able of Contents
SAVINGS - INVESTMENTS Model
In EGYPT
Cherine Mohamed Morsi
School of Computing, Engineering and Technology
University of Sunderland
E-mail: shereen_morsi@ hotmail.com
Professor Alfredo Moscardini
School of Computing, Engineering and Technology
University of Sunderland
E-mail:alfredo.moscardini@ sunderland.ac.uk
Abstract
The purpose of the System Dynamics method is to study the relationship between structure and
behavior in non-linear, dynamic systems. In such systems, the significance of various structural
components to the behavior pattern exhibited, changes as the behavior unfolds. Changes in
structural significance, in turn modifies that behavior pattern, which, in turn, feeds back to
change the relative significance of structural components. We develop a macroeconomic model
which we can study the characteristics of this feedback between structure and behavior. This
model is based on multiplier-accelerator model, and inventory - adjustment model. This work is
an extension of the work by Nathan Forrester on the use of basic macroeconomic theory to
stabilize policy analysis. Our main contribution, in this paper, is embedding the gap between
savings and investments that already exist in Egyptian economy and how eliminating this gap.
Explaining the reasons beyond this problem need first exhibit Egyptian economic cycle
representing in production Cycle: that produce gross domestic production (GDP), The GDP
depends on potential production (which consists of Labor force and capital that available in our
society) and total demand in short-term. Capital Formation cycle: That depends on Total
Domestic Investment (which consists of public investment (government sector) and private
investment (business, household sector). The Total Domestic investment depends on what ‘s
available from local resources (Government's revenue and total local savings).
The macroeconomic level contains many feedback loops that require from us to offer a structural
interpretation of the behavior exist in Egyptian economy.
Introduction
Collecting savings and directing them to the various investment fields are the main requirements
of development, therefore achieving increasing rates of economic development. This requires the
presence of local savings sufficient to finance the investment necessary to achieve the required
accumulation of capital to make the economics growth exceeds the population growth.
Thus we see a relationship between the savings and the economic growth, the more the
savings, the more the investments and the higher the rate of growth of production through the
accumulation of capital.
This paper is trying to explain the previous savings - investments problem by using system
dynamic approach that will help us evaluate the current problems and the proposed solution.
80000 5
70000 +
60000 4
50000 4
Investments
40000 5 e
j====S avings
30000 5
20000 5
10000 +
0
1992 1993 1994 1995 1996 1997 1998 1999 2000
Through the graph, it is obvious that investments is increasing more than the increase of local
savings, this gap means there is a shortages in capital requirements to build internal production
capacity to achieve economic growth and development. That creates a tendency to resort to
internal and external sources of finance. One of the most important external sources is external
debt. Managing internal and external debt represents a real challenge to the state. With the
shortage of domestic Savings to feed the required growth, the dependency on intemal and
external capital flows, including debt, becomes a necessity. But the effects of the build up of debt
have crucial negative effect on the recipient economy in the long run.
Guided by the economic models suggesting that growth rate can be stepped up by
increasing Savings for Investment, the government has often resorted to local and foreign capital
borrowing to supplement domestic savings in their efforts to fuel industrialization and production
capacity. The borrowed capital is also often used to finance capital imports necessary to expand
the export industries and for capital outlays for upgrading the infrastructure.
Conceptual Model
Dynamic Hypothesis
The inadequacy of domestic capital and savings leads to a shortage of satisfying domestic
development and industrialization plans. In the beginning of the borrowing process, capital and
investments increase significantly, levels of expected income and production increase and further
development targets are set for the future, so local and foreign debt is required.
The process is reinforcing and growing significantly .A buildup of internal capacity mean
achieve desired capital may lead to the easiest way which is borrowing, but at a certain point of
time the debt increase and we should pay it in maturity period.
So to achieve high economic growth depend on the recourses that available to invest, but when
trying to reach this highly growth by using debt it lead to decrease the income of our country to
pay the loans by interest rate and the effect of it appear on low level of savings and this increase
the gap between the savings and investment.
