so we talk about nominal and real a lot in this class. Let's see how it applies to exchange rates. So the nominal exchange rate is the rate at which one currency trades for another. It's just the current exchange rate, the rate at which one currency trades for another right now. Okay so when we think about nominal exchange rates, that's like you go to the bank and they tell you you can trade 108 Japanese yen for $1. So if you go to the bank, if you go to the bank and you give them $1 they will give you 108 yen. Right they will give you 100 8 yen for that $1. Okay that's the nominal exchange rate. So we say the currency appreciates there's currency appreciation when your currency can buy more of the foreign currency. So now you can imagine instead of offering 100 and eight yen per U. S. Dollar, what would be a number where you get um where the dollar has appreciated. So you would be able to get more yen. Right, the currency would appreciate. The U. S. Dollar would appreciate when you can get more yen for that dollar. So now the bank offers you say 100 and 12 yen. For $1 instead of 108. Before now you're getting 100 12, you're getting more yen per dollar. Your, your dollar has appreciated. The opposite is depreciation when your currency can buy less of the foreign currency. So now you go to the bank and you say hey let me get all that yen you're offering and now they come up to you and say oh today you can only get 102 yet you only get 100 to now your dollar has depreciated, right? You're getting less of the foreign currency um uh based on based on the exchange rate, right? So the nominal exchange rate determines what the exchange rate is and then a currency appreciates when you get more of that foreign foreign currency or depreciates when you get less of it. Okay, so I want to make a note that when one currency appreciates the other depreciates. Okay, the other currency depreciates always, there's always this vice versa effect because if the dollar got stronger, that means that the yen got weaker compared to the dollar, right? Because if you walked into the bank here where the currency appreciated and you walked in with $1 and they gave you 100 and 12 yen. Well if someone went into the bank and went in with yen, they would need 100 and 12 yen to get $1. Right? So the yen, it got more expensive to get dollars. Their yen got depreciated when the U. S. Dollar appreciated. There's always this vice versa balance going on. Okay, so that's the nominal exchange rate, that's basically the current exchange rate on the market. But now when we talk about real exchange rates while we're taking out the idea of how much 11 currency uh compared to the other. And we're focused more on how much goods cost in each country? So rather than the price of the currency, we're focused on the price of domestic goods in terms of foreign goods. Okay so now we're thinking okay um in the U. S. You can buy how many Big Macs for the same amount of money that you can buy Big Macs in a foreign country or how many um basically any product, right, how many gallons of milk can you get in the U. S. For the same amount of money that you would exchange and get in a foreign country. So let's look at the example here. So real exchange rate, it focuses on purchasing power, right? How much stuff can you get with the same amount of equivalent money in both countries. So let's see this example where we're thinking about the cost of sandwiches. So the cost of a sandwich in the U. S. Is $3 and that same sandwich costs £1.5. So it sounds like you've got a good deal. If you go to Britain right? There's only 1.5 is the price in Britain compared to $3 in the US but we have to focus on is that exchange rate? How much is the exchange rate and how much can we actually get of each? Good. So if the exchange rate is £0.5 per us dollar, what is the real exchange rate? So now we're thinking about how many sandwiches we can get with the same amount of money in each country. Okay so the way we do this is we're gonna take the the exchange rate we have we're gonna take the 0.5 great british pounds divided by the one U. S. Dollar. Okay. And what we're gonna do is we're gonna multiply it by the price of the goods. So what we're gonna do, we'll multiply it by the price of the goods because the goods is almost in its own sense, its own exchange rate. Right? You could you could buy a sandwich in the U. S. For $3. How many sandwiches will you get in? In great Britain with those same money. Okay. So what we're gonna do is we're gonna put the the U. S. On top because we want all of the units to cancel us dollars on top $3 for a sandwich divided by 1.5 great british pounds. And notice we've got pounds on the top, pounds on the bottom dollars on the bottom dollars on the top. And all the units cancel. And we're left in terms of sandwiches. Now we're left in Sandwich terms in the amount of goods. So when we do all this math. 0.5 divided by one 0.5 divided by one. Times three divided by 1.5. Well in this case we get 11 sandwich. That means in the US uh and great Britain, you get one sandwich in either place. The exchange rate is one. Uh The real exchange rate is one sandwich in the U. S. For one sandwich in great Britain. Now let's look at the next example where a sandwich costs $3 in the US and the cost is 1.5. And the way that worked was because look the price of a sandwich here was double the price and pounds. Right? And the exchange rate was half half of £1 for $1. But now when we don't make it. So so even we'll see that the real exchange rate can be different. So now a sandwich costs $3 in the US and costs £1.5. Right the same as before. But the exchange rate is now £0.6 per us dollar. So before we move on did the dollar gets stronger or weaker? Did the did the dollar appreciate? Get stronger or depreciate get weaker compared to the previous example. The dollar appreciated right? Because before you went to the bank and said here's a dollar, give me pounds and they give you half a pound. Now you go to the bank with a dollar and they give you 0.6 you get more pounds per dollar. So if you think about it before um you were getting one sandwich for one sandwich there. But now since the dollar is stronger and the prices of sandwiches have stayed the same, you would imagine that you can get more sandwiches in Great Britain than you did before. So let's go ahead and see how this works out in the math. So now our exchange rate is 0.6 um great british pounds divided by $1 times. Now we want to do the exchange rate of the sandwiches $3 for us dollars sandwich and 1.5 for the great british pounds. Right, great british pounds there and again all of our units cancel us dollars with us dollars pounds with pounds. And now let's do this exchange rate. So now let's see what our real exchange rate is. 0.6 divided by one times three divided by 1.5. So now our exchange rate is 1.2 sandwiches in this case. Okay so now what this tells us is that the U. S. Can you can um you can take one sandwich in the U. S. And go to great Britain and get 1.2 sandwiches. Okay 1.2 uh great british sandwiches for every one us sandwich. Okay so notice we're focused on goods rather than dollars and pounds. Now because we want to see the purchasing power of these currencies. So since the dollar got stronger here, the the U. S. Can buy more sandwiches with their currency in in great Britain. Okay so sometimes it's it's one thing to say oh we got we can get more pounds or less pounds but really we want to focus on how much can we purchase because if the prices are way more expensive overseas even if we're getting more money well it doesn't really mean we're getting more stuff for our money. Okay so that's the idea of the real exchange rate. Can we have a formula for our real exchange rate here? It's where we're gonna take our nominal exchange rate like we were doing up here in U. S. Dollars. So great british pounds to us dollars right? Foreign currency divided by U. S. Currency and then we'll multiply it by the the opposite in the price levels so that we can cancel out all of our units and be left with just uh value of goods. Okay so that's what we do remember. This is foreign currency. So this nominal exchange rate in U. S. Dollars is foreign currency divided by us dollars. Okay foreign currency divided by U. S. Dollars times U. S. Dollar prices over foreign currency and then they all cancel out those units and we're left with just the numbers the real exchange rate. Okay so let's pause here and you guys try to solve the real exchange rate in this next problem

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Problem

Problem

The exchange rate between the USD and GBP is currently $1.61 = 1 GBP. If the price level in the US is 108 and the price level in the United Kingdom is 114, what is the real exchange rate?