SUMMARY
This is a very simplified simulation of an economy where the government issues money as needed to make its purchases at a rate selected by the user. Taxes are collected at a rate selected by the user. There is no simulation of a banking industry. Perhaps this implies a cash economy or 100% reserve, with banks performing a check clearing function. The system is not constrained by capacity limitations and does not deal with how much spending is on capital and how much is on consumption. Perhaps this implies either excess capacity or that there is a correct allocation between investment and consumption that supports the GDP growth shown.
Three tabs are included:
Basic Simulation – shows details of a simulation.
Comparison – Shows results of 5 different simulations to allow the user to compare the effect of different sets of coefficients.
Documentation – this material appears on the documentation tab.
Per values of the coefficients in the Basic spreadsheet, the Government spends some amount each period, taxes a set percent of total earnings, and issues money as required to make up the difference; recipients of earnings spend some percent of prior period earnings and a different percent of prior period savings. Initial balances of money and earnings can be set. All of these coefficients can be changed by the user.
GDP grows more quickly when the recipients of earnings spend their earning more quickly. If private spending is too high, a boom and bust follow.
The user is encouraged to experiment with the coefficients and observe these effects.
There is no reason to believe that an actual economy would follow the trends in the simulation, given that people make decisions.
Click on the Basic Simulation tab at the bottom to see the detailed simulation, or the Comparison tab to see the results of 5 sets of coefficients plotted together.
DESCRIPTION OF THE SIMULATION
The simulation involves a Private Sector and a Government Sector. There is no Banking Sector and Investment is ignored. Growth is not capacity constrained. This implies either that there is existing excess capacity, or that the portion of purchases devoted to investment is managed in such a way as to provide the facilities required for the projected GDP. Later versions will include more complex simulations.
The simulation is an example of the sectoral monetary stockflow consistent (SFC) approach to macroeconomic modeling. In the matrix below, all rows and all columns sum to zero, thus ensuring that ‘everything comes from somewhere and everything goes somewhere’. It draws on the work of Wynne Godley (19232010) , Professor of Applied Economics, University of Cambridge see Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth.
Quoting Godley's Obituary in The Guardian.
“During his Treasury years, he was hugely influential, and officials still acknowledge his lasting contribution. But in later years he was often a voice crying in the wilderness, and his uncannily accurate warnings of the present financial crisis were largely ignored by policymakers, to everybody's cost.”
In matrix form, the relationships in the simulation are as follows

Recipients of Earnings 
Producers 
Government 
Sum 
Private Sector Purchases 
Pp 
+Pp 

0 
Government Purchases 

+Pg 
Pg 
0 
Earnings 
E 
E 

0 
Tax 
T 

+T 
0 
Change in Assets 
D 

+D 
0 
Sum 
0 
0 
0 
0 
Where row numbers are from the Basic spreadsheet.
Pp – Purchases, private sector – (calculated)
Pg – Purchases, governmental sector – (input)
E  Earnings – (calculated)
T  Tax – (calculated)
D  Government Deficit = Increase in money held by private sector
Banking Sector is not included, Investment is ignored, all profits are passed to the Recipients of Earnings and taxes are collected there.
Private sector purchases in this simplified simulation models is the sum of 2 components:
A percent of prior period disposable earnings
Ppe = PCE * Yd(1) Purchases, private, earnings = coefficient * Prior Period Disposable Earnings
A percent of prior period savings.
Pps = PCS * Hp(1) Purchases, private, savings = coefficient * Prior Period Savings
Pp = Ppe + Pps Purchases, public = sum of the two above
Taxes are computed as a coefficient times total Earnings. This does not imply a flat tax, merely that the total tax collected can be represented as described.
In the matrix above, every column defines a common macro economic equation.
The Recipients of Earnings column reflects the equation
E = Pp + T + D :==: Earnings go to purchases, taxes, and increase in money held by the private sector.
The Producers column represents
E = Pp + Pg :==: Earnings come from sales to the private sector plus sales to the government.
The Government column represents
Pg = T + D :==: Government purchases equal the sum of taxes plus the deficit.
Comparison with traditional model.
Earnings in this model is the sum of the traditional factors Wages, Interest, Rent and Profits.
Recipients of earnings in this model is traditionally called Households.
Producers in this model are traditionally called Business
Change in Assets: Not normally included in the traditional model.
HOW TO USE
Basic Simulation Spreadsheet
The user can change The Propensity To Purchase From Prior Period Earnings, The Propensity To Purchase From Prior Period Savings, the Tax Rate, the Governmental Expenditure period by period for periods 1 through 17, and 2 starting values: prior period GDP and the starting amount of money in the system. The fields that can be changed are included in light green boxes. The remaining fields containing formulae are protected from accidental erasure. To change these fields one must first turn off the protection feature. For example, in OpenOffice 3.2.1 go to Tools>Protect Document>Sheet and remove the check mark; or in Excel 2000 go to Tools>Protection>Unprotect Sheet.
Comparison Spreadsheet.
Five simulations are shown simultaneously on 2 charts. This allows side by side comparisons of different sets of assumptions.
Each simulation is represented by 5 coefficients
1 – The Propensity to Purchase based on Prior Period Earnings
2 – The propensity to Purchase based on Prior period Savings.
3 – The tax Rate
4 – The Annual Rate of Government Spending
5 – Starting GDP
6 – Starting Savings or Money in Circulation
The user can input the coefficients for each simulation, to see the effect of varying coefficients. One chart shows resulting GDP, the other shows the cumulative amount of money created – which in the current system would be called the public debt – and which is also equal to the total amount saved by the private sector.
Interesting aside. Thomas Edison is quoted in the New York Times of 12/4/1921 as suggesting that the government should issue money instead of bonds.
TECHNICAL DETAILS
To make this simulation accessible to a wide audience a spreadsheet has been used rather than one of the simulation software systems more commonly used for econometric modeling. For the same reason, to eliminate the need for the user to understand use of programs such as zip or tar, documentation has been included on a page in the spreadsheet.
Created in Linux/Fedora on a 1024x768 monitor using the Sun/Oracle program CALC. Filed using the xls format from the 1997 and subsequent versions of EXCEL. Goal: to make it work on all windows, Mac, and Linux systems that use EXCEL compatible spreadsheets.
Please comment as you may see fit at
mailto:knox@knoxdata.com?subject=Comments on simulation.
LICENSE
Economic Simulation by Richard Knox is licensed under the
Creative Commons AttributionShareAlike 3.0 Unported License.
To view a copy of this license, visit http://creativecommons.org/licenses/bysa/3.0/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.
In summary, You are free:
© Richard Knox, 2011