Structural Assumptions:
To capture the process, we must start with describing the internal mechanisms of capacity
buildup via capital acquisition, the domestic savings and the total domestic investments flows
that lead to the aggregation of domestic income or production (GDP). This cycle can be
describes with the multiplier accelerator mechanism first developed by Samuelson 1939.
The first important concept in the multiplier-accelerator model is the mutual dependency
of consumption and output. Consumption depends on the level of output, and output responds to
the level of aggregate demand. Together represent the multiplier process; it is positive loop
feedback reinforcing process. Through the multiplier, a disturbance in demand produces a
change in output and a proportional change in consumption, which feeds backs to further
disturbance in aggregate demand.
The second important concept in the multiplier -accelerator model is that investment
depends on demand. The model represents investment as a function of the change in
consumption, but the underlying concept is that increased demand requires increased capital
stock to maintain factor balance in the production process. For the purposes of this study it is
convenient to restate the relationship by expressing desired investment as a function of desired
capital and desired capital as a function of the expected long-term demand. This dependence of
investment on demand creates the accelerator process. Through the accelerator, a disturbance in
demand produces a change in output and a proportional change in desired capital and desired
investment, which disturbs demand.
Here a minor modification was made to the model; investment is determined by a simple
stock adjustment formula for capital. Total capital investment is the sum of capital depreciation
plus the difference between desired and actual capital the actual capital stock is the accumulated
difference between investments depreciation. Another alteration of the basic model is the
introduction of the production capacity concept. In basic model, output is a one period lag of
demand, regardless of the capacity to produce. The assumption is changed so that output is
affected by potential output as well as demand. And potential output is formed as Cobb-Douglas
function of two factors, Labor force and Capital. Both Labor and capital are adjusted in response
to change in expected demand. Expected demand is a moving average of current demand.
Employment responds to short-term change in demand, while capital responds to long-term
change in demand. The difference between output and potential output is explained by change in
capacity utilization. Primarily through the use of over and under time.
These two modifications to the model developed by Samuelson has been suggested also
by Nathan Forrester in his distinguished study of the stabilization of the US economy.
We will introduce some modification to the assumptions of Nathan Forrester as well. In
his model, Forrester assumes that investment is determined by a simple stock adjustment formula
for capital .We will distinguish between desired investment, which is the difference between
desired and actual capital stock plus capital-depreciation. And actual investment, which depends
on the adequacy of total domestic investment capabilities. The model developed by Nathan
Forrester assumes the actual and desired investment are the same and the economy can
automatically provide the amounts required of investment, which is not true in the real world and
especially in the case of Egypt. For the purpose of this study we will cut the major loop of the
multiplier-accelerator model. Actual investment will be total domestic investment capacity and
its depends on private investment (come from local savings in banks and it depends in fraction of
investment for private sector) and public investment (come from government sector and it
depends on current revenue for government and fraction of investment)
Plus we will add foreign investment as fraction of GDP. The discrepancy between actual and
desired investment will represent the desired loan.
This paper will use the multiplier - accelerator model as a basic structure that show the
accumulation of capital need desired investment and according to shortage resource lead
government to finance by external debt and that will lead to accumulate loans and it will
decrease through the loan payment which take from total income of the country.
None of the above modifications change the theory underlying the models of Samuelson
or Nathan Forrester. They make more explicit the disequilabrium adjustment process that
produce the mechanism of building up capital and output in response to change in demand and
vise versa. These modifications serve the purpose of this study.
The Second important concept is the Inventory - adjustment model, inventory is treated as
the stock of finished goods, which increase by output and decrease by final sales, and inventory
feedback to output through desired inventory investment by expected demand, desired inventory
investment is equal the difference between desired and actual inventory, and desired inventory is
proportional to long-term expected demand.
The inventory loop adds to model to express about business cycle and determine the total
aggregate demand in Egyptian economy.
Causal Loop Diagram
Desired Loar Domestic Investment
Investmen:
ao
Desirec
Capital
Va Governmen Pot
9 Productioi
Spending
aC) inal Sales Debt
e
aa Lae) i Paymen
Employmen
Governmen’ _productio.
