9. Separated circular flows

1999-07-07
To Chap 8
Model S3  
  1. Separated circular flows
  2. Public sector
  3. Private sector
  4. Foreign trade

9.1 Separated circular flows

The payment flows of Model S3 are easily separated into individual loops. Eight separated flows can be defined, the same number as degrees of freedom, for the payment flows of figure 7.1:1. The eight flows can be combined to form the original 14 payment flows. Using separated payment flows gives very simple relations and we get an alternative method for studying the economy without the use of complicated mathematics. The parameters that describe the system can be calculated directly if the eight flows are known.

Figure 9.1:1. Payment flows a separated loops.

The public sector has three loops (Mdr =billion of Swedish crowns):

Earnings of publicly employed, Mdr/year X(2)
Pensions, Mdr/year X(5)
Compensation to unemployed, Mdr/year X(6)

These flows combine to three other flows on the right side of the figure (X(10) is shown i figure 7.1:1):

Expenditure on public production, Mdr/year X(1)=X(2)
Transfers, Mdr/year X(4)=X(5)+X(6)
Taxes, Mdr/year X(10)=X(2)+X(5)+X(6)

The production of the private sector can be described by three loops:

Earnings of privately employed, Mdr/year X(12)
Dividends to capital owners, Mdr/year X(7)
Investments, Mdr/year X(17)
Total profits, Mdr/year X(14)=X(7)+X(17)

The private consumption can be calculated from these flows:

Private consumption on goods and services, Mdr/year X(11)=X(7)+X(12)

The foreign trade can be described in the same simple manner:

Exports, Mdr/year X(18)
Imports, Mdr/year X(15)
Financial saving abroad, Mdr/year X(16)=X(18)-X(15)

The two most important parameters of the model can be calculated directly from these flows:

Tax ratio hs=X(10) / (X(2)+X(5)+X(6)+X(7)+X(12))
Profit ratio pv=X(14) / (X(12)+X(14))

The number of employees can be calculated from given yearly wages and salaries:

Yearly earning of public employees, kKr/year ow
Number of public employees, thousands X(3) = 1000*X(2)/ow
Yearly earning of private employees, kKr/year pw
Number of private employees, thousands X(13)=1000*X(12)/pw

Finally the unemployment and the pensions can be calculated:

Total potential workforce, thousands hNw
Number of unemployed, thousands X(9)=hNw-X(3)-X(13)
Compensation to unemployed, kKr/year twa=X(6)*1000/X(9)
Number of pensioners, thousands X(8)
Pensions, kKr/year twp=X(5)*1000/X(8)

It is now easy to see what happens in the economy by using these simple relations. Some consequences are immediate because they directly depend upon the changed flow. Other changes are indirect due to interdependencies between different flows. One such important coupling is the impact on the unemployment when the rate of employment changes in the private and public sectors. It is said below that a change sets the tax rate. The meaning is that if other flows but the first flow shall not change, then the tax rate has to adjust to the new conditions. If the tax rate is constant, then one changed flow will alter the flows of the whole system as described in chapter 8.

9.2 The public sector

Increased wages and salaries to public employees

An increase of the total earnings of the public employees gives a corresponding increase of the necessary tax revenues and the tax rate increases. If the increase is achieved by increased yearly wages and salaries, then no other changes will occur in the economy. If the increase comes from a greater number of people employed in the public sector, the number of unemployed will decrease and the transfer payments decrease. This in turn makes that the taxes increase by less than the original sum.

The total private consumption remains unchanged. The model does not show that incomes are redistributed among the employees. The private employees get a smaller net income due to the tax increase. If the public employees get a salary rise, then they also get a higher net income. In more people are employed, then each will get a smaller net income, while the total consumption among the public employees increases.

Increased pensions

Increased pensions give higher taxes. The employment is unchanged provided that the tax rate is adjusted to the new needs. The consumption is redistributed in favor of the pensioners.

Compensation to unemployed

The unemployment compensations has a direct impact on the tax rate. Every change that makes the unemployment decrease will also lower the tax rate.

9.3 The private sector

Increased earnings of private employees

An increase of the total earnings of the private employees may be the result of a bigger number of employees or of increased yearly earnings. If the productivity is constant and the number of employees increased, then the production and the private consumption increase. If the yearly earnings are increased instead and the profits are held constant, then the prices of the products will increase. This leads to a redistribution of consumption from public employees and capital owners to private employees. The profit ratio decreases. The tax rate decreases due to increased total incomes and a bigger base for taxation.

One part of the redistribution may be due to a smaller number of unemployed.

Increased dividends

If the profits increase due to higher prices and the production is the same, then there will be a redistribution in favor of the capital owners. Most probably, the composition of the production also changes in towards more luxury consumption. If the profits increase due to a higher productivity, then the production can be increased while the total wages and salaries are constant. Increased profits give a larger base for taxation, so the tax rate can decrease. This means that the employees (private and public) may increase their consumption somewhat, but the main part of the production increase goes to the capital owners.

Increased investments

Increased investments implies that the production has to increase by an increased productivity that is not followed by increased wages, salaries or dividends. The investment are free from tax so the tax rate does not change. If the investments are increased with the same total production, then money has to be taken from wages and salaries or from the dividends. The private consumption will decrease and the tax rate increases.

9.4 Foreign trade

Increased exports

An increase of the exports gives a higher financial saving abroad. The savings constitute one part of the total profits of the companies which thus increases. In the long run, the imports will also increase due to the higher availability of foreign currency. The imports will then replace domestic production. More goods are produced for exports and more goods are imported.

Increased imports

An increase of the imports gives less financial saving abroad. As stated above, Imports and exports will balance in the long run.


The excel calculus that describes Model S3 can be downloaded here. There a worksheet named "Separated flows" can be found. The calculus that follows uses the equations that were described above.

Now we will leave the simple models. Model D1 will include the financial sector and real measures of the volume of the production. Flows of commodities, production volume and productivity are treated in chapter 10. Chapter 12 will show the big model D1 that also can perform dynamic simulations.

Back to home page or contents. Next chapter Chap 10.