Taking the Circular Flow to the limit of equilibrium

As I said, I was going to post a version of the circular flow model for current conditions of the economy.

Setting up the model

Conditions for national accounts and other numbers are currently… (See these graphs CGINX, XM, Undistprof)

  • Real GDP of $15.650 trillion. (2009 dollars)
  • Effective demand limit of $16.1 trillion. (real 2009 dollars)
  • Effective labor share of 74%. (Effective labor share is a value determined from the relationship between labor share and capital utilization.) The index for Labor share (2005 = 100) as given by the Bureau of Labor Statistics is around 95. The index is translated into an effective labor share of 74%.
  • Gross private consumption $10.700 to $10.750 trillion.
  • Government expenditures $2.900 trillion.
  • Real gross private domestic investment $2.520 trillion.
  • Real net exports ($450 billion) annual basis.
  • Real exports $2.000 trillion.
  • Real imports $2.450 trillion.
  • Gross government borrowing $500 to $600 billion.
  • Undistributed corporate profits $1.0 trillion.

Assumptions  and constraints. These constraints are run in the Solver function of excel.

  • Net taxes (taxes – transfers) are 15% for both labor and capital.
  • All autonomous spending has been made equal to zero. Marginal propensities are for each dollar of disposable income.
  • Imports are roughly the same percentage for both labor and capital consumption. Imports for capital were set at 20% of capital disposable income, (capital income – capital net taxes).
  • Capital saving is equal to undistributed corporate profits of $1.0 trillion.
  • Saving is the money left over from income after taking out net taxes, consumption and imports.

The solver function asks for a target value.

  • Target value is setting GDP $56 billion greater than GDI. GDI is out-going income from firms. GDP is in-coming expenditures to firms from the economy. $56 billion was chosen because this value allows real GDP to increase until the equilibrium level of $16.1 trillion at the effective demand limit. GDI and GDP will be equal at the effective demand limit. GDP can be greater than GDI, because more money can be injected into firms in various ways. But it is difficult for GDI (out-going) to be more than GDP (in-coming), because that means firms are paying out more income than they receive. This limit on GDI is another way to see the effective demand limit. (note: You will usually see GDI higher than GDP before recessions. This is a sign that the effective demand limit is being reached.)

Solver asks for numbers to change in order to meet the target value. Numbers that solver changes are highlighted with yellow in graphs…

  • Marginal propensity to consume for labor.
  • Marginal propensity to consume for capital.
  • Marginal propensity to import for labor.
  • Marginal propensity to import for capital.
  • Marginal propensity to invest.

When all the above parameters are entered into solver, we get a circular flow for current data.

Circular flow ext 5

link to Graph #1

The Marginal propensities to consume for labor and capital are the primary results from the solver function. These MPCs satisfy the parameters given above. We see that labor spends 88 cents of every dollar of disposable income (income after net taxes). Of course, some labor spends more, some less. Capital income spends 59 cents of every dollar of its disposable income on consumption. Keep in mind that capital’s consumption assumes the saving of $1 trillion undistributed corporate profits. If overall capital saving is above undistributed corporate profits, consumption would be lower. If capital saving is below it, consumption would be higher.

The marginal propensity to invest comes to be 16.1%. Thus, there is investment of 16 cents for every dollar of real GDP.

Taking it to the effective demand limit

We can see in the above graph that in-coming GDP at the bottom is greater than the out-going GDI at the start. The increase is due to injections for economic growth. If we take that GDP at the bottom and then put it as out-going GDI at the top, it will flow through the economy and the GDP at the bottom would increase. If we kept putting the new higher GDP back up top, eventually GDI would equal GDP. The place where they are equal is the effective demand limit. At this limit, out-going money cannot be greater than in-coming money.

I will solve for the effective demand limit using the goal seek function in excel. I simply state that I want GDI and GDP to be equal, then I ask goal seek to increase GDI until it equals GDP. The GDI that results gives the equilibrium point of the economy in terms of real GDP.

Here is the result for the equilibrium GDP at the effective demand limit.

Circular flow ext 6

link to Graph #2

No changes to the marginal propensities, which are taken as constant parameters. The numbers just grew together within the parameters. But it is interesting to note that as the economy grows within these set parameters, an equilibrium point will be reached. There are various ways to determine this point in order to double-check the result.

And if we raised labor share?

If effective labor share was somehow raised to 76% (Bureau of labor statistics index of 97.4, 2005=100), what would happen to the equilibrium point of real GDP?

It must be said that labor share must rise on a consistent basis for this change to take place, because the income has to circulate through the economy for many quarters.

Circular flow ext 7

Link to Graph #3

All I did was change effective labor share from 74% to 76%, then solve for equilibrium GDP. As we can see, the equilibrium of GDP rose to $16.558 trillion. That is $450 billion more in output over graph #2, which is still less than full-employment as determined by the CBO estimation of potential real GDP.

Keep in mind that if labor share rose one quarter like 4th quarter 2012, then fell the next, the equilibrium level of GDP would not change. The change has to be consistent for the money to circulate properly. However, if effective labor share rises just a little to a new level, that’s a few more people that would be employed, even though it’s not full-employment.

The main argument to raise labor share is because GDP equilibrium is now below full-employment.

The marginal propensities did not change in graph #3. But would they change as the economy got closer and closer to the GDP equilibrium? That is a question to watch over time.

Note: These are preliminary numbers that need to be refined. I will look for insights in the comments section below.

For example, what really is the net saving of capital income? What really is the marginal propensity to import for capital income? What is the net tax rate for labor and capital? Answering just these three questions would allow us (through a deductive process) to precisely determine the marginal propensity to consume for both labor and capital.