The balance of trade (B.O.T) is defined as the value of exports minus the value of imports. The balance of trade is also known as the "trade balance".

Consider an economy which only imports and exports one good. The balance of trade in this scenario would be defined as:

$\text{B.O.T} = \text{Price of exports} * \text{Quantity of exports} - \text{Price of imports} * \text{Quantity of imports}$

It is worth noting:

$\text{value of exports} = \text{Price of exports}*\text{Quantity of exports}$

$\text{value of imports} = \text{Price of imports}*\text{Quantity of imports}$

The country has a positive balance of trade, which means that the value of its exports is worth more than the value of its imports, it is said to be running a trade surplus.

If a country is running a trade surplus than they will be lending money to the rest of the world so that they can purchase their goods.

Why is this the case? Suppose that Canada wishes to purchase a car from the USA and that is the only trade which occurs between these two countries, which means that the USA has the trade surplus. Canada must exchange some of its Canadian dollars into US dollars before it purchases the car. It then uses the US dollars it has purchased to buy the car. In this case, it has the car, however, the US now has the Canadian dollars that were used to purchase the US dollars. This is an asset for the USA and is considered debt for Canada since in the future it must exchange this Canadian dollar for some Canadian goods.

Conversely, if the balance of trade is negative (the value of exports are less than the value of imports) than the country is said to be running a trade deficit.

If a country is running a trade deficit than this means that they must be borrowing money from the rest of the world to pay for their imports.

In the example above Canada is operating a trade deficit and thus has a debt to the USA.

## Example 1 - Calculating balance of trade with one good

Consider a simple example which 2 countries, Country A and Country B, who both only produce one good. Country A produces wine and Country B produces cheese. Suppose the price of wine is $2 and the price of cheese is$1. Suppose that Country A exports 5 units of wine and imports 3 units of cheese. The balance of trade for Country A is:

$\text{B.O.T for Country A} = \text{Price of wine} * \text{Quantity of wine} - \text{Price of cheese} * \text{Quantity of cheese}$

$\text{B.O.T for Country A}=2*5 - 1*3 = 7$

Therefore Country A is running a trade surplus since the value of exports exceeds the value of imports. We can now calculate the balance of trade for Country B:

$\text{B.O.T for Country A} = \text{Price of wine} * \text{Quantity of wine} - \text{Price of cheese} * \text{Quantity of cheese}$

$\text{B.O.T for Country A}=1 *3-2*5=-7$

Therefore Country B is running a trade deficit since the value of exports is less than the value of imports. You might notice that if you add up the balance of trade for both countries, they sum to 0. This is not a coincidence. The balance of trade should always sum to 0, as an export for one country is an import for another so when you add them together they cancel each other out.

## Example 2 - Calculating balance of trade with two goods

Suppose now that Country A also exported beer as well as wine. Suppose that the price was \$1 and they exported 3 units. You would calculate the balance of trade as:

$\text{B.O.T for Country A} = \text{Price of wine} * \text{Quantity of wine} +\text{Price of beer} * \text{Quantity of beer} - \text{Price of cheese} * \text{Quantity of cheese}$

$\text{B.O.T for Country A} = (2 * 5) + (1 * 3) - 1* 3 = 10$

Again you can see that country A is running a trade surplus. I will leave it for you to calculate the balance of trade for Country B. Remember, you can see whether you have calculated it correctly by adding the two countries balance of trade together. If done right, they should sum to $0$.