Savings
Consumptio Transfer Mi
Disposabl
income
Desired
Employmen
Shortturm
Demand |
Aggregate
\ Demand
i, Desired a
sire
=A Inventory
jemand
Investmen
Desired
Raunt
Danger Loop (R11):
This loop start when the gap between total domestic investment desired investment
created, the government tends to borrow as a way for increasing resources to achieve wanted
investment and this will retum achieving high economic growth, the debt will increase and will
decreases by loan payment which lead to decrease permanent income, so the savings will
decrease and it will lead to another loop of borrowing.
Multiplier Process (R2):
In this loop consumption depend on the level of production, and production respond to the
level of short term expected demand, when production increase, the current disposable income,
and permanent income will increase so that will increase the level of consumption which makes
increase in demand and lead to produce more and so on.
Accelerator Process (R3):
The investment depend on long term expected demand, when investment increase the
capital, potential production, production, current disposable income and permanent income will
increase which lead consumption to increase aggregate demand and that will raise long term
expected demand and sequentially raise desired capital and desired investment.
Business Cycle (B3):
The effect s of this loop can be traced starting at aggregate demand, An increase in
aggregate demand raises short term expected demand, which pushes up desired employment
.The increase in desired employment raises employment and that will lead to greater production
and accumulation of inventory so high level of inventory will decrease level of desired inventory
investment.
FORMAL MODEL
Stock and F low diagram
Capital Formation
r™N O iO
apital
Capital #nvestment Cafital_Depreciation
es)
Total_Domestic_investment
=
N44 =
Money_Borrowed
M4
Desired ital xponent_on_Capital
Desiéd_Investment
Desired_loan
Real_Interest_rate
Time_to_Adjust_Capital
Long_term_expected_demand
Change_in_long_tert
RN
Time_to_adjust_long_term N44
Aggregate_Demand
Averagé_life_of_Capital
Demand For Production
Short_term_expected_demand
Flexibility_of_Capacity_Utilization
Time_to_adjust]employment
Potential output
<}
Y'in_Employment
Equilibruim_Capital
Equilibruim_P roduction
Desired_Employment
J
Exponent_on_Capital Capital
Short_term_expected_demand
hort_term_expected_demand
Change_in_short_ternt
I
Time_to_adjust_short_term n4
Aggregate_Demand
Inventory Adjustment
Desired_inventory_investment
Desired_Inventory
Time_to_adjust_inventory Gov_Spending
L |
Normal_inventory_Coverage Short_term_expected_demand
Income Creation
nS Timgrto_smooth_income
Perceived_Nebt
Margin_progenstiy_to_consume
Permenant_Income
“in_permenant_income
Gov_Transfer
Consumption
urrent_Disposable_Income
ee)
Output_GDP Tax_Revenue
Debt formation
Production
Saving sector
Investmeny fraction
Permenant_Income =
a i) Foriegr/ Investment
Saving_rate Investment_from_Savings
Average_propon$ity_to_save
Total_Domestic_investment
a
te al
Average_propensity_to_consume
Documentation
The following are the model variables with full description. Appendix (1) contains powersim
printout of all variables, equations and documentation sorted alphabetically
Production (GDP) :
Production is a weighted average of potential production and short-term expected demand.
Production = Potential_Production*(1-Flexibility_of_Capacity_Utilization) + Short_term_expected_demand *
Flexibility of Capacity Utilization
LE means Local Pounds
Production measured in (LE/Y ear)
Potential production measured in (LE/Y ear)
Short-term expected demand measured in (LE/Y ear)
Flexibility of capacity utilization measured in (Dimensionless)
Potential production:
Potential production is determined by labor force (represent in no. of employees) and capital
stock according to Cobb-Douglas production function.
Potential production= Equilibruim_Production*(Employment_to_Equilemployment)~*(1-Exponent_on_Capital)
* (Capital_to_Equilibruim_Capital)“Exponent_on_Capital
Equilibrium production measured in (LE/Y ear)
Employment to Equilibrium Employment measured in (persons)
¢ Capital to Equilibrium capital measured in (LE)
¢ Exponent on capital measured in (Dimensionless)
Employment:
Employment is the total man-hours dedicated to production.
