NBSIR 74-556

MATHEMATICAL

I CITY GAMES

NTIS
'Atti 0»

National Technical Information Service

U.S. DEPARTMENT OF COMMERCE

P.O. Box 1551

Springfield, Va. 22151

Price of City Games

Computer Files Includes

Related Manuals
CITY GAMES

MATHEMATICAL FOUNDATIONS

Written by John E. Nforiarty

Technical Analysis Division

Institute for /^plied Technology

National Bureau o£ Standards

Washington, *D. C. 20234

November 1973

Final Report

Sponsored by

National Technical Information Service

5285 Port Royal Road

Springfield, Virginia 22151

U. S. Department of Commerce, Frederick B. Dent, Secretary

National Bureau of Standards, Richard W. Roberts, Director
Acknowledgement

We wish to acknowledge the significant contributions made by

Mr. S. Guiland of Johns Hopkins University for his tireless effort

in proof-reading the draft of this text. Also the efforts of

Mrs. R. Ciufolo, Mrs. L. Groves and Miss C. Naas for their typing

and editing of this manuscript is appreciated.
TABLE OF CONTEOTS

Title Page

I. INTRODUCTION 1

II. PRIVATE CAPITAL ALLOCATION 8

A. Choice of Investment 8

B. Types of Investment 10

C. Generalized Private Capital Allocation Equation..... 14

D. Residential Housing 16

E. Commercial 20

F. Industrial 23

III. GOVERNMENT CAPITAL 26

A. Government Decision Objectives 27

B. Departmental Rates 28

1. Ratio for Education 28

2. Ratio for Adult Education 29

3. Ratio for Minicipal Services 29

4. Ratio for Welfare Payments 30

5. Ratio for Utilities 30

6. Ratio for Transportation 30

C. Budget Allocation 31

IV. TIME ALLOCATION 32

A. Allocations 33

1. Part-Time Work (r ) 34

2. Free Training and Adult Education (yAF^) 35

3. Paid Training and Education (yAP^) 35

4. Political Activities (.^pq) 36

5. Recreational Activities (yR^) 36

B. Decision to Invest Time 37

V. PUBLIC AND PRIVATE INFLUENCE 39

A. Voting 40

B. Allocation of Power 41

C. Power Objective 43

ill
Title Page

VI. OPERATION OF THE MODEL 45

A. Business Goods and Services 45

1. Demand 45

2. Supply 45

3. Price 46

4. New Prices 46

B. Employment 47

1. Demand for Jobs 47

2. Supply of Workers 47

3. Matching 48

4. Part-Time Employment 49

5. Salaries 49

C. Land Use 51

1. Residential 52

2. Industrial 53

3. Commercial 53

4. Government Facilities 54

D. Land Value 54

E. Rent 55

F. Location of a Commercial Site 56

G. Migration 58

H. School Assignments 60

I. Transportation 62

J. Value of Structure and Capital Equipment 64

K. Water 65

VII. POST SCRIPT 68

A. Glossary of Terms 69

B. List of Symbols 76

iv

I
I. INTRODUCTION

The CITY models are operational simulation games in which the participants make economic, government and social decisions affecting a hypothetical

metropolitan area. Through the use of a computer, the simulated urban system

responds to the participant's decisions as any real city would. Each player

is assigned to a team which shares an economic, government or social role.

The interrelated decisions made by teams will guide the way the simulated

city changes in composition and size.

The simulation approach to cities offers the players an opportunity

not only to make decisions but to implement them as well. They receive a feedback from their actions and see the effects from other forces that are constantly at work altering the effectiveness of the player's decisions.

Players therefore have a learning experience on how to deal with a changing

environment. Tne round- by-round play gives the players the necessary

experience in selecting the t>^e of analysis to move them towards their

objectives \\^iile the allocation of their time and Game resources is a critical determinant of the success they hope to achieve. As the Game

progresses, players learn to increase their involvement in the management

of the environment while at the same time learning about the relationships

between business and society.

The CIT\' model is really a series of Games . CITY I is the smallest

of the Games consisting of the Economic and Government decision makers

and operates on an IBiM 1131 computer. It is primarily designed for land use and business decisions with the Government Departments acting more in

the role of provider of servdces rather than regulatory agents. TELECITY

or CITY II is CITY I with a partially operative social sector and operating

on a IMivac 1108 Exec 8 from a teminal. CIT\' III and CITY IV contain the

Economic and Government decision makers and further ex^Dand CITY I by including

the Social decision makers. The primar>' difference between CITY III

and CITY IV is that CITY III is run on a Univac 1108 computer and

CITY IV is run on an IBM 360/370 operating system. CITY IV was further

expanded to include the water supply system kno\vTi as the 'Vater module."

When the 'Vater module" is used with CIT\' IV, the model is then knom as

1
the River Basin Model.

To simplify the description of the theory of these modules, this

manual is written for the four module game. The equations for the other . games can easily be obtained by eliminating the descriptors that do not

apply to the particular game of interest. The theoretical structure of

all models are consistant and relevant only within the range from a central

city area to a regional configuration. The description of the module

components and equations are meant to show the scope of decisions including

those by the users and by the programs and algorithms of the computer model.

All models have associated with them Players', Directors' and Operators'

manuals which should be used in conjunction with this manual. The numerous

details and particulars of each Game are described in the other manuals

whereas this manual describes the theoretical base for all Games in the

series.

To orientate the reader to this manual, it must be emphasized that all

models are based on a grid matrix to locate and tabulate the larger number

of interrelationships and to locate specific parcels of land or highways.

Within each square or grid, numerous restrictions and/or data are imposed

by each module. If a player and/or computer change is proposed for a particular location in the matrix, all conditions must be met or the proposal will not be accepted by the computer. The computer therefore acts as a large accounting system with minor simulation roles played in external

relationships to the theoretical city such as the business cycle or export

sales. The players serve as a decision making body which tries to optimize

their decisions for the purpose of achieving individual objectives. This

optimizing process might maximize individual goals but when placed in

competition for a finite number of available resources, it might well be

suboptinal for the entire city. It is within this framework that learning

occurs. The numerous interrelationships must be negotiated before any

system proposal can be obtained to improve the city as a whole. The computer

will consider all proposed changes and allow only those changes \^^ich meet

all constraints for a particular grid. In general, this process is expressed

in mathematical form as:

2
n n jn

D = I dm. + Z Z dh. . S.

.

1=1 1= 1 J=l

where

1 - the decision by player j at

S- . = one -zero variable location i is valid

0 - invalid decision

D = Total number of actual decisions made by all individuals at

all grid locations accepted by the computer as valid

drn^^ = Decisions made by algorithms designed into the model for all

grid locations i=l,2...n

dh^j = Decisions made by the players summed across all players at

all locations.

The total number of possible decisions, say TD, will always be TD > D

since conflicting proposals can occur for the same grid or land parcel.

For instance, the social players might propose a park for a particular land

parcel and the economic sector might propose a building on the same site.

The computer would then reject the t\\ro proposals as conflicting and TD > D. One of the objects of the game is to make TD D which iirplies negotiation

and well informed players.

As mentioned earlier, the decision process is constrained by resources

available to the players and to the computer. All games view resources

in two general categories, fixed and liquid. The total resources (TR) of

a particular system can be viewed as the sum of all fixed and liquid

resources in the system. The fixed resources (PR) include water, land,

people, buildings, roads, networks (utilities, transportation, communication,

etc.), capital equipment and the related maintenance items necessary to

keep in operation. In contrast, liquid resources (LR) are those items

which can easily be changed in the short run such as taxes, wages, sales,

social attitudes and the like. The total resources of a system are merely:

n m

TR = I m + Z LR.

p=l P i=l 1

3
where

p = parcels or grid locations and

i = entities of LR

Since player and computer decisions are always constrained by the

total resources available, the uniqueness of the model lies in the method

for relating a wide variety of specific resources to each other in a highly

interactive fashion. To capture the spirit of these interactions, all

mathematical descriptions will take the form of a definition of the resources

to be allocated or the receptors to handle the resource, and an objective

function describing the rationale for the allocation. The receptors are usually balanced by a matching function using supply and demand relations.

For example, if (TR) represents the total resources as described earlier,

realistically every resource available would not be changed in a single

round of the game. This is particularly true for the change in FR. Land

owners may not want to alter all of the property holdings or the government

might be satisfied with prior decisions and not want extensive changes to

the "status quo." To express this idea of partial resource allocation (PR),

as a mathematical function we write

PR = aCP + 3CG + yT + eP

where

PR is the partial resource allocation

CP is private liquid or semi-liquid capital

CG is public liquid or semi- liquid capital

T is available time

P is the sum of all public and private influence

a, 3, Y> £ are components which equate all of the resources to a least

common denominator

4
The objective function for PR is conceived of as balancing the

possible resource allocations such that there is a tendency to jnaximize

the total resource base of the system. This partial resource objective

function (PRO) is expressed as

n

PRO =^ 6 + Z PR.

1 1

where

PRO is the Partial Resource Objective Function

is added to represent those decisions which are made on a seemingly random basis

PR^ is the specific partial resource i

Since the player input equations are normally optimizing or satisfying

a rate of return or benefit ratio from the allocation of a finite set of

resources, it follows that the player objective function is merely:

n

max Z PR. from above.

i=l ^

This objective function represents all players by summing over all PR^s.

Each individual PR. is taken to be of the form:

1

B. - C.

PR. = -i—

i

V.

1

where

PR^ is the partial resource allocation of specific partial

resource i

is the estimated benefit from project i in the form of dollars

earned, service provided, expenditures saved, etc.

is the known expenditures such as current expenditures for

services, etc.

5
is the total value of the project

In all cases there must be some procedure established for choosing

among the many possible projects and this choice may be either the optimizing or satisfying assumptions. Associated with each PR,j is a project cost C^.

There is a limitation of the values of PR^ that will be acceptable and a limitation that the sum of the costs (C^) will not exceed the available

resources as measured in money, time or influence. Note that PR^^^ is indeed

a rate of return.

The computer equations are designed to balance or allocate supply and

demand. The general computer demand equation is

DC = (X

where

DC

X

X

n

Y

y.n

= demand (computer)

is some set of local system demanders such as population groups

businesses, etc.

are descriptors of the demanders such as class for population

units and land use type for business, etc.

is some set of local system decisions such as time allocations

for population units, operation level for business, etc.

are descriptors of the decisions such as parcel location for

population groups, maintenance levels for businesses, etc.

is a quantifier or scale for the units of demand.

