More Reflections on the Circular Flow of National Income

After posting an article about how imports create saving for investment, a conversation was started. The conversation led to doing more research and developing new explanations to understand the basic circular flow model. This is actually a very important issue to get right. The circular flow is such a basic part of understanding the economy.

Normal Flow diagrams are misleading

If you look at a typical diagram for the circular flow on the internet or in a textbook, you will see exports feeding directly back into firms. Here is an example.
flow 1
The implication in the typical circular flow is that what flows out of households is equal to what flows into firms.
GDP flowing out = Cd + s + T + M  (1) … where s = net personal savings.
GDP flowing in = Cd + I + G + X  (2)
It would seem then that these equations explain the diagram, but they are misleading.
You have to realize something important in the above diagram, that if you are not paying close attention, you will be incredibly misled. Look at Cd for consumption. It applies to domestically produced goods and services only. But now realize that when you see the variable C in the “official” national income equation, C includes all purchases, domestically produced goods and services and those produced abroad, imports. My sense is that many people would make the mistake to think that Cd represents C in the national income equation.
In the diagram in graph #1, we see…
Y = Cd + s + T + M  (1) … where s = personal savings.
But the government does not calculate consumption for just domestic goods. So we add imports (M) onto Cd, because the government counts them together.
Y = (Cd + M) + s + T   =  C + s + T  (3)…….. where C = (Cd + M) and s = net personal savings.
But when the government counts imports, we then subtract imports from the equation. But in order to keep the equation equal to Y, we must also add imports to another part of the equation. -M and +M balance each other out. The +M of Import dollars is added into Gross Saving.
Y =  (Cd + M) + (s + M) + T – M  =  C + S + T – M  (4) ……. where C = (Cd + M) and Gross saving S = (s + M)
In order for the diagram to be technically correct, consumption would include imports and then imports would have a minus sign, and Net saving would include both personal saving and “import dollars” saving. But that is too much to put in the diagram when the idea is to simplify. But the simplification becomes misleading.
There is another problem in the diagram.
Equation (2) is also misleading because it doesn’t use the correct definition of consumption either. It should also include imports in consumption (Cd) to be technically correct.
The second equation should be written like the official equation used for national income, where consumption includes imports, like this…
GDP flowing into firms = C + I + G + NX  (5) ……. where C = (Cd + M), consumption of domestic goods plus imports and NX = X – M.
To  make equation (2) technically correct, we have to subtract imports from exports (X) and add them into consumption of domestic goods (Cd). (+M and -M = 0.)
GDP flowing in = Cd + I + G + X  (2)
GDP flowing in = (Cd + M) + I + G + (X – M(6)  =  C + I + G + NX  (5) ……. where C = Cd + M
Now equation (2) is equal to equations (5) and (6).  But the diagram is misleading, because it shows only exports returning to firms. According to equation (5), the diagram should show both consumption (C) and net exports (NX) from the foreign sector returning to firms.

The Logic Puzzle to determine GDP

I am going to present a logic puzzle for equilibrium GDP (Y). I take out the government sector, because we just want to see the relationship between gross savings, investment, imports and exports. The debate that resulted after my last post led me to create this logic puzzle.

The puzzle sets up the correct equations in a flow format with GDP income being used in the first line, where you see consumption, gross saving and imports. The equation for the first line is Y = C + S – M, version of equation (4) without net taxes (T). Then you see the spending that returns to firms as GDP on the last line, where you see consumption, investment and net exports. The last line simulates the correct official equation for Y = C + I + NX, version of equation (5) without G.

In the first column, you have household consumption. In the second column, you have the financial sector which makes sure money goes to where it needs to go. In the third column, you have the foreign sector, where imports and exports are traded.

logic 1

Link to graph #2

There are constraints to the right.

  • Imports must be negative. If there were positive, they would be an export and would be moved to the exports box.
  • Exports must be positive. If they were negative, they would have to be put in imports.
  • The middle line where transfers of funds are made must equal zero, because this line is added to the first line, and the first line must equal the last line. Remember, this puzzle is for GDP in equilibrium. GDP does now change.
  • Consumption does not change from the first line to the last line. Remember that consumption includes money spent on imports.
  • The first and the last lines must equal GDP.