¢ Employment measured in (persons)
Change In Employment:
The Change in Employment determined by the net difference between Desired and actual
Employment and divide by time to adjust employment.
Change in employment = (Desired_Employment - Employment) /Time_to_adjust_employment
¢ Change in employment measured in (Persons/Y ear)
¢ Desired employment measured in (persons)
¢ Time to adjust employment measured in (years)
Desired Employment:
Desired employment is proportional to short-term expected demand. It’s equal to exponent on
labor in the production function multiplied by short-term expected demand divided by the wages.
Desired employment = (1- exponent on capital)* short-term expected demand / wages
¢ Desired employment measured in (Persons)
¢ Short-term expected demand measured in (LE/Y ear)
¢ Wages measured in (LE/persons/year)
Short-term expected demand:
Sectors that produce have their expectation about sales in future ,so short-term expected demand
determined as average of aggregate demand .
¢ Short-term expected demand (LE/Y ear)
Change In shot-term expected demand :
The Change in short-term expected demand determined by the net difference between aggregate
demand and short-term expected demand and divide by time to adjust short-term expected
demand.
Change short-term expected demand = (Aggregate demand - short-term expected demand)/ time
to adjust short-term expected demand
¢ Change short-term expected demand measured in ((LE/Y ear/Y ear)
¢ Aggregate demand measured in (LE/Y ear)
¢ Time to adjust short-term expected demand measured in (Y ears)
Capital:
The Stock of Capital is accumulated by investment and decreased by deprecation. Therefore, the
rate of change in capital is equal to the difference between Capital investment and Capital
depreciation.
¢ Capital measured in (LE)
Capital investments:
The Capital investment is the total investments that lead to increase the capital, and it is
summation of available of the total domestic investments and the money borrowed.
Capital investments = MAX (0,(Total_Domestic_investment + Money_Borrowed))
¢ Capital investments measured in (LE/Y ear)
¢ Money Borrowed measured in (LE/Y ear)
* Total Domestic investments measured in (LE/Y ear)
Capital Depreciation:
Physical capital is assumed to have a constant average service life. Capital depreciation is there
for proportional to capital stock.
Capital Depreciation = Capital / Average Life of Capital
¢ Capital Depreciation measured in (LE/Y ear)
Desired Investment:
The desired investments is determined by the difference between desired capital which the
county need to reach it to achieve highly economic growth and capital divide by the time need to
achieve this capital plus capital depreciation.
Desired investments = ((Desired Capital - Capital) + Capital Depreciation) / Time to adjust Capital
¢ Desired investment measured in (LE/Y ear)
¢ Desired Capital measured in (LE)
¢ Time to adjust capital measured in (Y ears)
Desired Capital:
Capital unlike labor is a long-lived asset for production sector. Capital should respond more
slowly than labor to changes in demand and inventory conditions. Desired capital is therefore a
function of long term expected demand.
Desired capital = Exponent on capital *Long term expected demand /(1/average life of capital)+ interest rate
¢ Desired capital measured in (LE/Y ear)
« Long term expected demand measured in (LE)
¢ Interest rate measured in (fraction/Y ear)
* Average life of capital measured in (years)
Long term expected demand
The long term expected demand is an exponential average of aggregate demand , and it consider
expectation of long term demand, and it initialize by equal the total production (GDP).
¢ Long term expected demand measured in (LE).
Change in Long-term expected demand:
The Change in Long-term expected demand determined by the net difference between aggregate
demand and Long-term expected demand and divide by time to adjust Long-term expected
demand.
Change Long-term expected demand = (Aggregate demand - Long-term expected demand)/ time to
adjust long-term expected demand
¢ Change long-term expected demand measured in ((LE/Y ear/Y ear)
¢ Aggregate demand measured in (LE/Y ear)
¢ Time to adjust long-term expected demand measured in (Y ears)
Inventory:
The rate of change in inventory is the difference between production and final sales.
¢ Inventory measured in (LE)
Final Sales:
The final sales represent the total demand in economy, so it’s the summation of consumption
plus investment and goverment expenditure.