In the same manner the computer model equation for supply is written:

sc = e^cw ,Z ) 7 7

6
where

SC supply Ccomputer)

W is some set of local system suppliers such as housing units,

employers, stores, etc.

w

n

are the fixed descriptors of these suppliers in the form of

housing t)T)es, workers per level, design capacity, etc.

Z is some set of local system decisions such as rents and quality

of housing, salar)^ level for employees, prices at stores, etc.

zn

are the descriptors of the decisions such as locations for

residences, businesses and stores, etc.

6

2

is a quantifier or scale for the units of SLipply.

Throughout this manual, these general form equations will be used

to describe the various game parts. General equations are given in

all cases and where necessary specific equations are detailed to clarify

the general equations

.

The reader of this manual is advised to use a Players , Directors

and Operators manual to clarify details which may not be fully explained

in this manual. If the program is used as a reference, slight differences

will occur in the variable names. Some of the symbols used in the main

program are also used in subroutines with different meanings. To protect

the continuity of this manual, duplicate symbols found in the program

have been changed in this manual so that one definition is assigned to

each variable. In all cases the program symbols are used.

7
n. PRIVATE CAPITAL ALLOCATION

In the general equation of partial resource allocation CPR) , the

term CP was introduced and defined as private liquid or semi-liquid

capital. It was further defined that all capital resources would not be

used during a particular game play which in turn led to the partial

resource allocation concept. Assuming this concept to be realistic, it

follows that any consideration of the total money stock available in a round for allocation may be defined as

n

MS = Z (S. + dl. + (aB - dC) .

)

i=l ^ ^

^

where

MS ,V. is the total money stock available in the system for

allocation in a given round

n is the total number of players who have money

• S^ is the available savings on private liquid capital for

player i

dl^ is the present value of the capital investment of

player i

(aB-dC)^ is the net amount of investment capital available after

all costs of borrowing are taken into account for player i

aE is the amount of money borrowed

dC is the present value of the cost of borrowing

A. Choice of Investment

When the cost of making an investment becomes a larger and larger

part of the money supply available, an investor is more apt to rank the net

rates of return for his investment and choose those that will give him a greater rate of return. In terms of probability one might say that the

probability that the net rate of return chosen is the one which gives the

maximum rate of return tends towards one as the available investment money
supply diminishes to zero or the cost of the specific investment chosen

increases to the money supply. Expressed mathematically;

pCN = N IMS -> 0:K. MS) ^ 1 max' ' 1

^

where

p is the probability function

N is the net rate of return on the chosen investments

N is the maximum rate of return

max

MS is the money supply

Y.^ is the total cost of player i's series of investments composed

of the actual cost of the investment and the cost of obtaining

investment information

The probability statement can be further defined if one lets ~

" where N. is the net rate of return for i's investment series, r. is the

1 ' 1 estimated rate of return from i's investment series, and C is the cost of

' 1 using money on i's investment series.

It then follows that N ^ N. and if u is the error bound in

max 1

^ estimating the net rate of return, then - y ^ 0.

Since all liquid capital is assumed to at least earn a rate of return

equal to the current rate of interest, it is assumed that the rational

decision maker, i, would tend to order his investment series so that the

first capital used would be borrowed as long as

(aB - dC)^ < r^

That is, the net amount of investment capital available after all costs

of borrowing are taken into consideration must be less than or equal to

the estimated rate of return in dollars. When it becomes no longer

profitable to borrow, i.e. (aB - dC) 11. > r. , the saving S. and then the

1

present value of invested capital dl . would be considered. The invested

9
capital is only considered when the series of investments from the previous

round (t - 1) yields a greater present value than that of a rearrangement

of the investment series in the present round, which is expressed as

dl. < dl.

\t-l) ^t

B. Types of Investments

Investors might wish to invest for long range potential or to make

quick profits for a single round. In each of these cases, different

objectives and methods for analyzing the investments must be considered.

In the long run, the investor is primarily concerned with the average

rate of return to be expected for each investment. As long as the average

expected value of the investment choice is greater than the cost, investment

will take place „ Decisions in this mode range from ones which consider

any investment that is profitable on the average to more careful choices

which can be ranked from the most to least profitable.

To clarify the above process and relate the process to the conputer,

one must first visualize the various players and then investment process

independent of the computer. An individual player has limited resources

to invest and will not always invest all resources in any given round.

For instance, a player might be saving for a future investment or be

content with his past investments and not want to invest at all during

a current round.

Consider each player who has investment potential on a single parcel,

A player might be from the Economics, Government or Social sectors and

the investment potential will be biased toward the individual player's

point of view. When individual investment is viewed this way, one can reason that the player would consider his investment associated with

some probability of obtaining the benefits as the player visualizes and

some probability that either no investment is made on the parcel or that

a proposed investment will be invalid for violations of zoning or the

10
like. Viewed this way, one can construct a player investment equation

to express the expected value of the net rate of return on all investjnents

for a specific parcel. This can be expressed as:

EN - 2

i=l

where

EN is the expected value of the net rate of return on all investments possible on a particular parcel

n is the number of potential investors for the parcel

is the cost of the investment distributed over time

is the estimated benefit of the ith player to invest on the parcel

is the total value of the investment series to player i

In this context, EN becomes a random variable in terms of the investment potential for a single parcel built upon an individual's probability

assessment summed over all players who have potential to invest in the

particular parcel. This is another way of expressing the thought process

of individual players before submitting their decisions to the computer.

One can further theorize that there is a maximum expectation possible on

a given parcel (EN ) and that EN > 0 for all parcels. The probabilit

max max ~ restrictions inposed by the money stock given earlier as

PCN = N IMS -> 0;K. ^ MS) ^ 1

^ max' ' 1

^

limits the value of EN „ to

max

lim EN

N^ ^max

= EN providing

V > dk V K.1

11
is based on, the concept of marginal analysis where the greatest rate of

return is sought for each land use at a specific location. Again, the

decision possibilities range from situations where any positive rate of

return is acceptable to when choices are carefully selected by ranked

maximum rates of returns. Expressed mathematically, this becomes:

^_ n m B. , - dK- . EN = Z E ^

i=i ri V,

where

EN is the expected value of the rate of return from individual

investments made at the margin for all parcels

ij is the estimated benefit

dK- . is the cost of the investments at all locations distributed

over time

V. . is the total value of the investments at all locations

11 n is the number of potential investors for a particular parcel

m is the number of parcels available for investment

It then follows that EN > EN > 0 then lim EN = EN

max - - - max

providing that

V. . > dK. - V K.

.

iJ - 11 11

Having considered the player investment in detail, one can now

develop this process in terms of the general computer equations. At any

particular time period, the possibility that the net rate of return is

at any point on the long or short continuums can be expressed as

n

N = E N.p. p. = p(N = N ) i-1 1 1 1 i

where

N is the net rate of return on the chosen investment

12
is the probability function

It then follows from the definition of expected value that:

n N = Z d. P. = EN

i=l ^

^

where

d^ is a specific decision by player i

Hence, EN can be viewed as the expectation of a particular parcel

and EN given earlier can be viewed as an estimator for total investment

in a particular round. The computer sinply views the equation:

n m B. . - dK.

.

EN Z E i=l j=l V.

.

as

m. .B - Z^C

- - P=l ^ p=l

EN. = ^ ^

m-i p=lP

=1 P

where

ENj is the expected rate of return for an investment of a given

type

Bp, Cp, Vp as defined before for a particular parcel

m is the number of parcels of a given type

The next chapter deals with the various types of investments available

to the players. It should be noted that when a player makes his investment

decisions, he places these decisions on a coding form for computer processing.

The conputer in turn acts only as an accountant and does not judge the

merits of any investment. If the investment is possible under the particular

game constraints, it will be allowed. The statistics published by the

13
computer for total investments are merely the summation of investments

successfully made during a particular round.

C. Generalized Private Capital Allocation Equation

Private capital is invested in fixed assets through three general

categories residential housing, commercial activities and industrial

plant and equipment. Since each of these categories can be subdivided

in types of land development and no two types of land development can occupy the same parcel of land, we can write the general equation of a particular type of land use summed over all parcels for the whole system.

Thus

m. f B - C

^ p=l I V

P

where

is the expected rate of return for all investments of a particular type j in the whole system

A

Bp is the benefit or income for a particular parcel's land use

Cp is the cost discounted over time for a particular parcel's

land use

Vp is the value of the investment on a particular parcel

. nij is the total number of parcels of a given type of land use investment

This equation then provides the expected rate of return throughout the

system for a particular type of investment. The following is a detailed

analysis of this type of capital investment in terms of the expected

rate of return.

The three general categories of fixed assets are subdivided as follows

14
1. Residential Housing

a) Single Family Dwellijig

b) Di4)lex and Garden i^artments

c) Multiple Units and High Rise y^artments

2. Commercial Activities

a) Personal Goods

b) Personal Services

c) Business Goods

d) Business Services

3. Industrial Plant and Equipment

a) Manufacturing

1) Furniture and Lumber

2) Stone, Clay and Glass

3) Primary Metals

4) Fabricated Metals

5) Non-Electrical Machinery

6) Electrical Machinery

7) Transportation Equipment

8) Food

9) Textiles, Apparel and Leather

10) Paper

11) Chemical, Plastics and Rubber

b) Non-Manufacturing

1) National Services

2) Construction Industry

The balance of this section deals with the development of the equations

for these general categories. The industrial category will be treated

as two categories: Manufacturing and Non-Manufacturing.

In each of the three major categories, we must develop equations

for income, expenditures and value in order to apply EN^.

.

15
D. Residential Housing

The income for a given residential property is the product of the

amount of space used and the rent per space unit for the property.

