Measuring national income — three approaches

Adding up a whole country

Every lecture so far has studied one market at a time. This one asks a much bigger question: how much does a whole country produce in a year?

The obvious answer is to add up the value of everything that is sold. Try it on a tiny invented economy with three firms. A farmer grows wheat and sells it to a miller for $300. The miller grinds it into flour and sells the flour to a baker for $700. The baker makes bread and sells it to families for $1500. Add up all the sales: $300+700+1500=2500$ dollars.

But the families received only $1500 of bread. The $2500 is too big because the wheat was counted three times: when the farmer sold it, inside the price of the flour, and inside the price of the bread.

This is the disruption. "Add up everything" sounds simple, and it gives the wrong answer. Measuring a country needs three careful ideas, and the surprising part is that all three must give the same number.

What GDP measures

Every word in that sentence does a job.

• Final goods are bought by their last user, such as bread bought by a family. Intermediate goods, such as the flour bought by the baker, are used up in making something else. GDP counts only final goods, because the value of intermediate goods is already inside the price of the final good. This is what fixes the wheat problem.
• Produced means made in this period. A family selling its five-year-old car to a neighbour adds nothing, because the car was counted in the year it was made. Buying shares and paying pensions are not production either.
• Within a country's borders is the meaning of domestic. A factory inside the country counts, even if foreign owners own it.
• In a given period means GDP is a flow, like water per minute through a pipe. A country's wealth, its houses, roads and factories, is a stock, like the water in a tank.

One flow, three places to count it

Now picture the whole economy as a loop of money and goods between households and firms.

Households provide the factors of production. Firms use them to produce goods and services, and pay households wages, rent, interest and profit. Households spend that income on the goods and services. The money goes round and round.

So there are three places to count the same flow: the output of firms, the incomes paid for producing it, and the expenditure on it. The claim of this lecture is that the three totals are always equal. It is not a coincidence, and it is not an approximation. To see why, we need each approach in detail.

The output approach: count only what each firm adds

The fix for the wheat problem is value added. A firm's value added is the value of what it sells, minus the value of the inputs it bought from other firms. It measures what this firm contributed.

The farmer bought nothing from other firms in this simple story, so all $300 is value added. The miller sold $700 of flour but paid $300 for wheat, so the miller added $400. The baker sold $1500 of bread but paid $700 for flour, so the baker added $800. Total value added: $300+400+800=1500$ dollars. That is exactly the value of the final bread.

This is not luck. Each firm's purchase cancels the earlier firm's sale: the wheat is added by the farmer and taken off by the miller, and the flour is added by the miller and taken off by the baker. Only the last sale survives. So the sum of values added always equals the value of final output.

Value added has a practical advantage too. In real data it is often hard to know whether a sale is final: the same flour is final for a family and intermediate for a bakery. Value added avoids that question.

Now sort some cases yourself.

The oven and the unsold bikes surprise most students. Both are investment, and both matter in a moment.

The income approach: where the value added goes

Now follow the money that each firm receives for its value added. It must go to someone. Some goes to workers as wages. Some goes to landowners as rent. Some goes to lenders as interest. Whatever is left belongs to the owners as profit.

Here is the bread economy again, with an invented split of each firm's value added:

Total incomes: $870+180+50+400=1500$ dollars. The same number again.

The key is the word "left". Profit is not a separate amount that happens to fit. Profit is defined as what is left after wages, rent and interest are paid. So for every firm, value added = wages + rent + interest + profit, always. If the baker had paid $900 in wages, its profit would be $-100$ dollars, and the total would still be $800. That is it. That is the whole idea. Income equals output because profit takes up whatever the other incomes do not.

Real accounts need one small adjustment. Taxes on products, such as a sales tax, are part of the price but nobody's factor income, so they are added to the incomes total, and subsidies are taken away.

The expenditure approach: C + I + G + (X − M)

The third approach counts spending on final goods and services. Economists sort the buyers into four groups:

• Consumption (C): households buying goods and services, such as food and haircuts.
• Investment (I): spending on new capital, such as machines, buildings and new houses, plus the change in firms' stocks of unsold goods. In economics, "investment" never means buying shares.
• Government spending (G): goods and services the government buys, such as teachers' work and new roads. Pensions and other transfers are left out, because the government buys nothing with them.
• Net exports (X − M): exports are local production bought by foreigners. Imports are taken away, for a reason explored below.

Why must spending equal output, when a firm could produce something nobody buys? The answer is in the unsold bikes. Goods made but not sold are counted as investment in stocks, as if the firm had bought them from itself. So every unit produced is either bought or added to stocks, and both count as expenditure.

Now the most misunderstood letter in the formula: $M$. Commit to an answer before you read on.

So the $-M$ is a correction, not a penalty. Spending on imports appears in $C$, $I$ or $G$, so the foreign part must be taken out again. If the family had bought a television made at home instead, $C$ would have risen and $M$ would not, and GDP would have risen by $1000. That difference is real. The mistake is only in thinking that the import itself pushes GDP down.

Gross, national, net: three more words

Sometimes the question is different: how much income do the country's own residents earn? Start from GDP and make two corrections. Add the income residents earn from abroad, such as profits from factories they own in other countries. Subtract the income that foreign owners take out of this country. The result is gross national income (GNI). Older books call it gross national product (GNP).

"Gross" means that nothing has been taken away for depreciation: the machines, buildings and vehicles that wear out while producing. Take depreciation away, and you get net national income (NNI). Older books call it net national product (NNP). It is closer to what the country could consume each year without running down its capital. Question 3 of Try it yourself works through all three measures.

Worked examples

Equal in theory, close in practice

If the three approaches are always equal, why do statisticians publish a "statistical discrepancy"? Because each is built from different data, such as surveys of firms, tax records and household surveys, and each source has gaps.

In the United States, the Bureau of Economic Analysis publishes GDP from spending and gross domestic income from incomes. The gap between them was within 0.6% of GDP in every year from 2015 to 2025, but it reached 2.3% in 1993 (BEA data, via the Federal Reserve Bank of St. Louis). The theory says what the answer must be. The discrepancy says how close the measurement got.

Three classic mistakes