In graph #2, you see a basic example without imports and exports. $900 of GDP is given with $800 going to consumption and $100 going to gross saving. The gross saving funds are moved straight down and spent as investment in the firms. Consumption and investment in the last line equal $900 again. The economy is in equilibrium and could continue on like this.

Now we put the puzzle to the test.

Given the numbers in black, how can you determine gross saving?

logic 2a

Link to graph #3

In the first line, you can see how the $900 of GDP is being used. $800 is being spent. $100 of that $800 is being spent on imports. Thus, $700 is being spent on “domestic” consumption.

Now, one might think that since $800 is being spent, there must be $100 of saving left over. But realize that this $100 is only personal saving. Keep in mind that there might be another form of saving. Here is what the puzzle would look like if you put the $100 of personal saving in gross saving.

logic 3a

Link to graph #4

So if you just put $100 in gross saving, the first line would add up to only $800, which violates the constraint for the equation, Y = C + S – M. Also, the middle line adds up to $100 (lend/borrow 0 + exports 100), which violates the constraint that the middle line must add up to zero. We know that there must be an accounting identity missing if the middle line does not add up to zero.

The first thing then is to make the first line add up to GDP, $900. So you know that Gross Saving is going to have to be $200 in order to satisfy the constraint of the equation Y = C + S – M. …. $900 = $800 + $200 – $100. Then you know that “lend/borrow” is going to have to equal -$100 in order for the middle line to add up to zero.

Here is what the solution looks like.

logic 4a

Link to graph #5

You can see that an extra $100 was added into gross saving and -$100 was put into the box for “lend/borrow”. These additions are the opposites of the numbers put into imports and exports. $100 extra into gross saving balances -$100 of imports. -$100 of lending balances $100 of exports. Thus, the solution requires that you make equal and opposite entries in saving and lend/borrow for the numbers entered for imports and exports. Gross Saving adds together $100 in personal saving plus $100 of some other type of saving.

What is that other type of saving? As I tried to explain in the previous post, imports create a saving in the financial sector. To show this, solve the following logic puzzle…

logic 5a

Well, you know that gross saving will have to be $200. “Lend/borrow” will have to be zero. And investment will have to be $200. The solution looks like this.
logic 6a
Remember that the $200 in gross saving was a combination of personal savings and $100 to balance the -$100 of imports. Well look, both types of saving ended up being used as investment. Do you now understand why I say that imports create saving that is used for investment.
How did this happen? Imports create funds of United States dollars that stay in the financial sector, while a foreign currency is used to pay the exporter in the foreign country. These US dollars must be used within the US economy, so they never actually leave the circular flow diagram. Whether they stay in a US bank or go offshore these funds are owned by foreign entities. Still, those foreign entities must use those funds to buy our exports, purchase US assets or invest in the United States. And as we can see in this last puzzle, if they don’t use the funds to buy our exports, the money gets used for investment in the US. The foreign entities can invest “their” US dollars in US stocks, US treasuries, US bonds, whatever, but those dollars “eventually” have to be used in the US. In essence, dollars to buy imports never leave the circular flow of the United States economy. Thus there must be an accounting entry to show where they are.
You can see why some countries use the US dollar as their currency, as in the case of Ecuador. If China has lots of excess US dollars that must be spent where US dollars are used, normally the United States, now they can use those dollars more easily, more efficiently in Ecuador. In effect, Ecuador has opened up its investment to the Gross Saving funds of the United States which result from our imports being greater than our exports, namely our trade deficit.

It is very important to understand the circular flow correctly since it is an essential foundation of understanding the economy. One must be clear about many things, including the definition of consumption, the role of the financial sector, the funds created in the financial sector when we buy imports and the required accounting identities to make it all balance.

The circular flow diagrams that you see in probably all textbooks are ultimately misleading in one way or another.

Note: I did a search for any flow diagram put to numbers. I change the search parameters many ways. And I only found one circular flow put to numbers in an accounting type style. And it was the one I just published last week. I am now wondering how prevalent the misunderstandings about the circular flow are.