The real exchange rate is a measure of the 'real' value of a currency - how many goods and services a unit of the currency will buy. The real exchange rate is calculated as the nominal exchange rate (quoted as units of foreign currency per unit of domestic currency) times the ratio of domestic price level to the foreign price level:
The real exchange rate is unitless. Let's suppose that a CD costs $16 in the US, 4 £ in Britain, and the exchange rate is 0.5 £ per $. Then the real exchange rate is 0.5x16/4 = 2. This means that your currency will buy twice as many goods in Britain as in the US. Specifically, if you have $16, you can buy one CD in the US. Alternatively, you can convert the $16 to 8 £, and buy two CDs in Britain. So one US CD is equivalent to two UK CDs. A US citizen traveling to Britain would find the UK relatively cheap.
Purchasing Power Parity
According to the theory of purchasing power parity, the real exchange rate should equal one. Purchasing power parity is the idea that an item should have the same price no matter where it's sold. For example, consider the Great Big Sea CD, The Hard and the Easy. In the US, the album was $14.99 on 12/10/2007. The exchange rate between the US and Canada was 0.9949 Canadian dollars per US dollar. If PPP holds, we'd expect the price of the album in Canada to be 14.91 Canadian dollars. PPP is approximately correct.
In the UK, the album price was £14.49. According to PPP, this implies an exchange rate of 1.03 $/ £. Clearly, PPP does not hold since the actual exchange rate was 2.06 $/ £.
Current and capital account
The current account is the trade balance, and records transactions in goods and services. Specifically, the current account = Exports - Imports.
The capital account records net asset transactions between countries, both financial and non-financial. The capital account includes foreign direct investment, equities and bonds, and investment in other assets (for example, bank loans and bank deposits).
The sum of the current account and the capital account must equal zero: Current Account + Capital Account = 0. This means that if the current account is in deficit, the capital account must be in surplus. For example, if the US is running a trade deficit (a current account deficit), it must be running a capital account surplus. If imports into the US exceed exports sold by the US, then US dollars will be accumulating overseas. Those dollars will be recycled into purchases of US assets, leading to a capital account surplus.
An important equation
From macroeconomics, we know that output can be divided into consumption (C), investment (I), government spending (G), and net exports (X-M), Y = C + I + G + (X - M). We also know that income can be divided into Consumption (C), savings (PS) and taxes (T), Y = PS + C + T. Combining these two equations produces:
C + I + G + (X - M) = S + C + T, or X - M = PS - I + T - G.
You should recognize X - M as the current account, and S=PS + T - G as private savings plus government savings. If the fiscal (government) authority begins to run a deficit (T-G<0), then either S must increase or X - M must decrease. Hence, a fiscal deficit entails a trade deficit when savings is fixed. The twin deficits are the trade and fiscal deficits.
Determination of the real exchange rate
The equilibrium value of the real exchange rate equates Net Exports and Total Savings:
As the real exchange rate rises, the quantity of imports rises, while the quantity of exports falls. A high real exchange rate implies a small value for X-M. Similarly, a low value for the real exchange rate implies a large value for X-M. Hence, X-M is a downward sloping line in this graph. Net savings is not affected by the real exchange rate, so S-I is a vertical line.
Effect of an increase in net savings
An increase in net savings (increase in S-I) leads to a fall in the real exchange rate. Net savings can increase because savings rises, investment falls, or the fiscal authority reduces its fiscal deficit or raises the fiscal surplus. A fixed amount of domestic currency will, after the change, purchase fewer units of goods overseas.
Effect of an increase in net exports
An increase in exports leads to an increase in the real exchange rate. Net exports will increase if exports rise or imports fall. A fixed amount of domestic currency will, after the change, purchase more units of goods overseas.