********************************************************
	.Saturday
********************************************************~
		Replicated by Julio Gomes and David Sirkin, MIT System Dynamics Group, from
		Roger Hall's ASQ article, "The Rise and Fall of the Saturday Evening Post"
		
		"Roger's model has a few problems in units and we kept them. We were able to \
		replicate the behavior in the ASQ
		     paper however, our problem shows a different behavior in relative growth of \
		revenue to period 3. We were not
		     able to find out why."
	|

Advertising Rate Change = 

(B * Advertising Rate / TIME STEP) * PULSE (ST,TIME STEP)*0 + (6/1000)*Change in Readers
	~	$/page/Year
	~	Change in advertising rates
	|

Thousand Readers = Total Readers Reported/1000
	~	thousand subscriptions
	~		|

Advertising Rate Per Thousand Readers = 

Advertising Rate /Thousand Readers
	~	$/page/thousand subscriptions
	~		|

Change in Total Expense Reported = IF THEN ELSE(T>=Accounting Period, (Total Expense-\
		Total Expense Reported
)/TIME STEP,0)
	~	$/Year
	~	How much the reported expense will change from a year to the other
	|

Circulation Promotion Expense Change = 

(C * Circulation Promotion Expense Rate / TIME STEP) * PULSE (ST, TIME STEP)
	~	$/Year/Year
	~	This is the rate of change of circulation promotion expense
	|

Subscription Rate Change =

(A * Subscription Rate / TIME STEP) * PULSE (ST, TIME STEP)
	~	$/subscription/Year/Year
	~	This is how much we want to pulse the subscription rate change
	|

Total Expense Reported = INTEG(Change in Total Expense Reported,Initial Total Expense\
		)
	~	$
	~	This is the total expense reported at the end of the year
	|

Initial Total Expense = (Production Expense Rate + Selling Expense Rate + Depreciation Charge Rate\
		 +
 General and Admin Expenses Rate
) * Accounting Period
	~	$
	~		|

Change in Regular Subscription Pipeout = 

((Last Regular Subscriber Batch * 5) - Regular Subscription Expiring Pipeout) / TIME STEP
	~	(Subscriptions/Year)/Year
	~	This structure was used to eliminate the simultaneous equation in the macro pipeout \
		for regular
		         subscriptions pipeout (see macro in the diagram provided last \
		class)
	|

Initial Total Revenue = (Circulation Revenue Rate + Advertising Revenue Rate) * Accounting Period
	~	$
	~	This is how much revenue we have in the begining through subscriptions and \
		advertising
	|

Total Revenue Reported = INTEG(Change in Total Revenue Reported,Initial Total Revenue\
		)
	~	$
	~	This is the total revenue reported at the end of each accounting period
	|

Regular Subscription Expiring Pipeout = 

INTEG (Change in Regular Subscription Pipeout, (Initial Total Readers - Trial Subscription Selling Rate
))
	~	Subscriptions/Year
	~	This is the result from the pipeline delay to define what is the rate of \
		subscriptions expiring
		         every year
	|

Revenue Closing Balance =IF THEN ELSE(Time <= 40+TIME STEP,Total Revenue/TIME STEP,
IF THEN ELSE(T>=Accounting Period,(Total Revenue/TIME STEP),0))
	~	Dollar/Year
	~	This is the flush out of revenue.  That is the revenue closing balance at the end of \
		the accounting
		         period.
	|

OUT T 0 = 

IF THEN ELSE (T 0 >= Flushing Interval, T 0 / TIME STEP, 0)
	~	Time Unit/Time Unit
	~	This is the flushing rate for one of the control variables that control the flushing \
		in the pipeline
		         delay function (macro in the original dynamo model)
	|

Flushing Interval = 0.2
	~	Year
	~		|

A = 0
	~	Dimensionless
	~	Step Height in the pulse formulation for subscription rate change
	|

A0 = -600000
	~	Subscriptions/Year
	~	Regresssion coefficients for regular subscriptions sold equation
	|

A1 = 1.34
	~	Dimensionless
	~	Regresssion coefficients for regular subscriptions sold equation
	|

A2 = -0.09
	~	$
	~	Regresssion coefficients for regular subscriptions sold equation
	|

A3 = 0
	~	Subscriptions/Year
	~	Regresssion coefficients for regular subscriptions sold equation
	|

A4 = 0
	~	Subscriptions/Year
	~	Regresssion coefficients for regular subscriptions sold equation
	|

A5 = 0
	~	Subscriptions/Year
	~	Regresssion coefficients for regular subscriptions sold equation
	|

