# Been tinkering in the Circular Flow laboratory

My last post on the circular flow using labor and capital incomes sure was a mess. As you would see, some of the post had to be scratched out. I was not happy with the circular flow. What you are witnessing is a creative process.

The circular flow model needed a lot of work. So I went into the laboratory and tinkered.

I first had to get the accounting right. Then I had to find the right numbers. Then I had to apply a process of deduction to calculate numbers that are not available, like… how much imports are purchased by capital income? Where would you find such a number? Well, I had to deduce it. Most of the numbers were found through the U.S. Bureau of Economic Analysis website. They have interactive tables there for national income accounts. (I will specify the tables and the lines for numbers below.)

Here is the product from the laboratory. Numbers are for 1st quarter 2011. (billions of 2009 \$\$). The model still looks the same, but the accounting is correct now. The main difference is that imports had to be negative. Let’s start at the bottom of the flow and work up. I will state the number and then how it was determined. For all tables, go to this BEA link. The numbers for 1st quarter 2011 are in the first column of the tables.

• In-coming GDP… table 1.1.6, line 1. (real GDP)
• Consumption… table 1.1.6, line 2
• Govt. spending… table 1.1.6, line 22
• Investment… table 1.1.6, line 7
• Net exports… table 1.1.6, line 15

Note: The four account numbers do not add up to the real GDP number given in table 1.1.6, line 1, because there is a residual in the data.

• Exports… table 1.1.6, line 16
• Imports… table 1.1.6, line 19. (Imports is made negative because it is the loss of funds from the circular flow.)
• Govt. borrowing… I did not find this number in real 2009 dollars, so I took the ratio of nominal numbers to determine this number. First number… Government consumption, table 1.1.5, line 22. Second number… Net government saving, table 3.1, line 26. I divided the second number by the first. Then I applied that ratio to the Government spending number in real 2009 dollars.
• Net taxes (total) = Govt. spending – Govt. borrowing
• Saving (total)… Difference between imports and total net taxes.
• Lend (-)/borrow… This is the combined amount that the financial sector gives to the government and to currency exchanges for exports. It has two ways to be determined. One, Investment minus Saving. Two, the negative of exports and govt. borrowing added together.

Now we go to the upper half of the circular flow. I give the order that numbers need to be deduced.

• Out-going GDI… table 1.1.6, line 1. (real GDP)
• Effective labor income… effective labor share * GDI… effective labor share was 76.0% in 1st quarter 2011.
• Net tax rate (labor)… table 2.1, line 26 divided by line 1.
• Net taxes (labor) = net tax rate * effective labor income
• Saving (labor)… I first find the percentage of household net saving to total net saving. Table 5.1, line 8 divided by line 3. Then I multiply that ratio by total saving, which is \$5370 in the graph.
• Imports (labor)… Determining this number is more involved. In this model, Total income = consumption + taxes + saving + imports. I subtract taxes from both sides to get disposable income. Disposable income = total income – taxes = consumption + saving + imports. We already know labor disposable income from effective labor income minus labor net taxes. Now, we need the personal saving rate to determine imports. The personal saving rate = (saving + imports)/disposable income. (Saving plus imports are the “saving” funds left over after consumption.) Now we can solve for imports. Imports = personal saving rate * disposable income – saving. We already have labor disposable income and labor saving. To find the personal saving rate go to table 2.1, line 35.

Note: The difference between imports and saving is what a person actually saves. If labor imports are greater than labor saving, households have a negative saving rate. If labor imports are less than labor saving, households have a positive saving rate.

• Consumption (labor) = effective labor income – labor net taxes – labor saving – labor imports
• MPC (labor) = labor consumption/labor disposable income… (marginal propensity to consume)
• MPS (labor) = (labor saving – labor imports)/labor disposable income. (MPS = personal saving rate) … (marginal propensity to save)

Note: The percentages next to the labor numbers are just their percentage of total labor income. The same applies to capital.

This completes the labor section. Now we move on to the capital income section.

• Effective capital share = 1 – effective labor share
• Effective capital income = effective capital share * GDI
• Net taxes (capital) = total net taxes – labor net taxes
• Net tax rate (capital) = capital net taxes/effective capital income
• Saving (capital) = total saving – labor saving
• Imports (capital) = total imports – labor imports
• Consumption (capital) = total consumption – labor consumption
• MPC (capital) = capital consumption/capital disposable income ... (capital disposable income = capital income -capital net taxes)
• MPS (capital) = (capital saving – capital imports)/capital disposable income

Note: The numbers from labor and capital combine into boxes that are checked against the numbers in the bottom half.

Comments on getting better numbers would be appreciated. The government does not provide data specifically for this flow. So some percentages were used to represent the “effective” laborer and the “effective” owner of capital. I am sure the numbers aren’t perfect, but they begin to reveal new insights.

There you have the living, breathing circular flow with working parts. I hope you find it as interesting as I do.