# Extending the preliminary circular flow model with labor share

I want to expand on the last post where a simplified circular flow model was given incorporating labor share of income. That circular flow did not include sectors for a government nor foreign markets. I now will expand that model to include those sectors and more.

## Extended circular flow for labor share

Here is the model in equilibrium. The model seeks to simulate the real economy. Dollar values are in billions. There is much to unpack here, let’s get started.

First we see that the out-going (GDI) of the firms equals the in-coming (GDP) at the bottom. Thus, the circular flow is in equilibrium.

Then we see that the GDI is split into labor and capital incomes, 80% and 20% respectively. Then we see that the income of each is divided into the categories of national accounts (consumption, taxes, saving and imports). All but consumption are leakages from the circular flow.

Underneath each category there is a percentage for its share of the income and the real dollar amount given to the category. For example, 80% of labor income is directed to consumption giving \$6,400 billion. Net tax rates include government transfers and are estimated. The net tax rates are kept constant in this post.

Below consumption is a box that is grayed, where you will see 77.6%. This value comes from the equation to determine consumption, which uses a value for autonomous spending. 77.6% is the marginal propensity to consume in the equation. The equation used in this model is…

Consumption = \$1 trillion + 77.6% * (labor income – net taxes)

\$1 trillion is the autonomous spending… 77.6% is the marginal propensity to consume… (labor income – net taxes) is disposable income.

So even if labor share of income was put at 1%, consumption would still be at least \$1 trillion. The same equation was used for capital income using a marginal propensity to consume of 30% and autonomous spending of \$60 billion.

Imports are also based on an equation of autonomous spending. In the case of labor spending on imports, the equation is…

Imports = \$50 billion + 10% * (labor income – net taxes)

\$50 billion is autonomous spending on imports… 10% is the marginal propensity to import (MPM).

Capital spending on imports uses an autonomous amount of \$200 billion and an MPM of 25%.

After determining net taxes, consumption and imports, the remaining balance is put into saving. In graph #1, saving is negative for labor, but positive for capital.

We then move down the flow adding together the categories from labor income and capital income. For example, the \$6,976 billion we see in consumption comes from labor consumption, \$6,400 billion and capital consumption, \$576 billion.

Then we have total net taxes going to the government. Then we have a saving rate of 3.28%, which comes from dividing the saving by GDI, \$328/\$10,000. This rate for saving simulates the national private saving rate. Then we have total imports of \$1,376 billion, which is close to the national average of imports being 14% of GDI.

Then we go through the financial sector which receives or gives out money to the government, foreign markets and firms. In the graph above, the government borrows \$480 billion to meet its expenditure goal because net taxes are insufficient.  Also, exports are less than imports, so the economy is a net borrower with foreign markets. In graph #1, the financial sector adds to the saving balance funds of \$1,272 billion which will go to investment in capital, residential, non-residential and the means of production in the economy.

Note: I did not extend the financial sector to consumption in the form of consumer lending. The reason is that the overall outstanding consumer debt is currently fairly stable.

At the last line, we have the total expenditures (injection returns to the economy) as added from the leakages through the financial sector. The exception is that net exports are determined by subtracting imports from exports.

Investment uses an equation that also includes autonomous investment with a propensity to invest. Investment changes based on national income. So when we change GDI, investment will change.

Investment = \$300 billion + 13% * GDI

\$300 billion is autonomous investment… 13% is marginal propensity to invest… GDI is found at the top of circular flow.

Below the last line are values given for the percentage of GDP. All these percentages are based on normal values in the economy.These values add together to give the national income accounting for GDP.

GDP = C + G + I + NX

C = consumption, G = government spending, I = investment, NX = net exports.

For examples, consumption as a percentage in the national accounting equation is normally between 68% and 71%. Government spending is usually between 16% and 22%. Investment is usually between 13% and 18%. Net exports are now usually -4% of GDP.

So throughout the circular flow model here, the numbers have been chosen to reflect a normal state of the United States economy. I must say that the value for labor share of income is based on the effective labor share value that is used in this effective demand research. As well, the model does not include changes to interest rates, nor exchange rates.

## What happens if labor share drops?

The main point of doing this extended circular flow model is to see what happens if we drop labor’s share of income. We saw in the more simplified circular flow using only investment that the equilibrium level of GDP fell. But will it happen here too, incorporating all the extra variables mentioned above?

Let’s see. I will now drop the labor share from 80% to 75% and then solve for the equilibrium GDP. The drop will simulate the drop in effective labor share after the crisis, which dropped from 79% to 74%.

I will hold three values constant, tax rates, exports and government spending. Exports are determined outside the circular flow and government spending is budgeted. I will also hold the marginal propensity to consume for labor and capital constant. I will hold the marginal propensities to import constant too. As well, the marginal propensity to invest will be held constant.

I first change the value of labor share from 80% to 75%, then I use a function in excel, Goal Seek, to find the value of GDI (out-going at the top) that will equal GDP (in-coming at the bottom). As I do the Goal Seek action, many numbers change. First, we notice that GDP has dropped 6.25%. This drop actually simulates fairly closely the 8% fall from potential GDP (CBO projection) that real GDP has suffered. And people are wondering what is happening. This model shows one way that real GDP has fallen to a new lower equilibrium solely due to the unusual drop in labor share since the crisis.

There is much more to see when we compare graph #2 to graph #1.

• Even though GDP has fallen, and labor income has fallen, capital income has actually risen by 17%! This result explains the record profits of corporations.
• The consumption rate of labor has risen from 80% to 81.8%. Labor is having to spend more of its income. This makes sense. Capital is spending less of its income on consumption, 29% to 28%.
• Saving rate has fallen for labor, but risen for capital. The overall saving rate has gone up from 3.28% to 3.76%. … (\$352/\$9348)
• Imports have not changed much.
• Government borrowing has increased from \$480 b. to \$561 b. to meet its budget. An increase of almost 17%, which matches in percentage terms the increase of capital income.
• Total consumption as a % of GDP has decreased from 69.8% to 68.4%. A decrease of 2%.
• Government spending as a % of GDP has risen from 18.0% to 19.3%. An increase of 7.2%.
• Investment as a % of GDP has increased from 16.0% to 16.2%. Total investment dollars have fallen some.
• Net exports as a % of GDP has risen slightly from -3.8% to -3.9%.
• A critical thing to see here is that the expenditures for GDP at the bottom have not changed very much. A little percentage here, a little percentage there. But the end result is a big change in the equilibrium level of GDP, which again, has fallen 6.25%.

This circular flow model shows that the equilibrium level of GDP can fall just from a lower labor share. Effective demand falls. It is then conceivable that GDP could fall to an equilibrium level below full-employment.

Just as Keynes said it could…

## Raising investment by raising marginal propensity to invest

One more idea… How much would investment have to increase to get GDP back up to \$10,000 billion? But I do not want to know directly that number. I want to know how much the marginal propensity to invest would have to change.

In order to that, I set GDI equal to 10,000, then I use Goal Seek to find the value of marginal propensity to invest that allows GDP to reach an equilibrium of \$10,000 billion.

In graph #2, the marginal propensity to invest was 13% for every dollar of GDP over \$300 billion. Take a guess before you go any further reading this. How much do you think the marginal propensity to invest would have to rise in order to take the economy back to \$10,000 billion? 15%? 18%? 20%? 25%?

Take a moment just to guess before you look below… 