This is expressed as

B = R • S

P P P

where

Rp is the rent per space unit

Sp is the number of space units occupied

Let

where

S = Z T • K

P c Pc ^

T is the number of population units of class c on property

c

K is a conversion factor for the class

c

Since we are summing over all available classes, i.e., high, middle and

low income classes in each parcel of land, S may be substituted into the

^ P

equation = R^ * S^. When this substitution is made, you get:

B = R (Z T • K ) P P c Pc ^

And summing over all parcels we get total income

m. /V m. E^B = Z^R (Z T • K ) p=l ^ p=l ^ ^c

The expenditures for a property (C^) are found by summing for each

property the utility, tax, maintenance and water costs. This can be

expressed for a single parcel as:

16
c = iir + TX +Mr +m'R

p p p p P

where

UTp is the parcel utility expenditure

TXp is the total parcel tax expenditure

MT is the maintenance cost

P

is the water cost

TXp, the total parcel tax expenditure, is the sum of three taxes: property,

income and sales taxes.

The residence's maintenance expenditure is the sum o£ its expenditures

for personal goods and personal services. The number of consumption

units required for maintenance is a function of the total percent depreciation,

the level of the residence, and the number of PG and PS units required

for each percent depreciation. Total percent depreciation is the sum of

normal depreciation and depreciation due to other factors. = D^^ + Dq.

T)-^ is obtained from the Master Tables,"^ and Dq is due to over use and

abuse of the residence o This is usually provided on the residence output.

Note that the Master Table also provides the amount of PG and PS units

required for each 1% of total residence depreciation. Let Mp^ and Mpg

be the amount required for each percent depreciation. Thus with a level

of residence at three, the amount PG and PS units required are:

^T

* ^G * in PG units of consumption

* Mpg * 3 in PS units of consumption

The price that the residence owner pays depends on where he purchases PG

and PS and this is obtained from the Commercial Detail Output.

Since we are interested in the cost for all parcels, C^ is merely

summed over all parcels to get:

1

RMB Economic Sector Manual P. 129,

17
m. m.

= CUT + TX + MI + WTR )

Finally we must calculate the value (Vp) to complete Nj . The value

of a property is the sum of the value of the land occupied and the value

of the structure,,

The value of the occupied land depends on the level of development

of the three types of residential development. The term levels refers

to level of development and not the condition of the structure. It is

important to remind ourselves that when we refer to a level 1 (e.g., RBI or a duplex type of dwelling at one level of development) we are in

aggregate terms and for this example we are really talking of a type

of housing which provides dwellings for six to twelve thousand people

distributed throughout the parcel or square mile. In other words we are not talking about a single duplex building but instead we are referring

to a large group of buildings aggregated by type. Since no two types

could occupy the same parcel even among housing, we cannot have a RA and

RB type in the same parcel. In addition, since we know that each of the

three types of housing only occupies two percent of the land at a level

one development, we may develop each type to a maximum of level fifty

which would occupy one hundred percent of the land. A RB developed to a level of fifty would provide housing for fifty times the population

density of 300,000 to 600,000 persons, llius the product of level development, the space required for each type of housing and the unit market

value of the land on the parcel is the value of the occupied land. This

value of occupied land can be expressed as

p ^1 p

where

LND

P

is the value of the occupied land on parcel p

is the number of levels of property development

is space in units of percentage of the unit value of land

required for a single level of development of type h (h = RA, RB

where RA, RB, RC refer to the types of single, duplex or multipl

dwellings

18
U is the uQit value of land at parcel p (e.g., LND for an P 2 , P

RB3 = 3

• ^ • 635,000 ^ $38,100)

The structure value for a given property is the original cost of a

level of the structure [type specified) times the value ratio times the

number of levels on the parcel „ The structure value may be expressed

as

BLDG = L • 0, • VR

p p h p

where

BLDGp is the structure value of parcel p

is the number of levels of property development

Oj^ is the original cost of a level one development of a structure of type h

VRp is the value ratio of building on parcel p

As earlier stated, V^ for a particular parcel is equal to the sum

of the value of land and buildings or

V = LM3 + BLDG

P P P

V = L •a'U + L '0, "VR

P P n p p h I

V = L (S, • U + 0. • VR ) p p

^ n p h p'^

Summing over all parcels of land we have

m. m- V = L (S, • U + 0, • UR ) p=l P p=l P h p^

Finally substituting into we have:

19
N.

m. m- R T • K )

- 1^ (UI + TX + MT + WTR

p=l P c Pc ^ p=l P P P P

p=l p h

E. Commercial

The income for any commercial establishment is sinply the product

of the number of units sold and the price per unit or:

B = US • P

P P P

where

US is the units sold

is the price per unit

As before, summing over all parcels results in:

m . ^ m

.

B = Z-^ US • P

p=l P p=l P P

The expenditures for a given commercial property are simply the sum

of the utility, tax, maintenance, water, salary, transportation, and

goods and service costs. This is written as:

cpppp = ur + TX + Kr + wiRPPPP +sl +tr +gs

where

C , UT , TX , NTT and WTR are defined as before

P P P P P

SL are salaries paid

P

^

TRp are transportaiton costs

. GS is the cost of goods and services

p

s

It is important to note that the price is set by the seller or owner

of the commercial plant. The buyer who requests the number of units he

20
needs is granted the units if the seller can supply thejn. The conimercial

establishment is either business cojiunercial (BG and BS) or personal commercial

(PG and PS) . BG and BS purchase their needed supplies from the outside

systems whereas PG and PS purchase their supplies from the local BG and

BS establishments. The customers of BG and BS are either private (i-®., PG,

PS and Industrial establishments) or public (i.e.. Municipal Services Highway

Department, etc^),

BG and BS spend money for service charges, GS^, which represent the

purchases from the outside system. On the other hand PG and PS spend

money for business goods and business services whigh are together referred

to as GS c This GS is the sum of goods and services that are required

p p

s ^ for the PG and PS to operate. In both cases for BG, BS and PG, PS,

GSp is directly related to the number of capacity units sold. Hence the

model assums that the commercial establishments only purchase as much as is required for them to produce the number of capacity units sold. This

relationship is found in the Master Table for commercial business. The

production of 1 CU (capacity unit) of PG requires the purchase of o037 CU

of BG and .017 CU of BS.

Transportation costs incurred by commercial business are dependent

upon the number of capacity units purchased, the type of buyer and seller,

the distance travelled to the destination and the type of roads used.

Regardless of the distance travelled, a business pays a base cost to

travel to a destination. Thus the total transportation cost can be

expressed as follows.

TRp = (CU^ • BTC) + {CUp • BTC • L • [(4 * NT^) - RT^]

}

where

CUp is the number of capacity units consumed

BTC is the base transportation cost per unit consumed

thus (CUp • BTC) is the base transportation cost to business

and L is the length of a parcel side in miles for this model

Nip is the number of parcel sides travelled along the least cost

route between origin and destination

21
RTp is the sum of the road types traversed along the least cost

route

BTC is the transportation cost per unit per mile travelled and it

is numericaHy the same as BTC

hence [(4 * NT ) - RT J is the weighted sum of parcel sides travelled

P P

from origin to destination along least cost route. The parcel

sides or roads are weighted according to the road quality; the

best road being of type 3 and the worst being of type 1. Thus

four parcel sides of type 2 produce a weighted sum of (16 - 8)

8 parcel units. Hence if each parcel side is 1 mile long, then

the weighted distance travelled is 8 mile units and the cost

with a ETC of $400 per mile per unit for 3000 units is

TRp = (3000 * 400) + {3000 * 400 * 8} = $10,800,000

Note BTC and BTC are obtained from the Commercial Master Table.

Again summing over all parcels of land you have:

m. m.

C = (in + TX + MT + WTR + SL + TR + GS ) p=l P p=l P P P P P P P

Finally the value of the property is calculated in the same manner

as housing or

V = L (S, * U + 0, « VR ) p p p h p^

or summed over all parcels

m. m- V = L (S, • U + 0, • VR ) p=l P p=i P'^ P h p^

Substituting the values of B^, C^ and into the general formula

for EN- we have for commercial investment:

22
EN

m. jnI? US • P - (m + TX + NTT + WTR + SL + TR + GS ) N - P=l P P P-1 P P P P P P P

^f^^ ^Cs^ • Up ^ °h " ^p^

F. Industrial

The income for a given industrial property is the product of the

price per unit (industry specific) and the number of units produced on

the properties. This is defined as:

B = P • UP

p m p

where

P^ is the industry specific price

UPp is the number of units produced

UPp for all industrial property is at a maximum of 1000 units per level,

The actual number produced depends on the employment effect and the

value ratio of the property.

Thus

UP = EE 'VR

P P P

where

EE is the enployment effect

and

VR is the value ratio of the property , i.e., 90/100 or .9

The value ratio is determined by the amount of depreciation that

occurred during a given round but it is limited by the level at which

maintenance is seto So that if the maintenance level is set at 70^ then

the value ratio cannot fall below this level of 70*^. In fact, maintenance

is automatically done each year to keep the property at this value ratio.

The employment effect, EE, is the product of the maximum employment

effect, 1000, and the fraction of the total number of eirployees hired to

23
the total number of enployees required.

EE ^ EE^,^ • EH/ER

max ^

where

EE are the maximum employment effect

max ^ ^

\ -HI are the employees hired

ER are the employees required

P^, the price per unit of industrial product is determined by the

national business cycle price relative and this normal price per unit

for the industrial type.

Thus

P = NBCPR • NP

m m

NBCPR is the national business cycle price relative which is generated

by the outside system i.e., the computer. Its range is .90

to 1.12, In each round, the current NBCPR is printed under

the Transactions with the National Economy.

NP^ is normal price per unit of the industrial type sold and is

obtained from the Master Table for Industrial Establishments

for each type.

Summing over all industries properties of a type:

m. /s m.

^, p ^, P • UP = P UP

p=l ^ p=l m p m p

The expenditures for an industrial property are the same set as those

for commercial properties 0-^^, TX^, MIp, NIR^, TR^, SL^, GS^) plus terminal

usage costs (TM^) and expenses connected with pollution control (PTN^)

.

As before the expenditures are found by summing these values for each parcel

and then summing for all parcels to get:

24
m. m.

C = (UT + TX + MT + WTR + TR + SL + GS + TM + PTN ) p=l P p=l P P P P P P P P P

The value of industrial property is the same formula as for commercial

property, namely:

m. m. V = L rs, • U + 0, • VR ) p=l P p=i P'^ P

h P'

Substituting these values into EN. we have:

m. m. Pm UP - Z^ (UT + TX + MT + WTR + TR + SL + GS + TM + PTN ) n=i P n=l P P P P P P P P P

EN. = H-J: 2-!;

v\ • Up ^ ^

• p=l

25
III. goverjnment capital

The main objective for the government is to maximize total benefits

to the system by the allocation of funds among the various departments.