Final Sales = consumption + capital investments + government expenditure
¢ Final sales measured in (LE/Y ear)
¢ Consumption measured in (LE/Y ear)
¢ Capital investment measured in (LE/Y ear)
¢ Government expenditure measured in (LE/Y ear)
Desired inventory:
Desired inventory is assumed to be proportional to short-term expected demand.
Desired inventory = Normal inventory coverage * short-term expected demand
¢ Desired inventory measured in (LE)
¢ Normal inventory coverage measured in (Y ears)
Desired inventory investment:
The desired inventory investment is determined by the difference between desired and actual
inventory.
Desired inventory investment = (desired inventory - inventory) / time to adjust inventory
¢ Desired inventory investment measured in (LE/Y ear)
¢ Desired inventory measured in (LE)
¢ Inventory measured in (LE)
¢ Time to adjust inventory measured in (Y ears)
Permanent income:
Permanent income is average of current disposable income , the rate of change in permanent
income is the fraction of the discrepancy between current disposable income and permanent
income .
¢ Permanent income measured in (LE/Y ear)
Change in permanent income :
The change in permanent income is the difference between current disposable income,
permanent income and perceived debt service.
Change in permanent income=(Current disposable income-permanent income-perceived debit service)/
time to smooth income.
¢ Change in Permanent income measured in (LE/Y ear/Y ear)
¢ Current disposable income measured in (LE/Y ear)
¢ Perceived debit service measured in (LE/Y ear)
¢ Time to smooth income (Y ear)
Consumption:
The consumption is the amount of money spend on domestic products and services per year.
Consumption = Permanent income * Average Propensity to consume
¢ Consumption measured in (LE/Y ear)
Total Savings:
Total Savings are the total deposits that exist in Banks from Government sector plus Non-
Government sector and it is increased by saving rate and decreased by private investments.
¢ Total Savings measured in (LE)
Saving rate:
The saving rate is the rest of income that not consume and it depends on average propensity to
save and permanent income
Saving rate =Permanent income *A verage propensity to save
¢ Saving rate measured in (LE/Y ear)
¢ Average propensity to save measured (fraction/year)
Investment from Savings:
The investment from savings means the resources that available from internal country and
directed to invest in all projects .
Investment from savings = Dleaymtr(otal_Local_Saving,1,1,Total_Local_Saving)*Invest_frac
¢ Investment from savings measured in (LE/Y ear)
Total Domestic investments
The total domestic investments determined by total investment from government sector and non-
government sector plus foreign investment .
Total Domestic investments = Investment_from_Savings + Foriegn_Investment
¢ Total Domestic investments measured in (LE/Y ear)
Investment fraction:
The investment fraction is determined as percentage of local resources available.
And it put as constant depend on the actual situation in country.
Tax Revenue:
The tax revenue is the total amount of money gained by the government from taxes per each
year; it is defined by total GDP multiplied by the tax fraction.
Tax Revenue = Production * TaxFraction
* Tax Revenue measured in (LE/Y ear)
Total Debt:
The total debt is considered the outstanding of loans and it accumulated by both money
borrowed and accrual of interest rate and depleted by debt service rate.
¢ Total debt measured in (Units)
Money Borrowed
The money borrowed is consider the gap between desired investment and domestic investment ,
and the size of this gap determine the loan that will take from abroad. and time taking to get this
loan .
Money borrowed = MAX (0,Desired_loan/Time_to_acquire loans) * Effect_of Debt Output_on Desired_Loan
¢ Rate of money borrowed measured in (Units/Y ear)
¢ Gap (LE/Y ear)
¢ Time to acquire loans (Y ears)
Desired Loan:
The desired loan initialize when there is a difference between desired investment and total
domestic investment and this difference lead to borrow local or foreign loan.
Desired Loan = MAX (Desired_Investment-Total_Domestic_investment,0)
Loan Payment:
The loan payment is the acquired loan according to maturity date.
