price setter, basically everyone is better off when the currency is stronger, the benefits look to accrue evenly between the local producers and the exporters (i.e. in local dollar terms both get the same income as before, but they can both buy more chocolate with those dollars).

Let’s assume now that New Butterland is not a price setter, but a price taker on the international markets, Great Shortenia has re-entered the market.  So what happens now when the exchange rate changes?  The butter price on international markets stays the same, but goes down in NB$ terms, butter is now $8 per kg, chocolate is $40 per kg.  Our terms of trade haven’t changed, New Butterland gets 1kg of chocolate for every 5kg of butter.  So we get:

  • The neighbour makes 10 loaves of bread.  Sells 5 loaves to the butter maker for $25, and keeps the other 5.  Buys 0.5kg of butter for $4, and buys 525g of chocolate for $21.00.  So the neighbour each day has 5 loaves, 0.5kg of butter, and 525g of chocolate.
  • The butter maker makes 10kg of butter, sells 0.5kg for $4 to the neighbour, buys 5 loaves of bread for $25.  Sells 9.5kg of butter to the Belgians for $76.  And buys 1.375kg of chocolate at $40 per kg.

What this maths tells me is that when you are a price taker and your exchange rate changes, what happens is that the country as a whole is no wealthier or poorer – the terms of trade stay the same in real product (i.e. grams of chocolate we get per kg of butter exported).  But the exporters become worse of relative to the local producers.

In one sense this could tell us that those of our exporters who are exporting commodity products (and are price takers) are harmed by a high exchange rate.  Those of our exporters who are exporting differentiated product (and are price setters) are not impacted by a high exchange rate.  And to the extent that any of our exporters are price setters, the country as a whole is wealthier when we have a higher exchange rate.

We can extend this example to account for other changes, maybe when the price of butter changes the local price of bread also goes down.  We can also talk about the psychological implications for the butter maker when they’re making fewer dollars (even if each of those dollars buy more than they used to, and therefore they’re actually just as wealthy as they used to be).  And we can talk about the impacts on inflation and the relative flexibility of wages upwards and downwards (i.e. it’s easy to give someone a pay rise, harder to give them a pay cut, when the exchange rate goes up you need to give people a nominal pay cut, even if their pay packet still buys the same bundle of product as before).

Refer this table for the summary of the positions:

Base Price Setter Price Taker
Butter Maker Bread Maker Butter Maker Bread Maker Butter Maker Bread Maker
Product Price Product Price Product Price Product Price Product Price Product Price
Exchange rate 1 0.8 0.8
Butter price ($) 10 10 8
Bread price ($) 5 5 5
Chocolate price ($ per kg) 50 40 40
Make Butter 10 100 10 100 10 80
Make Bread 10 50 10 50 10 50
Consume Butter 0.5 5 0.5 5 0.5 4
Consume Bread 5 25 5 25 5 25 5 25 5 25 5 25
Sell Butter 10 100 10 100 10 80
Sell Bread 5 25 5 25 5 25
Buy Chocolate 1500 75 400 20 1875 75 500 20 1375 55 525 21
Income 100 50 100 50 80 50
Implied Income Euro 100 50 125 62.5 100 62.5
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3 thoughts on “Exchange Rates

  1. The exchange rate really just reflects changes in the relative values of butter, chocolate, and bread, doesn’t it? In each case, you’ve fixed the value of the New Butterland Dollar at one fifth of a loaf of bread.

    In your “price setter” case, the exchange rate presumably changes because Belgians value butter more (relative to chocolate), and are willing to part with more chocolate for the same amount of butter.

    In your “price taker” case, what seems to be happening is that the New Butterlanders are valuing bread more (relative to chocolate), but the value of the dollar is fixed relative to bread, so it isn’t so obvious that this is what’s happening.

    (By the way, I think you mean $0.80:€1, rather than $1:€0.80, don’t you?)

  2. Yes, I agree I meant $0.80:euro1. Updated in the post.

    What I’m trying to reflect is the current debate in NZ about exchange rate, and whether the NZ dollar is over valued, and if so, what we’d do about it being over valued. My point is that a higher exchange rate doesn’t in absolute terms hurt anyone. Either you hold your prices constant in NZ dollars, or you allow them to drift down. Either way, the country as a whole ends up wealthier, and I haven’t seen a mechanism in this discussion yet that makes the country poorer.

    I think the main situation where people could get poorer is if we allow our prices to reduce in NZ dollars (price taker), but we refuse to adjust our wages in NZ dollars due to the upward stickiness of wages. In this situation we become uneconomic and can’t sell our products overseas any more.

    This is another way to say that the main issue with exchange rates is that people don’t like their nominal wages reducing, even if their real wages are actually the same or going up.

  3. Sometimes i can undrestand Eric, often not. I don’t know why there is this clamour in NZ to lower our dollar. NZ First who claim a lot of superannuants votes is desperate to lower the dollar. This would seriously disadvantage older people on fixed incomes, and those who are fortunate enough to go overseas . The Greens would go further they want to print money [ quantitative easing ] and give it to their favoured people. This is why we have to stick with NZ at Govt. here

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