A6 = 8e-005
	~	Subscriptions/Year
	~	Regresssion coefficients for regular subscriptions sold equation
	|

C0 = 0
	~	$/Year
	~	Regression coefficients for the editing printing & distributing expense \
		equation
	|

Previous AP Readers = 

INTEG (Change in Readers, Initial Total Readers)
	~	Subscriptions
	~	This is the number of readers we had at the end of the previous accounting \
		period
	|

Profit Margin = 

(Total Revenue Reported - Total Expense Reported) / Total Revenue Reported
	~	Dimensionless
	~		|

Pulso = IF THEN ELSE(T 0>=Flushing Interval,1/(TIME STEP)*(PULSE(Time, TIME STEP)),0)
	~	1/Year
	~		|

B =0
	~	Dimensionless
	~	Step height for the advertising rate change equation
	|

B0 = 790000
	~	Subscriptions/Year
	~	Regression coefficient for the trial subscriptions selling rate equation
	|

B1 = 0.034
	~	Subscriptions/Year
	~	Regression coefficient for the trial subscriptions selling rate equation
	|

B2 = 0
	~	Subscriptions/Year
	~	Regression coefficient for the trial subscriptions selling rate equation
	|

B3 = 310000
	~	Subscriptions/Year
	~	Regression coefficient for the trial subscriptions selling rate equation
	|

B4 = 320000
	~	Subscriptions/Year
	~	Regression coefficient for the trial subscriptions selling rate equation
	|

C = 0
	~	Dimensionless
	~	Step height to the change in circulation promotion expense equation
	|

G0 = 2065
	~	Pages/Year
	~	Regression coefficients for the magazine volume page rate equation
	|

C1 = 0.0018
	~	$/(Pages*Subscriptions)
	~	Regression coefficients for the editing printing & distributing expense \
		equation
	|

C2 = 1.02e+007
	~	$/Year
	~	Regression coefficients for the editing printing & distributing expense \
		equation
	|

Change in Readers =

IF THEN ELSE (T >= Accounting Period, (Total Readers Reported - Previous AP Readers) \
		/ TIME STEP
, 0)
	~	Subscriptions/Year
	~	This structure calculates the relative change in readers compared to the \
		last Accounting Period
	|

Change in Total Revenue Reported =IF THEN ELSE(T>=Accounting Period, (Total Revenue-Total Revenue Reported
)/TIME STEP,0)
	~	$/Year
	~	How much the reported revenue will change from a year to the other
	|

Change in Total Readers = 

 IF THEN ELSE(T >= Accounting Period, (Total Readers - Total Readers Reported) / TIME STEP
, 0)
	~	Subscriptions/Year
	~	How much the number of reported readers will change from a year to the \
		other
	|

Circulation Promotion Expense Rate = 

INTEG (Circulation Promotion Expense Change, Initial Circulation Promotion Expense)
	~	$/Year
	~	This is how much the firm spends on promotion expenses to obtain more \
		subscribers
	|

Change in Revenue = 
IF THEN ELSE(Time<=40+TIME STEP,(Total Revenue Reported-Previous AP Revenue) / TIME STEP\
		,IF THEN ELSE
 (T >=Accounting Period,
(Total Revenue Reported-Previous AP Revenue) / TIME STEP, 0))
	~	$/Year
	~	This is tohe rate that updates the revenue every accounting period
	|

Magazine Volume Page Rate = 

G0 + G1 * Advertising Pages Selling Rate
	~	Pages/Year
	~	This is the regression equation to define the magazine volume page rate
	|

Second Regular Subscriber Batch = 

INTEG (R1 - R2, (Initial Total Readers - Trial Subscription Selling Rate) / 5)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for regular subscribers \
		time in the
		         system.
	|

Second Trial Subscriber Batch = 

INTEG (T1 - T2, Trial Subscription Selling Rate / 5)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for trial subscribers \
		time in the
		         system.
	|

ROUT = Last Regular Subscriber Batch * Pulso
	~	
	~	This is a function for one pice of the pipeline delay function for regular \
		subscribers.
	|

G1 = 1.3
	~	Dimensionless
	~	Regression coefficients for the magazine volume page rate equation
	|

Depreciation Charge Rate = 

Fraction of Revenue Charged to Depreciation * (Total Revenue Reported / Accounting Period\
		)
	~	Dollar/Year
	~	This is how much it depreciates in a year.  It is modelled as a fraction \
		of reported revenues.
	|

Editing Printing and Distrib Expense Rate = 

C0 + C1 * Magazine Volume Page Rate * Total Readers + C2 * Special Events Switch * (step\
		 (1, 59) + step
 (-1, 66))
	~	$/Year
	~	This is the regression equation to determie what is the expense rate in editing, \
		printing, and
		         distributing the magazine.
	|