Before we can consider an allocation scheme, we must first define the

sources of income available to a governmental jurisdiction in the game.

The government income is derived from property taxes , income taxes , sales

taxes, auto expenditure taxes, bonds [2 year short-run and 25 year long-run),

charges for services and transfers of funds, i.e., fines, bribes, etc.. It

should be noted that aid from state and federal sources are not treated

as income but rather as a reduction in the cost of the local projects

they support.

Having considered the sources of income, we can now express the supply

of allocatable funds for a jurisdiction (MG^) as:

4

MG. = E (TX.) . + B. + C. + TR.

1 i=l 1 J J J J

where

4

i-1 1 J 12 3 4

and

TX-^ are property taxes

^2 are income taxes

are sales taxes

TX4 are auto expenditure taxes

B.

J are bonds (long and short)

C.

3 are charges for services

TR- are transfers from all other sources including the outside

system

26
A. Government Decision Objectives

The main objective for the government is to maximize total benefits

to the system through the allocation of funds among the various departments

If one considers the money supply available for each jurisdiction (MG^), a limit is obviously placed on the supply of money available for distribution

Each governmental department places a demand on this supply which suggests

a balanced budget to be one where supply equals demand. To quantify this

idea, consider for each department, or r^ which is the ratio of demand to

supply for services provided by department d, or:

is the demand for departmental services

is the supply of services by department d

Since these services are directly related to the money available,

one can talk about services as well as money. For instance, to reduce

the student -teacher ratio you must either build a new school or hire more

teachers since its not realistic to reduce the pupils unless there is

heavy out migration. Both of these solutions reduce taxable income which

directly relates services available to money available for services in

each governmental department.

The objective for each department is to bring r^ to 1.00 from either

side for a balanced budget. If r^ > 1.00, then > and there is not

a sufficient supply of services from department d. Conversely, if

< 1,00 then < and the supply of services from department d is

in excess of the demand for those services and a wasteful condition exists.

If one now assumes that the overall government ratio is a function

of all department ratios, then it is possible to determine an overall

set of Ar^ based or estimated changes in supply and demand, Ard, which

will bring the overall government ratio to 1.00. In other words, the

where

27
total demand for govemment services and the supply of all government

services are balanced.

be the overall govemment ratio and

n

n

d=l

^

where

, r^ is a departmental ratio

is a weighing factor

In this case, = 1<,00 when all r^ =1.00, or when tradeoffs (as

determined by the w^ ) balance. When R^ > 1.00, the total demand for

services exceeds the supply and when R^ < 1.00, the supply exceeds the

demand and a wasteful condition exists.

Hence the objective function is to bring R^ as close as possible

to 1,00 with the constraints of a finite amount of allocatable funds

MG^ and that all individual departments meet as much of their estimated

demands without exceeding the amount of money required to finance their

decisions.

B. Departmental Ratios

1. The rati

supply and demand as

1. The ratio for education (I^^^) can be expressed in terms of

n

I sc

E P • SP

D T c c sc c=l

S m

sc

Z SC * VR • T

p=l P P P

28
is the population by class

are the students by class

is the school facility by parcels

is the value ratio

is the capacity as a ftmction of teacher mix

The ratio for adult education (I^) can be expressed as n m

^ Z Z EF

T = -i^= c=l p=l

^

AE c^AE^ Z Ph + Pm

p=l P P

is the time allocated to free- adult education .by parcel- and

class

are the PH's hired

are the PM's hired

The ratio for municipal services fl ) is ^ ^ ms'^

m

Z LU ° L • MU

D -1 P P ms _ p=l ^ ^

Ims

S„ m

Z MS " VR * T

p=l P P

is the land use

is the number of levels on property

29
is the MS units demanded per level of land use

is the number of facilities per parcel

is the value ratio per parcel

is capacity as a function of worker mix

The ratio for welfare payments (Jy^ is:

J _ Actual _WL_ payments

WL Desired or estimated WL payments

The ratio for utilities (I^jp) is

. m

E LU * L • UU

T ^

p=l P P ur e

E ur • DZ

p=l P

equals UT units demanded per level of land

is the utility of a plant facility on a parcel

is the optimal operational capacity of a utility plant

is the land use

is the number of levels of development on property

The ratio for transportation (I-pj^) is:

n m n

(a3Y) E PW- + E (PS. + L.)

= _IR = i=l ^ p=l 1=1 P

TR

30
where

a

is the average travel tiine

ft is the aveTac^e cost

Y IS 1"hp avpT?^pp 1 Tironvpni PTicp

is a measure of the mean ecological distance

PW. are workers

PS.

1 are shops

L.

1

is the inter-business transport

P is parcel

LRC is the lowest real cost. This cost is at a minimum when

a = 3 = Bp and Y

= 0

C. Budget Allocation

The total budget to be allocated to each department must be the entire

supply in order to avoid wastefullness . This decision format for allocation

can be expressed as

n

MG. ^ max Z (IG + ? + P.)

J 1=1 ^

^

where

IG^ are the specific services indexes for each department

^ is a random factor for deciding expenditures

P^ is the sum of all public and private influence which affect

allocation decisions

Since the objective is clearly to spend all available funds, i.e.,

IG^ > 1, the tendency will be to allocate the government capital resources

to departments with the highest ratios. This is the reason for optimizing

with a maximum.

31
IVo TIME ALLOCATION

The social sector directly influences and controls the government

through its voting power and the economic sector through its ability to

boycott. In addition, it has the ability to allocate the leisure time

of small aggregates of workers which produce coiiplex interactive effects

throughout the entire model. Leisure time is that time not spent in

full-time work, eating, sleeping and personal care. It is divided into

100 units which can be allocated to part-time work, adult education,

political activity or recreation. In addition, the time used to travel

to and from work is subtracted from the leisure time. A further reduction

of leisure time occurs due to sickness as a result of the high health

index at a workers resident location. With this in mind we would describe

the total amount of allocatable time, T, as:

T = Tu • bPk

where

T is the total amount of real time units of leisure time used

in the entire system

Tu is the specific amount of time per unit

bPk is the total number of people in the system by socio-economic

class weighted by the real value of their time units (b)

In theory, this model is sufficient, but in practice it takes into

account such detail that the model would become extremely conplicated.

32
To avoid this difficulty, define the real time available as:

T = CT^, + T^)bPK

where

Tj^ is the fixed amount of time that is more or less available

and falls outside short-run discretionary allocations

is the amount of real time actually available to be allocated

in the short- run

A. Allocations

Let Tj^ be defined as before and

T = T + T + T

T I

where

Tj is the time spent in traveling to work

is time lost to illness

Tj is time spent in involuntary activities

Using the above definitions, can then be considered as resource

improving uses of time which can be controlled as time allocations.

Let

33
where

w

T

AF

PA

X

R

is time spent in a part-time job

is time spent in paid training and education programs

is time spent in free training and education programs provided

by the local school system

is time spent in political activities

is time spent in recreational pursuits

Associated with each of the pursuits in is a rate of return for

the time invested given by:

1.

where

w

SAL

r + Yi w ' ]

SAL

N

is the rate of return from part-time work

is the full-time salary offered to the class c

is the relative value of part-time work to class c

is a function designed to make the absolute value of rw

relative to other time pursuits for comparison and is defined

as

m

E P

m

Z JOB

IND.

c=l

where

is the population units by class wishing to allocate time

units to part-time jobs

34
JOB

Pt

IND.

2.

where

AEL

c

^2

where

P

FAE.

1

IND.

3.

where

are part-time jobs offered by all ejnployees for a class

(of class M 5 L)

is an indeterminate quantity such as propensity, likes,

dislikes, etc.

YAF^ = Y2^^^^c^

is the rate of return for free training and adult education

is the change in education level for class c

is a function designed to make the absolute value of

relative to other time pursuits for comparison and is

defined as

m

= f<

Z P

•=i ML.

2Jl i, IND)

n

Z FAE.

i=l

'

is the number of population units wanting to allocate time

to free training and education

is the supply of free education and training programs provided

by the local school systems

is an indeterminate quantity such as prosperity, likes,

dislikes, etc.

yAP^ = y^ CAEL^ - PR^)

is the rate of return for paid training and education

35
AEL^ is the change in educational level for class c

PR^ is the cost of spending one-time ujiit in private education

and training

is a function designed to make the absolute value of r^^

relative to other time pursuits for comparison and is

defined as

Y3 fcc^, im.)

where

C

AE

IND.

is the cost of private training and education

is an indeterminate quantity such as propensity, likes,

dislikes, etc«

4.

where •

rPC

AVT

Y4

is the rate of return for political activities

is the increase in voter registration for class c

is a function designed to make the absolute value of rp^

relative to other time pursuits for comparison and is defined

as :

•

where

rP

P

IND„

Y4 = f(rPp,IND.)

is the expected return fromi political power

is an indeterminate quantity such as propensity, likes,

dislikes, etc.

5.

36
where

APS,

Yc

where

RT.

PLA.

IND.

is the rate of return for recreational activities

is the decrease in personal dissatisfaction due to recreation

for class c

is a function designed to make the absolute value of yR^ relative

to other time pursuits for comparison and is defined as: r

Y. = f

m

Z P

. RT.

IND)

n

E PLA.

i-^1

'

is the number of population units wanting to allocate

recreational time

is the supply of park land and other recreational facilities

usually provided by the planning and zoning department

is an indeterminate quantity

B. Decision to Invest Time

Let T be the pursuit one choses to invest time in. given some return

rate from T„ Then:

T = T

w

T = T

AP

T =

T =

T

AF

T,

T = T.R

if r > T.j^^f r.-np> T w APC 'APC RC

^APC - ^w' ^AFC ^PC ^RC

^AFC - ^APC ^PC ^RC

- ^w' ^APC ^AFC» ^RC

^RC - ^w' ^APC ^AFC» ^RC

Further, if r is the return rate from. T and B is a benefit from all

time allocatable investments, then:

37
where :; j' .".