Loan payment = Total_Debt / Maturity_period
¢ Loan payment measured in (Units/Y ear)
Perceived Payments:
The payments are depend on the rate of money borrowed, lending rate of this loan, and how
many years loan will stay until become acquired to pay.
Perceived Payment = (DELAY PPLINF(Loan_Payment,4,5))
¢ Payments measured in (Units/Y ear)
Lending rate:
The lending rate is interest rate that should pay over the loan in the end of maturity date of loan.
And the rate of lend is average by 7% annually.
Interest Rate:
This interest rate is determined by debt and lending rate; after it calculated it add to stock of total
debt.
Interest Rate = Total Debt * Lending rate
¢ Interest rate measured in (Units/Y ear)
Foreign investment:
The foreign investment is the total amount that foreign companies invest it in Egypt.
And it will be one of alternative policies.
Effect of total debt to production to acquire another loan:
The effect of total debt to production to acquire loans means ,it represents state of the country by
the ratio of total debt to production ,if this percentage high ,the country has to stop financing
capital stock by borrowing money ,because the main problem in debt payment .
GRAPH(Percentage_of debt _to_production,0,0.1,[1,0.93,0.85,0.74,0.66,0.57,0.53,0.46,0.4,0.33,0.26,0.2,0.
,0.13"Min:0;Max:1"])
Model Behavior
In this part we will try to describe the major phases of behavior of the model in the base run. and
then describe the simulation results for two alternative policies and compare the results.
1-Analysis of the Base Run:
The model in the base run is simulated a period of 50 years, and there are two main
phases of behavior that we will discuss in detail.
20,000:
= Desired_Investment
ae Total_Domestic_investment
= Perceived_Payment
=— Money_Borrowed
20,000:
= Saving_rate
= Capital_investment
—+t
120,001
115,00
110,00
Production
105,00 ==
Aggregate_Demand
=
18,000. —— Capital_Depreciation
—2—Capital_investment
The simulation shows significant oscillation in most variables .All variables share the same
length of cycle period.
In general we can say that in the high part of the cycle the dominant loops are the multiplier,
accelerator loops, while in downward part of each cycle the dominant loops are representing in
financing gap and debt payment. These oscillations indicate the effect of the existence of
negative feedback loops and delays.
The general behavior of the system can described from economic point as follows:
There is a planned desired investment according a high total demand, but Total domestic
investments are not covering it, due to the saving rate is less than the investment rate. The gap
between total domestic investments and desired investments will be overcome by borrowing
money to build production capacity, when desired loan acquire, investment in new capital stock
increase and it required increase labor force and that lead to increase production capacity and
current disposable income which affect on saving rate by increasing it, but the saving rate rise
depends on average propensity to save and this average needs to increase first.
The production rise will lead to increase consumption, so the total demand will increase which
will lead to another cycle another, and the gap between saving and investment already exist ,so
the country will borrow again ,but the outstanding of total debt grows significantly and debt
payment is higher than loan acquisition rate .this mean the percentage of total debt to production
is high. This high percentage will lead to decreasing money borrowed .The effect of it lead to
capital investment starts fall below capital depreciation and according to it capital stock starts to
fall.
If we simulate for more than 50 years, the results will be oscillations every 10 years but at lower
levels, because the economy is trapped in loans that on the long run will highly decrease the
levels of demand, production, and income.
Appendices
init Capital = 258000
flow Capital =-dt*Capital_ Depreciation +dt*Capital_investment
doc Capital = The Stock of Capital is acumaleted by capital investment and decreased by
capital deprication , Therefore the rate of change in capital is equal to the difference between its.
init Employment = 10
flow Employment = +dt*Change in Employment
doc Employment = The Employment is defined as total employees are share in production.
init Inventory = 30000
flow Inventory = +dt*Production -dt*Final_ Sales
init Long_term expected demand = 100000
flow lLong_term_expected_demand = +dt*Change_in_long_term
init Permenant Income = 80000
flow Permenant_Income = +dt*Change_in_permenant_income
doc Permenant_Income = Permanent income is an exponential average of current disposable
income.