Expense Closing Balance = IF THEN ELSE(Time <= 40+TIME STEP,Total Expense/TIME STEP,IF THEN ELSE\
		(T>=
Accounting Period,(Total Expense/TIME STEP),0))
	~	$/Year
	~	This the flush out of total revenue at the end of one accounting period.  The author \
		decided to do a
		        discrete formulation.  This is the continuous pulse function that we have in \
		dynamo but
		         we do not have it in Vensim.
	|

Fifth Regular Subscriber Batch = 

INTEG (R4 - R5, (Initial Total Readers - Trial Subscription Selling Rate) / 5)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for regular subscribers \
		time in the
		         system.
	|

Fifth Trial Subscriber Batch = 

INTEG (T4 - T5, Trial Subscription Selling Rate / 5)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for trial subscribers \
		time in the
		         system.
	|

First Regular Subscriber Batch = 

INTEG (Regular Subscriber Input - R1, 0)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for regular subscribers \
		time in the
		         system.
	|

First Trial Subscriber Batch = 

INTEG (Trial Subscriber Input - T1, 0)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for trial subscribers \
		time in the
		         system.
	|

Fourth Regular Subscriber Batch = 

INTEG (R3 - R4, (Initial Total Readers - Trial Subscription Selling Rate) / 5)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for regular subscribers \
		time in the
		         system.
	|

Fourth Trial Subscriber Batch = 

INTEG (T3 - T4, Trial Subscription Selling Rate / 5)
	~	Subscriptions/Year
	~	This is one of the six stocks in the pipeline delay function for trial subscribers \
		time in the
		         system.
	|

R2 = Second Regular Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the regular subscribtion pipeline delay used to figure out \
		regular subscribers
		         expiring rate
	|

T3 = Third Trial Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the trial subscribtion pipeline delay used to figure out regular \
		subscribers
		         expiring rate
	|

R3 = Third Regular Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the regular subscribtion pipeline delay used to figure out \
		regular subscribers
		         expiring rate
	|

General and Admin Expenses Rate = 

Fraction of Revenue Spent on Gen and Admin * (Total Revenue Reported / Accounting Period\
		)
	~	Dollar/Year
	~	This is modeled as a fraction of revenues
	|

T5 = Fifth Trial Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the trial subscribtion pipeline delay used to figure out regular \
		subscribers
		         expiring rate
	|

IN T 0 = Time Unit
	~	Year/Year
	~		|

Initial Advertising Rate = 19500
	~	$/page
	~	This is the initial advertising rate (price)
	|

Initial Circulation Promotion Expense = 1.5e+007
	~	$/Year
	~	This is the initial expense in promotion
	|

Initial Subscription Rate = 3.08
	~	$/subscription/Year
	~	This is how much is charged for a subscription
	|

Initial Total Readers = 3.25e+006
	~	Subscriptions
	~		|

Last Regular Subscriber Batch = 

INTEG (R5 - ROUT, (Initial Total Readers - Trial Subscription Selling Rate) / 5)
	~	Subscriptions/Year
	~	This is a piece of the pipeout delay for regular subscribers.
	|

Last Trial Subscriber Batch = 

INTEG (T5 - TOUT, Trial Subscription Selling Rate / 5)
	~	Subscriptions/Year
	~	This is a piece of the pipeout delay for regular subscribers.
	|

T2 = Second Trial Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the trial subscribtion pipeline delay used to figure out regular \
		subscribers
		         expiring rate
	|

TOUT = Last Trial Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the trial subscribtion pipeline delay used to figure out regular \
		subscribers
		         expiring rate
	|

Trial Subscriber Input = Trial Subscription Selling Rate
	~	Subscriptions/Year
	~	This is a piece of the regular subscribtion pipeline delay used to figure out \
		regular subscribers
		         expiring rate
	|

T4 = Fourth Trial Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the trial subscribtion pipeline delay used to figure out regular \
		subscribers
		         expiring rate
	|

R4 = Fourth Regular Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the regular subscribtion pipeline delay used to figure out \
		regular subscribers
		         expiring rate
	|

ST = 45
	~	Year
	~		|

Previous AP Revenue = 

INTEG (Change in Revenue,Initial Total Revenue)
	~	$
	~	This is the revenue we generated in the previous accounting period.
	|

Regular Subscriber Input = Regular Subscription Selling Rate
	~	Subscriptions/Year
	~	This is a piece of the regular subscribtion pipeline delay used to figure out \
		regular subscribers
		         expiring rate
	|