\ • V':--; r

- .'^i^ ^w' ^F' '^P' ^k^

An investor in allocatable time will tend towards majximizing B by

finding the best mix of time investments according to:

max B = max I r.Ti-1 ^ ^ :

38
V. PUBLIC AND PRIVATE INFLUENCE

Public and private influence is by far the most difficult to capture

in quaatitative form. It is desirable to include this so called "power"

into the game since voting, economic suasion, and influence peddling in

the form of bribes and boycotts are all part of a real city. For the

purposes of the game, this quantity must be in the standard form of

supply and demand recognizing that government officials vote on issues

and private sector members vote for government officials. This dual role

can be readily seen to apply in the ecoj omic and influence roles as well.

It is within this dual functional idea, that this model is built. One

could for instance, claim that public influence is related to legal

cases it wins, the percentage of expenditures for influencing voter groups

and commercial enterprises and the moral suasion of the incumbents.

On the other hand, private power can also take a large number of forms.

We could include voting power, lobbying, migration, bribes and numerous

other influences such as protests that influence government decisions.

The ratios for economic power were described in Chapters II and III

and have the built-in bias of determination for public and private goals.

It is therefore convenient to express total power as

n

P = E P . + P . i=l

where

P is the total power in the system at a particular point in

time

Pp^ is the private power, both social and economic for all

individuals

is the public power for all individuals

To develop this particular model, we must develop equations for

voting, a scheme for allocating power and a supply and demand ratio in

39
tenns of money to measure this influence so that it will he compatible

with other functions of the partial resource allocation defined earlier

as

;

• PR ^ aCP + 3CG + 6T + eP

In other words, e must be defined explictly as well as P.

A. Voting

Voting can be described as

m n

POP = 1 X, Z R C

k=l 1=1 1

where '

.

- P '

,

POP^ is the total number of people who vote

Xy. is the propensity of each class to vote

Pj^ is the number of people who actually vote

i

C is a random factor

Since the above equation is difficult to use in its present form,

we can consider the probability that a voter will vote for a particular

candidate or issue. IVhen this is done, P-j^ then becomes:

n

1=1

where

i is an individual member of a class

6^ , is the propensity of that individual to vote

is the probability that i will vote

In other words, given the inclination to vote (6^), there is a probability that he will vote (p^^) •

40
The aboye statements can be further described as when i is an individual, then Vi3 and 0 < < 1. Now if we let be the probability

that a vote will be cast for an alternative j on an issue, then 0 < g. < 1.

]Vhen this is true, ^(p^gj^) becomes the probabilit)^ that i will vote for

i in class k and POP then becomes

V

m

[POP ) . = CZ A. k-1 ^

n

1=1 k

and finally for all issues we have

m

Z (POP ) m m

= E CE X, n

Z (6.p.g.)

. , ^ 1^1 1-^ 1=1

Based on the above equation, one can now define C, given as a random

factor, as influence or the abstract quantity that sway voters by emotional

or financial means at the last minute on issues and intended voting

desires

.

B. Allocation of Power

The objective sought in influencing is to allocate that maximum amount

of influence in the public and private sectors. This allocation can be

expressed as

n

P - max Z P + P

i-1 Pi ^i

subject to:

It is not reasonable to assume that a democratic government can exist without some influence from both the government and private sectors,

41
Based on the assumption that power exists in both sectors, one can then

look at the distribution of this power between the sectors and the

incremental cost associated to change this power ratio. With public and

private power always in existance, we must consider incremental changes

ill costs for this ratio. If influence is viewed in purely capitalistic

terms, there will always be a supply and demand for influence. In this

format, one can now refer to ratio's in the same manner as the government

ratio's of Chapter III.

Let $ be defined as the incremental cost to change the ratio

P

r when

P

D . . , p S ^ P

in terms of supply and demand.

D D

Now if r = we can solve for S and find that Sp = -2- . The

p S p ^ r

^ P^ P

change in required to meet new conditions will become:

D' D

AS = S' - S = —E. . -£

P P P ^ P P

when S' , r' and D' are the new conditions.

P' P P

Rearranging the terms in AS^:

D' r - D r' AS = ^ ^ P—

P r' rp p

and noting that

/\p = j-i „ X or r' = r + Ar

p p p P P P

AD = D' - D or D' = D + AD

p p p p P P

42
we can substitute these values into AS^ atid get;

T CD + AD ) - D + Ar ) AS = P P P V 2 E

P

r [r + Ar ) P P

Expanding

rD +rAD -rD +DAr

AS = PP PP PP PP

r + r Ar

P P P

Collecting terms

r AD' + D Ar

AS = P P P P

P 2 r + r Ar

P P P

Since the cost per unit of supply is known for each sector and is

C , then the incremental cost to change the ratio becomes: p7 O

r AD C + D Ar C

$ = C AS = P P P P P P

P P P 2 r" + r Ar

P P P

This latter equation might be viewed as the incremental cost to change

the power base.

C. Power Objective

The power base can now be defined as:

P = V + E + IN

P

where

V are votes

is the economic power

43
IN is influence

This equation may be re-written as m

P = $ 2 CPOP^) • + E + 11^

where

IN is defined in terms of jnoney persuation and the first term

is the incremental cost of swaying elections.

44 ^'
VI. OPERATION OF TliE MODEL

The previous chapter related to the development of the partial

resource allocation for the general system. In the game, the variables

for the fixed and liquid resources must be related to each other to

integrate all city functions. This process is accomplished through a series of operating programs plus the decision choices of the actual

players. The section's of this chapter will describe the major operating

programs and the calculations they perform,

A. Business Goods and Services

lo The total demand for business goods and business sewices is

given by:

n TL TD. , = 2 la.LU. + C PG + B PS + E Z£. (DEP. + MT. - VR.) + G

(BS/BG) 1 X pg s ps s ^^-j^ 1^ 1 1 1^

where

TD^p^,^g^-^ is the total demand for business goods and services

LU^ is the land use at a particular site i

PG are sales of personal goods

PS are sales of personal services

are the number of levels at location i

KX- ,C ,B ,Zi. are constants

pg' ps' 1

2: The supply in the commercial sector is dependent upon level,

employment and value ratio given by:

m

TS = DC I L.VR. (1-

^

-)

i-1 ^ ^ E"

45
\\rhere " -

' ' ^

' ^ :

TS is the total supply V'-

DC is design capacity bA' -^

; ^

•

are the number of levels at location i

VR^ is the value ratio at i

is the nimiber ,o£ employees at i by class k

i is the total of employees needed at that location

3. Price is a function of the total demand and total supply

curves and is given by: . , , y • .f/i (t-1) y

p X ^ . . . , ..... n

where

P is the average price paid last year

'

is the price of goods or service for the last round (t-1)

n is the number of i goods or i services rendered last round

4. The new prices for goods or services are dependent on the

change in demand and the change in supply for the next round.

This may be expressed as: ,

.

•

P = R

APo - APs

where

P is the new price for goods or services

APo is the change in price if supply is kept constant

46
APs is the change in price if dejnand is kept constant

R is a functional miltiplier

p" is the average price paid last year

B. Enployment

The enployment process matches the people who are looking for jobs

with the employers who are trying to obtain workers for needed skill

levels

.

1. Demand for Jobs

Tlie demand for jobs is a function of the amount of new industry

in the system, the expansion of government services, the displacement of

workers from firms going out of business or site location changes of

existing firms. In the game, the demand is also caused by jobs not

filled from the previous round.

This demand for jobs is:

is the total demand for jobs by each income class

is the amount of new industry constructed during the previous

time period

are the new government positions

are jobs created due to employee displacement

are job openings from the preA^ious round.

Supply of Workers

The supply of workers is given by:

where

J

^k

2.

47
where

P^^ is the total worker supply by socio -econojnic class

P^j^ are workers who desire to move by skill category

' , P^ are new residents in the system

PLj^ are people who have moved in the system or have otherwise

vacated their original jobs

^xk ^^^^ remaining imemployed persons

.. . 3, Matching

The process of matching the supply and demand for workers

is accomplished by locating workers by skill and educational level to

fill the demand,whereas the workers are interested in obtaining positions

which majcimize that income and/or achieve their satisfying objectives.

To accomplish this matching process, the supply (P--. ) is ranked by

educational level, the most skilled first in the form:

P-T majc(S , + KS - T ,) jkp ^ epk ep epp'

if . . m m

. Z P. > E k=l k=l ^

then

P = max [S , T

. + KS , n ^^

- ^ tl jkp ^ ep'(k-l) ep' (k-1) epp'J

where

P^^ is the supply of jobs by parcel and class

"^ep'k

"^^ ^^^^ salary offered on parcel position

48
Tgpp, is the transportation cost to travel from home to work

K is the percent change in job attractiveness to entice worker

to change positions, i.e., salary, etCo

This process continues for each class until

matched with are employed

matched with J-j^.-j^ are unemployed

P-|^ not matched are unemployed

4, Part-Time Enployment

Part-time jobs must be matched against workers who desire

part-time work. The matching is performed in the same manner as for

full-time work, namely:

n

SPT, = E Te. Z

where

m

Z = Z R

k=l ^

and

SPTj^ is the supply of part-time jobs by parcel

Te^^ is the transportation cost per individual

Z is the sum of available jobs by parcel

5. Salaries

The salary that can be offered at a given location varies

with transportation costs, unemployment and salaries offered at other

locations. Salary may be computed according to the formula:

49
where

m

S = Z S.E.

l E. U

1(1) =

m

Z T.

m n

Z E T. T = tlJ=L

m

Z E.

3

and upon substitution

S(}) = m

Z S.E.

m

Z E.-n

J 3-1

n /m n

Z T. / Z Z T

i=l ^/j=l i=l

m

S(}) =

IPZ S.E.

J 3

r- Z E,

±1 3

Z E.

.1=1 '

n m

Z T. Z E.

x=l " j = 1

J m n

Z, Z Z T. . i=l

ni m n

BZ, Z E. Z S. Z T.

1^,1 Z T- .

' J=i 1=1 '

/50
where

jn n

B Z E-S. I T- 1 ^ i-1

^ m n

Z Z Z T. .