init Short_term_expected_demand = 100000
flow Short_term_expected_demand = +dt*Change_in_short_term
doc Short _term_expected_demand = The Short term expected demand is an exponential
average of aggregate demand
init Total Debt =0
flow Total_Debt = +dt*Interest_rate -dt*Loan_Payment
+dt*Money_ Borrowed
init Total_Savings = 17000
flow Total_Savings = -dt*Investment_from_Savings +dt*Saving_rate
doc Total_ Savings = it is the total saving from government sector that exist in central bank
aux Capital_Depreciation = Capital/Average life of Capital
doc Capital_ Depreciation = Physical capital is assumed to have a constant average service life
. Capital Depreciation is there for proportional to capital stock.
aux Capital_investment = MAX (0,(Total_Domestic_investment+Money_Borrowed))
doc Capital_investment = It is the total investment that lead to increase the capital , and it is
summtion of avaliable real total domestic investment .
aux Change in Employment=(Desired_Employment-
employment)/Time_to_adjust_employment
doc Change in Employment = The change in Employment is equal the discrepancy between
desired employment and actual employment divided by time to adjust employment.
aux Change in long term=(Aggregate Demand-Long_term_expected_demand)
/Time_to_adjust_long_term
aux Change in permenant income = (Current Disposable _Income-Permenant_Income-
Perceived | Payment)/T ime_to_smooth income
aux Change in short term = (Aggregate_ Demand -
Short_term _expected_ demand)/Time_ to adjust. short term
doc Change in short term = The change in short term is the difference between current
aggregate demand and expected demand divided by time to adjust short term demand.
aux Final_Sales = Capital_investment+C onsumption+G overnment_ Expenditure
doc Final_Sales =it is the sum of consumption , investment and government expenditure .
aux Interest_rate =Total_Debt*Lending rate
aux Investment_from_Savings =Total_Savings*Investment_fraction
aux Loan Payment =Total_Debt/Maturity_period
aux
Money_Borrowed=MAX (0,Desired_loan/Time_to_acquire_loans)*Effect_of Debt to_P
roduction_on_Desired_loan
aux Production=Potential_Production*(1-Flexibility_of_Capacity_Utilization) +
Short_term_expected_demand * Flexibility_of_Capacity_Utilization
doc Production = Production is a weighted average of potential output and short term
expected demand , And the weighting parameter is the flexibility of capacity utilization .
aux Saving_rate = MAX(0,Permenant_Income*Average_proponsity_to_save)
doc Saving_rate = The govenmnet saving rate is the annual saving from govrnment sector
aux Aggregate Demand = Final _Sales+Desired_inventory_investment
aux Average proponsity_to_ save =(1-Average_propensity_to_consume)
aux Capital_to_Equilibruim_Capital = Capital/Equilibruim_Capital
aux Consumption = Permenant Income*Average propensity _to_consume
doc Consumption = The consumption function is based on the permenant income hypothesis
of Fredman . Consumption is equal to a constant fraction of permenant income, the constant of
disposable income spent on consumption goods equals the average proponsity to consume.
aux Current Disposable_Income = Production-(Tax_Revenue-Gov_Insurance)
doc Current_Disposable_Income = Current disposable income is defined as total output less
net taxes
aux Desired _Employment=((1-Exponent_on_Capital)*Short_term_expected_demand)/W ages
aux Desired Inventory = Normal_inventory_Coverage*Short_term_expected_demand
aux Desired _inventory_investment=(Desired_Inventory-
Inventory)/Time_to_adjust_inventory
aux Desired _Investment=Capital_Depreciation+(Desiredt_Capital-
Capital)/Time_ to Adjust_Capital
doc Desired_Investment = Fixed Capital investment is given by a simple stock adjustment
formula . the base rate of investment is equal to physical capital depreciation .The base rateis
modified by the need to expand or contract the capital stock . desired investment is therefore
equal to capital depreciation plus a fraction of the discrepancy between desired capital and actual
capital stock and divided by time to adjust capital .