S.(j) are the total salaries

E^- are tlic number of employees at j

is the salary per worker at j

is the transportation cost for work i

Z-j, is the total labor force by class

B is the coefficient of unemployment

C. Land Use

in the previous section concerning the allocation of private capital

sources, we assumed that an allocation could be made for a particular

land use type. In general, if L^^j is the cost of locating a specific

land use in a particular location, then:

n

Land Costs - Z min L- - i=l

subject to:

Formal Zoning

Presenc of Utilities

Topographical Features

and

Y > B + D + LC d - c

51
where

Yj is the discounted income '-• •

B is the structure cost

cD is the demolition condition '

LC is the land cost

One can further require that

MS, > B + D + LC

L - c

and

G

= 7 . V -^-^

where

MSjj^ is the money supply available for land

is a constant gross income per land use

Within this framework a model for specific land uses can be developed.

1. Residential

Residential land use can be modeled as

n

Lj. - Z min L. . = aTEI. + a^LC. + a^T. R-T ij li 2i 3i 1=1

where

EI^ is an environmental index for a parcel

LC^ is the parcel land cost

is the average transportation cost

a-j^ "^2 "^3 coefficients to relate the variables to each other

52-
2. Industrial

Industrial land use is:

n

where

and

I i=l 1

^

A = 32LC. . 33CH. . 34T. . 33W, . 3,MS.

is the average transportation cost

LC^ is the parcel land cost

CH^ are the utility charges

Tj, are the taxes

are the water charges

MS^ are the municipal service charges

3^ are coefficients to relate the variables to each other

3. Commercial

The commercial land use model is

where

n

L - E min L. . =y .A. + y oB. c ^^-^ ij ' 1 1 ' 2 1

A- is the same as industrial n

B. = max T. C. . 1 i=l

53
is the best relative con^etative advantage for a new location

given all existing land uses

are coefficients to relate the variables to each other

4* " Government Facilities

- .': n m

^

-

' Lg - ina:x: B = Z EN..

' i=l 3=1

given:

The existing govenunent land uses (Lg^^)

Location of all other land uses (LU^)

Location of all people by class (P^j^)

^ij are any government services to be located in a specific

jurisdiction

D. Land Value

Land value is a function of the proximity of the particular parcel

of land to various facilities and the presence of certain amenities. In

equation form this becomes

LV = BV + e^T^ + + z^E + Z + e^T^

where

LY is the land value of a particular parcel

BV is the base value which is usually the agricultural value

or approximating the construction value

or

3.

54
T

i is the distance to the nearest terminal

R is the distance to the nearest residence

E is the distance to the nearest employment opportunity

Z is the presence of zoning by type

T is road access by type of road

E. Rent

The rent for a particular dwelling can be calculated according to

the following formula:

where

BQiA /yEI

n

X R.S.

i^l ^

^ R =

QI =

EI =

n

Z S.

i=l ^

n

E QIn

n

Z EIi=l

^

n

55
and

n

E S.

1=1 ^ c n

I Z i=l ^

K is

R. is

1

Qo -1

OT^ 1

bi - IS

1

Qi is

EI is

is

z. is

1

is

EI^ is

F, Location of a Coinmercial Site

In order to locate any non-residential income producing property,

one must consider:

1, Cost-distance to the nearest terminal

2. Cost-distance to suppliers of goods and services

3. Cost of treating water

4, Suitability of site for development which includes zoning,

utilities and space. ,

56
To construct this model, jnatrices must be constructed whose cells

reflect the status of each site,, Let the matrix T contain for each cell

the cost-distance from each parcel to the nearest terminal o If the parcel

is suitable, enter the value, otherwise the cell has a value of 0. Construct

a matrix S such that each cell contains the cost, price and transportation

cost from the nearest supplier of goods and services. If the cost value

is suitable, enter this value in the cell, otherwise enter Oo In a similar

fashion construct W and X where each suitable cell in W contains the water

costs (or 0 if unsuitable) and each cell in X contains the taxes on the

property (or 0 if unsuited)

o

Combining these matrixes

K=T + S + W + X

and . is the total cost associated with each cell i

.

Let i represent a cell where the products of the activity which we are locating are consumedo For each i, there exist the following known

quantities

C^ the current cost per unit of transporting goods from point

of sale

the number of units consumed by i

Now for any potential site j, (K^ > 0) calculate W^^ which is the

cost per unit of transporting goods and/or services from point of sale j

to consumer i. The sale for j is given by:

n

s. = z u,

J k=l ^

\^^ere

W-11< C- and n is the nimaber of cases where W- • < C.

ij 1-

The gross income is

57
n

I . = P

* S . - P Z U

k=l

and profit by

n

Finally calculate 0^ for all j where > 0 and the site selected, S is

given by:

Go Migration

People move in and out of the urban systems on the bases of

opportunities available to them. They move within the urban system

or ultimately out of the area on the basis of the ability of the local

system to satisfy given needs. One measure of population movement is

the net population change of the urban system. This change can be

represented as: /

S = j3 <p. is maximum

AP^ = NG^ + IN^ - OUT,T

where

is the total population change in a specific time period

is the natural change (births - deaths)

is in -migration

is out-migration

Further

,

n

kCT-1)

or NG^ = E K R

Vk(t-l)

58
where the natural growth rate is a function of the total population

segregated by socio-economic class.

n

where in-migration is largely a function of the number of jobs available

in the system in the previous time period for each socio-economic class.

K~-L

where

n n m = :i: aP, . + i n.R.

1=1 1=1

and

MV is the number of people who migrate

MS are movers who stay within the local system

ciPy.^ is the percent of the population by socio-economic class

are people who are displaced by the razing of residences

is a random number of people who move

aU^j^ is the percent of under employed

3U , is the percent of unemployed

r K

MS can be further described as:

n

MS = EI - E EI. > 0

max 1

where

Elj^g^ is the maximum available environmental index available to

residences

59
EI. is the present environmental index for a particular parcel

or

EI = PI + + cRQ + dMS + eSc + gTx

where

EI is the environmental index

PI is the water pollution index

is the rent

cRQ is the residence quality

dMS are movers who stay within the local system

eSc arc the residential services

gTx is the tax rate or welfare level

H. School Assignments

The school model considers the needs of the various socio-economic

classes and conpares these needs to the service levels of the schools.

When there is more service available than the local district needs, the

model parallels the concept of excess capacity in the plant or factory.

Conversely, when there is not enough capacity in the public system, the

shortages are assigned to the private sector, i.e., private education.

The process of school assignments or establishing school districts

can be done in terms of supply and demand. In this light, several objective

functions are possible such as minimizing cost, maximizing service along

with containment within political boundaries, neighborhood boundaries

and so forth„ The sinplist way to model is based on school districts.

Let D be the total student demand by socio-economic class on all school

s

^ districts then:

n

= E a R

k=l ksd

60
where

a is the nmnber of students per population class

pksd is the population by class by school district

Since the obiective is to let P = S where S are the total services

s s s that meet the total demaQd, we must consider the effective supply of each

school within a district and the demand on that school. In other words

Dj^/Kj^ < 1 when K^^ = n and D-^ is the demand on school L and K^^ is the

effective supply or capacity of school L given the quality thresholds of

cost and socio-economic class for n students o The definition of K-^ becomes

n

Kt ~ E Cj jR, . L . T dsd Ki 1=1

is the physical capacity of the school plant in a specific

school district

is the index for the quality of the school

For a second school, say m, let D /K < 1 and K = m in the same > / > mm m

manner as before and then determine:

where

^dsd

\i

m

m dsd Ki L

This process is repeated for all schools in the system and each K is summed

to determine S o If

s

m

2 K. < S

- 1 J s

then excess capacity exists and of course if

61
m

Z K. > S

s

this surplus must go to the private sector or the public school system

must be expanded. In terms of cost, S^^ = (Pp^y'

^L'

^^^-'^^ school -

L, the cost of the physical plant (Pp^-p) » the cost of maintaining the

quality threshold in teachers, supplies, etc., and the transportation

costs for bussing must be minimized. This is performed by arranging the

students within school districts to minimize the total cost of all schools

in the system. If additional constraints are placed upon this objective

such as segregation ratio, the model simply requires new school districts

which do not minimize the costs due to excess bussing but do comply with

ratio definitions.

I. Transportat ion

Transportation represents movements of people and goods to jobs and

shopping locations. There are four modes of transportation considered in

the journey to work. Namely car, bus, rapid rail and walking. The cost

is measured in terms of time, money and inconvience (ecological distance).

All work travel is calculated at peak hours. The traveling to and from

commercial and industrial sites for non- employment purposes are calculated

at off-peak hours and only consider car or truck and walking as alternative

modes

.

Since we are interested in minimizing travel costs, we first must

consider Tew or the transportation to jobs. Let

Tew

n

= Z min E.

where

E

'p,p^ is the ecological distance between points P, and p

also let

62
where

i equals trips

A is the dollar value of time T

M is the money costs of travel

C is dynamically adjusted congestion factor for iterative

trips, i.e., historical value

let

If is the transportation to shopping and commercial centers, then

n

T = E min C

^ P^=l n 2

where

C is the money cost of travel between points and P^- ^-^^ ^^^j.

be the money cost of a specific trip such thMt

Mr^ = minCH + B + C + W)

where

H is highway

B is bus

C is rapid rail

W is walk ; Finally the total transportation cost T is

n n

T = [Tew I E. + T ) Z MT.

1=1 1=1

where the cost to work is

63
n ji T = Tew Z E. I MT.

and the cost for shopping is

n

T , T E MT. shop s 1

The travel for industrial or commercial for non-employment purposes

d in MT.

is, of course, found in T^ with rapid rail eliminated as a possibility

1

J. Value of Structure and Capital Equipment

The fixed capital assets are assumed to decrease in value or depreciate

each time period. Expenditures to repair or modernize the asset will negate

the depreciation at the time period the inprovement was made and the

depreciation will begin again for the asset.' s new value.

The value of an asset at time t + 1 is

subject to

where

NC is the original cost

NV^ is the present value in a given time period

^^t+1 depreciation during a given time period in percent of

original cost

M^^^ is the maintenance expenditure made during a time period.

Depreciation or land use can be determined as

64
n

DL „ = Z Id. MS + d^^FL^ f d,^FR._ + d,^ U J 0=1 "^"ie'^'cinsp ' "2eJlp ' ""36 KP 4e dup 5e pwhere

DL

'ipi

MS,

le dmsp

2e£p

4e dup

dp U

5e p

is the total depreciation for each land use on each

parcel in the system

is the municipal service quality index per parcel by

land use

is the coefficient of time by land use type

is the depreciation of land use due to floods

is the depreciation due to inadequate fire protection

is the depreciation due to inadequate utility capacity

K. Water

The water sector is designed to replicate resources of surface water,

rivers, lakes and run-off. By relating the supply of water of a given

qualit)' to the demand for that quality of water, the need for water supplies

is adjusted by inrporting water and upgrading the quality of available

water.

The demand (D^) is given by:

n n

where

^d

L

P

WC

KP

^d= \

" \ ^PjCP^^^W ^^swCWe)

p=i ^ ^ p=i

is the demand for water in a given water district

is land use on a parcel

is water consumption

is the population of a given class or a parcel

65
Lg^ is the ijuported water

We is the water quality

The supply CS^) is given as:

"A

" lV

where

Sd is

is

TMd is

\

is

D is

P

The total water supply is then found as:

m m

T,,r = Z S , + E W + S W , T d 1 sp o d=l p=l ^

where

W is surface water

sp

outside purchase water

If the demand is greater than the supply, there is a tendency to

buy outside water such that:

local RWp =^ ACDp/Sp)

where

A = cost of bringing the present quality of water up to the desired

quality

66
If the quality of water is less than sojne staadard, or if

RW > 1 then

P

S - D - o p p

67
VII. POST SCRIPT

As stated in the Introduction, further clarification of the terms,

game procedures and exanples of computer outputs will be found in the

Computer Operator's, Director's and Player's manuals associated with

each game. The primary purpose of this manual is to give the serious

reader a detailed understanding of the mathematical models associated

with the games and not the computer programming techniques utilized to

make the models operational.

It is hoped that the user might utilize some of the models in his

own programs or modify them for his own needs. Each major model can be considered and analyzed apart from the actual CITY game. The programming

becomes complex only when all the models are integrated within a single

game, such as CITY IV. It is then necessary to account for the interrelations between models as well as the model solutions themselves.

To further help the reader, a Glossary of Terms and a List of

Symbols is included in this Chapter. Only those terms which are unique

to the Game or conplicated in their definition are listed. Terms such

as School Assignments or Transportation are defined in the text in their

usual sense and have not been included in the Glossaryc

Everywhere possible, the actual conputer symbols are used. A few

symbol changes have been made in this manual where a symbol in a main

program might be the same as a symbol used in a sub -routine or function.

68
Glossary^ of Terms

Average Rate of Return - The expectation over the longrun for each

investment made by an investor. Since some investment might

not be profitable in the first few years and extremely prc^itable

in the last years, a more representative yield on the investment

would be the average return over the entire life of the

investment.

Budget Allocations - In the Game context, the Government has a fixed

amount of money at the beginning of each round. This money,

acquired from debt and income, must be distributed to each

governmental department in its entirety to avoid wastefulness.

The proportionate distribution to each department becomes

the budget for that round.

CIT\' I - A two module game consisting of the Economic and Government

sectors played on an IBM 1131 conputer. ^^anuals are available

for purchase describing the details of this game at the National

Technical Infoimation Service (NTIS)

.

CITY II - This game is essentially CITY I with a partially operative

Social Sector and operates on a Univac 1108, Exec. 8 computer

from a terminal o There are presently no manuals available

for sale for this game but arrangements can be made through

NTIS for acquiring a set.

CITY III - A three module game consisting of the Economic, Government

and Social sectors played on a Univac 1108, Exec. 8 computer.

Manuals for this game are available for purchase from NTIS.

CITY W - Cin^ IV is for the most part identical to CITY III and is

\NTitten for an IBM 360/70 computero Manuals for this game

are available for purchase from NTIS.

69
7. City Model - The City models are operational simulation games in

which the participants or players make decisions that affect

a hypothetical metropolitan area built into the computer.

CITY I, II, III, IV and the River Basin are different versions

of the City Model.

8. Commercial Expenditures - These are the sum of the utility, ta:K,

maintenance, water, salary, transportation, and goods and

service costs.

9o Commercial Income - The income for any commercial establishment is

the product of the number of units sold and the price per

unit.

10. Computer Model Equations - These are the generalized computer equations

for supply and demand. The format of the general equations

is followed throughout the models

o

11. Decision-Making Bodies - In the gaming context, the decision makers

are the players. When one or more players are assigned a role, such as the School Department, the players are then

known as a decision-making bodyo

12. Departmental Ratios - Ratios that relate supply and demand to

education, adult education, municipal services, welfare

payments, utilities and transportation.

13. Director's Manual - A City Games manual written expressly for the

Game Directoro The manual contains the technical details

for running a game including the computer commands and options

open to the Director for various gaming plays „ Each game

has its own unique Director's manual.

70
14. Expected Value - A player investment criteria used to express the

average value of the net rate of return on all investments

made specific land parcel.

15. Fixed Resources - These resources include water, land, people,

buildings, roads, networks (utilities, transportation,

communication, etc.), capital equipment and the related

maintenance items necessary to keep them in operationo

16. Government Decision Objective - To maximize the total benefits to

the system through the allocation of funds among the various

departments

.

17. Grid Matrix - In all models, a grid or checker-board arrangement is

used. Each square or grid is used to identify and locate

the numerous interrelationships, specific parcels of land

and roads. The matrix then becomes the entire checker-board

or the sum of all the individual grids.

18. Housing Income - The income for a given residential property is the

product of the amount of space used and the rent per space

unit for the property.

19. Industrial Expenditures - These are the sum of the utility, tax,

maintenance, water, salary, transportation, goods and services,

and terminal usage costs and the expenses connected with

pollution control.

20. Industrial Property Income - The income for a given industrial

property is the product of the price per unit (industry

specific) and the number of units produced on the properties.

21. Industrial Value Ratio - The value ratio is determined by the amount

of depreciation that occurred during a given round limited by

the level at which maintenance is set.

71
22. Investment Capital - In the game, investment capital or money that

a player has to invest. The rational is that the net amount

of investment capital available after all costs of borrowing

are taken into consideration must be less than or equal to

the estimated rate of return in dollars.

23. Investment Series - In the game, investment series refers to all of

the investments made by a player in a given round. For

example, if in round one a player invested $25,000 in various

investments, this would be known as his investment series for

round one,

24. Liquid Resources - Those items which can easily be changed in the

short-run such as taxes, wages, sales, social attitudes and

the like.

25. Matching - This is the process of locating workers by skill and

educational level to fill the demand from the job market.

The workers who are located must then be interested in the

job offer because it will maximize their income and/or achieve

their satisfying objectives.

26. Migration - People move in and out of the urban system on the bases

of opportunities available to them. The game accounts for

this in and out migration as well as the natural birth-death

growth to consider the net population changes of the Urban

System.

27. Modules - The computer program considers each major game function

separately. For example, the Economic Sector is a module

, -f in terms of the computer programming. CITY III is a three

module game consisting of the Economic module, the Government

module and the Social module. These modules are referred to

in the gaming instructions as Sectors. The distinction is made

72
so that if one refers to a sector, the game play and the

players are referred to the Players ' manual . The module

terminology has meaning to the computer operator and the

Game Director.

28. Money Stock - This term refers to the total money supply in the

system at any given round of play.

29. Objective Function - This is the mathematical expression of the goals or standards set by each sector and the sub-division within

a sector, such as the School Department's goals, for each

game play.

30. Operator's Manual - A City Games manual written expressly for the

computer operator. The manual contains directions, explanations

and exhibits to guide the operator through a game play. Each

game has it's own unique Operator's Nbnual.

31 o Partial Resource Allocation - In a game play, it is not realistic

to assume that every resource available would be changed.

A resource committed in a prior game play may still be the

best committment for the player. The player would only

invest part of his remaining resources in the current round.

The concept of not investing or altering all resources during

a particular round is known as a partial resource allocation.

32. Player's Manual - A City Games manual written expressly for the player.

The manual contains directions, explanations and exhibits to

guide the player through a game play. Each game has its ovm

unique Players' Manual.

33. Private Capital - Private capital or money is invested in fixed assets

through three general categories: residential housing, commercial

activities and industrial plant and equipment.

73
34. Private Liquid Capital ~ Liquid f^esources were defined as those

resources which could easily be changed such as taxes, wages,

sales and the like. Private capital is non-government money

invested by the private citizens and therefore Private Liquid

Capital refers to the liquid capital of private investors.

35. Property Expenditures - The expenditures for a property are found

by summing for each property the utilities, taxes, maintenance

and water costs.

36. Public and Private Influence - This refers to the so called "power"

or "political power" exerted by individuals or groups to gain

an objective. The game considers voting, economic suasion,

and influence peddling in the form of bribes and boycotts as the tools for a power base.

37. Rate of Return - The amount of money earned from an investment

divided by the investment results in a percentage figure or rate of return. If a principal sum is invested and the net

return from the investment is 10^, then the rate of return

on the investment is 10?, if a single payment or the rate can

be in terms of conpound interest over time.

38. River Basin Model - This game is CITY IV with the water module

attached. It is the largest of the present series of games

consisting of four modules.

39. Semi -Liquid Capital - Semi- liquid capital is another term meaning

private liquid capitals The term arises from the definition

of partial resource allocation and supplies that only some of the private liquid capital will be reinvested during a particular game round or play^

74
40 o Structure Value - The structure value for a given property is the

original cost of a level of the structure (type specified)

times the value ratio times the number of levels on the parcel.

41o Time Allocation - The ability to allocate the leisure time of small

aggregates of workers in the Social Sector. This time allotment

produces complex interactive effects throughout the entire

model and can become a significant source of worker "power."

42. Total Resources - The total resources of a particular system can be

viewed as the sum of all fixed and liquid resources in the

system.

43. Water Module - This module is added to the CITY IV game and considers

the water distribution problems within the entire river basin

rather than just the metropolitan area of the particular game

in play.

75
B. List of Symbols

Symbol

A

aB

(aB-dC)

.

A.

1

•A

P

B

G

BG

B

,

1

B.

1

B. .

BLDG

I B

P

bPk

B

ps

BQIf

BS

BTC

BTC

BV

Page(s}

63,66

8

8

53

66

37,51,54,63

52

21

53,54

5,11

12

26

19

13,14

32

45

55

21

21

22

54

Symbol

^AE

^dsd

CG

CH.

1

3 CP

Pg

rP P

2

cRQ

CU

cu

D

^AE

DC

dC

dh. .