aux Desired_loan = MAX (Desired_Investment-Total_Domestic_investment,0)
aux Desiredt_Capital= Exponent_on_Capital * Long_term_expected_demand
/(1/Average_life_of_Capital +Real_Interest_rate)
doc Desiredt_Capital = Capital is a long lived asset for the production sector . And desired
capital is therefore a function of long term expected demand .
aux
Effect_of_Debt_to_Production_on_ Desired_loan=GRAPH(Percentage_of_debt_to_production,0
,0.1,[1,0.93,0.85,0.74,0.66,0.57,0.53,0.46,0.4,0.33,0.26,0.2,0.17,0.13"Min:0;Max:1"])
doc Effect_of_Debt_to Production on_Desired_loan =it represent state of the country by the
ratio of total debt to production .
aux Employment_to Equilemployment =Employment/Equilibruim_Employment
aux Gov_investment =Tax_Revenue*Gov_investment_frac
aux Gov_Saving = Tax_Revenue-(Current_gov_expenditure)
aux Non gov =Saving_rate-Gov_Saving
aux Perceived_Payment = DELAY PPLINF(Loan_Payment,1,5)
aux Percentage_of_debt_to_ production =Total_Debt/Production
aux Potential_Production=Equilibruim_Production*(Employment_to_Equilemployment) \1-
Exponent_on_Capital)*(Capital_to Equilibruim_Capital)*Exponent_on_Capital
doc Potential_ Production = Potential output is determine by the stock of capital and
employment as cobb - Douglas production function.
aux Tax Revenue =(Production*Tax_rate)
aux Total_Domestic_investment = Investment from _Savings+Foriegn_ Investment
doc Total_Domestic_investment = The total domestic investment determined by govrnment
investment and private investment plus foriegn investment
const Average life of Capital = 15
doc Average life of Capital = A simple time constant for the exponential decay formula .
The average life of capital will be set to the value of 15 years. A lot of empirical studies suggest
the same value .
const Average propensity_to_consume = .83
doc Average propensity to consume = The portion of income that is directed to
consumption rater than savings and investment is relatively high
const Current_gov_expenditure = 26211.4
doc Current_gov_expenditure = Government Expenditure consider the total amount that the
government spend on paying (salaries or wages, pensions, commodity and service requirement,
defense outlays, subsidies, social funds and others) .
Government expenditure put as constant and increased annually by 10% as analysis of historical
data.
const Equilibruim Capital = 258000
const Equilibruim_Employment = 10
const Equilibruim_Production = 100000
const Exponent_on Capital =.25
const Flexibility_of_Capacity_Utilization =.5
doc Flexibility_of_Capacity_Utilization = it controls the under overutilization of plant and
undertime and overtime for labor . it is supposed to vary between 0 and 1 the parameter is set her
to .5 representing the case of egypt with little flexibility of capacity utilization due to the
inadequacy of resources.
const Foriegn Investment = 1000
const Gov_Insurance = 10000
const Gov_investment frac =.15
const Government Expenditure = 20000
const Investment fraction =.65
const Lending_rate = .07
const Maturity_period =5
const Normal_inventory_Coverage = .30
const Real_Interest_rate = .03
const Tax_rate = .30
const Time to acquire loans =1
const Time to Adjust Capital =3
doc Time to Adjust Capital = It represents the entire delay between the recognition of a
change in capital needs and actual capital stock. the adjustment time reflects planning and
delivery delays plus purposeful smoothing of investment activity.
const Time _to_adjust_employment =.5
const Time_to_adjust inventory =.5
const Time to_adjust_long term =3
doc Time_to_adjust_long term = it insulates capital investment from short run swings in
demand Becasue capital has a long life , it should be adjusted only to relatively long run changes
in demand . the smoothing time should be long enough to filter out most business cycle
flctuations.
const Time_to_adjust_short_term =.5
doc Time _to_adjust_short_term = it must be long enough to smooth out minor shifts in
demand but short to permit recognition of business cycle variations in demand . The smoothing
time must be approximately one year or less to track business cycle fluctuations.
const Time to smooth income =2.5
doc Time_to_smooth income = Milton Friedman, in his theory about consumption function,
estimates the time to smooth permanent income to he 2.5 years.
const Wages = 7500
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