Page(s)

40,41,63

36

61

4

53

5,9,57

53

26

4

13,14,16,43

45

63

60

21

21

3,52

29

6,46

8

27,65

3

76
List of Symbols (Continued)

Symbol Page(s) Symbol Page(s

^i 59 % 30

d.

1

13 DZ 30

*^ie^dmsp 65 65

di, 8 65

10

4e dup 65

10 d, U

Be p

65

dK 11

dK. 11 E 55

dK,. 12 E* 46

\ 61 EE 23

65 EE

max

24

64

cp

29

dm^ 3 EH 24

D

ms

29 EI 55,60

dMS 60 EI 56

17 EI

max

59

17 EI^ 56

D

P

42,66 EI, 52,56,60

42 E.

J 51

D

s 60 46

D

sc

28

17

EL

c EN

35

11

30

EN

max

11

77
List of Symbols (Continued)

Symbol

EN

EN

max

EN.

P1P2

ER

eSc

FAE.

FR

FR

GS

P

gTx

H

i

^AE

IG

I.

3

Page(s)

12

12

13

44

62

24

60

35

3

3

41

20

60

52

63

3,4,9,40,57,63

29

31

58

Symbol

Ims

IN

IND.

IN^

I sc

^TR

^ur

j

J

J,

J.k(T-l)

JOB

K

K.

1

K. . ij

K.

3 h

h

Page(s)

29

43

35

58

28

30

30

30

3

47

47,59

59

35

49,57

16

9

12

57

58

61

45

78
List of Symbols (Continued)

Symbol Page (s) S>TTlbol Page (

L 21,62 MG.

3 26,31

LC 52 m. 13,14

L

c

53 17

LC

1

52 ^Vs 17

Lg 54 MS 8,9,59

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L-1 31,45,46 MS

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LND

p

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p

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Lr 52 m 59

LRC 31

LR.

1

3 n 8,11,12

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LU.

1 45,54 N

max

9

LU

P

29,30 NBCPR 24

LV 54 NC 64

L\ 66 .- -Nc

34

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M 63 58

m 12 58

79
List of Symbols (Continued)

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N.

1

N.

11

N.

1 NP,

MP

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OUT.

OUT,

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p

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P . gi

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Page(s)

9

54

14

47

24

21

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19

58

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4,39,46

4,9,31

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29,34

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PLA.

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54

48

48

40 ,49

65

61

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23,24

35

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40

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39

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80
List of Symbols (Continued)

Symbol

RTPS

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PS1

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PW.

Qi

Qlf

Qii

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r

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^£

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Page(s)

37

17,21,45

47

31

48

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58

31

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56

56

56

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18

28

28

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56,59

Symbol Page

r

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rP

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SC

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66

57,58

29

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81
List of Symbols (Continued)

Symbol

SL

P

Sms

S

o

S'

P

sp

SP

c

SPT,

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51,57

62

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Symbol Page(s)

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T 29

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T 16 pc

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TMd 66

TR. 26

J 20,22

TS 46

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82
List of Symbols (Continued)

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TX

U.

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UP

us

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UU

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V.

1

V. . IJ \

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p

VR

VR.

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66

34,64

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26

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33

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23

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30

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19,29,30

7,57,63

65

28

66

53

57

7

66

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6,57

6

6

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6

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56

51

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83
List of Symbols (Continued)

Symbol

a

a3

(a,6,Y)

aCP

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aPki

aUdk

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6CG

6U

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yAF

yAP^

Page(s)

4,31,61

52

52

52

31

40

59

59

59

59

4,31

40

59

4,31

34,54

35,54

36

36

36

35

35

36

Symbol Page(s)

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APS^

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54

54

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84
List of Symbols (Continued)

Symbol Page(s)

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42

Symbol Page(s)

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56

58

85

the coniM >

ii3 BIG CITY f;

J con't from pq.1 ,col . 2 our local demand, and con- sumers are. satisfied with

the service. We have had

* no boycotts or strikes during the Pu3t year." 5 Mr. Bigq expressed soT^e

'i, concern tnat the national " service sector- insurance finance/ r,i.j, real estate,

etc. - were not exptindinq

as rapidly here as in the

nati on.

con't from pg. 1 ,col . 3>i income people, in the poorer neighborhood, 2 out of five

are unemployed. We are hurting" This is the result of Ic-.v income families being sirnolj left to occupy depreciated tracts such as and-

. There is no lovi incorr.e housing being built

in the area. Certainly not

in the suburbs. In the city we have ovorcrov;dinq. The

Counci Ir.an waved at the Quality INdex Map and the Zoning Map on his wall.

"In the county now we are providing jobs in industria

parks for county residents. Residents prefer jobs nearest to their homes, and since ig City is largely develcoed, all metropolitan

frowth favors full employ- nent in the county."

"I do not for a moment agree vrith the Mayor on cutj

Vr.e was recovery - re;.ar;cable

-re^ t

,jnemplo^"=f.2 interest The cuts! 01- ^ p^gr

.ate average'!

f/<:'orporations

yn^th-^^^^^

moven^ent as

. of ^ ,cporWd a favorab\e

ba^^-^ralfbUl ion worth

of ''°°t-;i (half) ^"<* ^'^''^"^'Vndustrial,

;^ea 5how^ " ;<.rvative

,.eturn on co..s-

' „t<; in the na ^nvestr*3ntsj_ ^„ xional e^;';":^,,^, averto the ^^'"^^ITeco.omy.

Our

purchases fro^ ^^^^^or^,

viere only ^ v;as far l^^^'^ff^rieral ^^^^"Ition t'a^-es. ":?r.V and business

\ ^.rpn'v.eeping

l^, census,

co-^ ^ut

« health gro'^'th rt^eVror^c^-^

and stagnation

poouTat^on °f ^^\bout half

that f)^^"''=;ubstantial represents s but

concern ent-rely

is concentrate^^^ ^.^^

personal - have .^gs con

^''^ ''*na 3.C0T.

Con on pq 2C01.1 riTv cnv-icit^AN

Bi9 '^^^^L this Borninq. '

rented on the

^ ^^^^l^fd'to the t.. bleTM '\'^„d develoc:^e"t ''•^"''Mc^ng the metroP^ biems facii'y

a'^^*-".ratchcri He

'frt "Only 20"; ^"^.r'abor force ;M county lovi class, ^^^'l'^ity labor fore

This IS ment hits

CON'SUL'. FOR ZOt mends c faci 1 i t. The STudy deficient

tional Ian not be suri our institL public libr hospital , a rented and c Other cities average mile of public institutional

land for 100,000 people. By this standard, 3iq City should

have 10 sq. miles, and the coulty another 5 square

''''' ct bv the niy

first oy

pie . then by ^one

con pg.

..Ktive. square

ting welfare payments," said miles. V/e have none. the Councilman. He said he did back the Mayor's proposals of last month, for the city to invest in land and utility :ervice extension

With respect to park land,

the metropolitan area is better supplied. Ue have nearly 5 square miles of

parks of the 111 square/

to make sore packanes of i;n-t mile/to l.-nd area in the developed land available for city, of 514 square miles industrial and job developi

n^ent in the city. He said

j he planned to discuss with | area congrossrion f-e pcndini bills v,+iich v.'ould subsidize'

low-incom-:; housing. Placirc^

low-inco-^e housing in the

j county, near major industrial developments, would reduce

uncm-jloyrentin the county.

Th.c- Bunk Foundation, en- dowed by the late John Bunk, the founder of the Bunk (3) Coroor.Hti on , has already

3 oi,tess for

Holiday crowds from all parts of the city. The library must be centrally

located, despite high land costs. Amonn the alternatives discussed

in the report are sites near the old rented library downtown, fu- ture slum clearance sites in the harbor area, and existinq nark

land in one of the large and more

central squares in Big City, for example 36-102. The new map of Total Planning and Zoninq Land and Public Institutional Land

is on di spicy at city hall. Even on park land, the rn'nimum unit of develooment for a aublic institution cost', 31 mil. 4% of a square n;ile. This minimum park land provides receation space for

4P.C0 ti';; units of rccrcetion. Fed- eral-state aid can obtained for park developnent subject to aooroval;

87
BIBLIOGRAPHIC DATA

SHEET

1 . Report No. 3. Recipient's Accession No. COM-74 -10703-1

4. Title and Subtitle CITY Gi\MES

MATHEMATICAL FDIMDATIONS

5. Report Date September 197^

7. Author(s)

Mr. John E. Moriar^ty^

8. Performing Organization Rept, No.

9. Performing Organization Name and Address

National Bureau of Standards

Department of Commerce

Washington, D. C. 202 3U

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

National Technical Information Service

5285 Port Royal Road

Springfield, Virginia 221^1

13. Type of Report & Period

Covered

14.

15. Supplementary Notes This manual is to be used along with CITY I or CITY IV Games, Player'

Director's and Operator's manuals.

16. Abstracts rpj^g QjTY models are operational simulation games in iniiich the participants

make economic, government and social decisions affecting a hypothetical metropolitan

area. Through the use of a computer, the simulated urban system responds to the

participant's decisions as any real city would. To simplify the description of the

theory of the CITY GAMES modules, this manual is written for the four module game.

|

The equations for the other games can easily be obtained by eliminating the descriptj

that do not apply to the particular game of interest. The theoretical structure of if models is consistent and relevant only iMithin the range from a central city area to

regional configuration. The description of the module components and equations are meant to show the scope of decisions including those by the user and by the programf^

and algorithms of the computer model.

17. Key Words and Document Analysis. 17a. Descriptors

-X- Computers

-X- Simulation

-X- Mathematics

-X- Equations

17b. Identifiers/Open-Ended Terms

-X- Mathematical foundations

-X- Computer Programs

-X- Computer simulation

Simulation module

I7c. COSATI Field Group

19. Security Class (This

Report)

UNCLASSIFIED

21. No. of Page

92

20. Security Class (This

Page

UNCLASSIFIED

22. Price

18. Availability Statement ^his manual is available only with

the lease of the CITY I or CITY IV Games systems,

COM-7I4-IO7OI and COM-7U-IO7060

"ORr.'i MTIS-35 IREV 10-73) ENDORSED BY ANSI AND UNESCO. THIS FORM MAY BE REPRODUCED USCOMM-OC 8265