T 0 = 

INTEG (IN T 0-OUT T 0,0)
	~	Year
	~	This is the control variable to control the flush out of a some variables
	|

T1 = First Trial Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the trial subscribtion pipeline delay used to figure out regular \
		subscribers
		         expiring rate
	|

R1 = First Regular Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the regular subscribtion pipeline delay used to figure out \
		regular subscribers
		         expiring rate
	|

Relative Growth in Revenue =

zidz ((Total Revenue Reported - Previous AP Revenue), Previous AP Revenue)
	~	Dimensionless
	~	This is the relative growth in revenue from accounting period to \
		accounting period
	|

R5 = Fifth Regular Subscriber Batch * Pulso
	~	Subscriptions/(Year*Year)
	~	This is a piece of the regular subscribtion pipeline delay used to figure out \
		regular subscribers
		         expiring rate
	|

Trial Subscription Expire Pipeout = Last Trial Subscriber Batch * 5
	~	Subscriptions/Year
	~	This is the rate of subscriptions that expire every year
	|

Total Readers Reported = 

INTEG (Change in Total Readers, Initial Total Readers)
	~	Subscriptions
	~	This is the total number of subscriptions reported at the end of an \
		accounting period.
	|

Relative Growth in Readers =

zidz ((Total Readers Reported - Previous AP Readers), Previous AP Readers)
	~	Dimensionless
	~	This is the relative growth in subscriptions from accounting period to \
		accounting period
	|

Third Trial Subscriber Batch = 

INTEG (T2 - T3, Trial Subscription Selling Rate / 5)
	~	Subscriptions/Year
	~	This is one pice of the pipeline delay function for trial subscribers
	|

Third Regular Subscriber Batch = 

INTEG (R2 - R3, (Initial Total Readers - Trial Subscription Selling Rate) / 5)
	~	Subscriptions/Year
	~	This is one pice of the pipeline delay function for regular subscribers
	|

OUT T = IF THEN ELSE(T>=Accounting Period,T/TIME STEP,0)
	~	Time Unit/Time Unit
	~	This is the flushing rate for one of the control variables that control the flushing \
		in revenue or
		         expenses, etc in an account period
	|

IN T = Time Unit
	~	Year/Year
	~		|

T = 

INTEG (IN T - OUT T ,0)
	~	Year
	~	This is the control variable to control the flush out of a some variables
	|

Time Unit = 1
	~	Year/Year
	~		|

D0 = 8530
	~	Pages/Year
	~	This is the regression coefficient for the advertising pages selling rate \
		equation
	|

Advertising Pages Selling Rate = 

D0 + D1 * Advertising Rate Per Thousand Readers + (D2 * (step (1, 41) + step (-1, 42)\
		) + D3 * (step 
(1, 42) + step (-1, 45))) * Special Events Switch
	~	Pages/Year
	~	Number of pages of advertising sold per year
	|

D2 = -1055
	~	Pages/Year
	~	This is the regression coefficient for the advertising pages selling rate \
		equation
	|

D3 = -356
	~	Pages/Year
	~	This is the regression coefficient for the advertising pages selling rate \
		equation
	|

Advertising Revenue Rate =

Advertising Pages Selling Rate * Advertising Rate
	~	$/Year
	~		|

Special Events Switch = 0
	~	Dimensionless
	~	This is a switch that turns on the war events and other special events \
		described in the article
	|

D1 =  -985
	~	(Pages*Pages*thousand subscriptions)/(Year*$)
	~	This is the regression coefficient for the advertising pages selling rate \
		equation
	|

Accounting Period = 1
	~	Year
	~		|

Regular Subscription Expiration Rate = Regular Subscription Expiring Pipeout
	~	Subscriptions/Year
	~	This the number of regular subscriptions that expire every year
	|

Advertising Selling Expense = 

Commission on Advertising Sales * Advertising Revenue Rate
	~	Dollar/Year
	~		|

Circulation Revenue Rate = 

(Trial Subscription Selling Rate + Regular Subscription Selling Rate) * Subscription Rate
	~	$/Year
	~	This is how much the company makes per year fromthe subscriptions it sells
	|

Fraction of Revenue Charged to Depreciation = 

0.01
	~	Dimensionless
	~		|

Fraction of Revenue Spent on Gen and Admin = 

0.01
	~	Dimensionless
	~		|

Trial Subscription Expiration Rate = Trial Subscription Expire Pipeout
	~	Subscriptions/Year
	~	This is the rate of trial subscriptions that expire every year
	|

Trial Subscription Selling Rate =

B0 + B1 * Circulation Promotion Expense Rate + B2 * Magazine Volume Page Rate + Special Events Switch
 * (B3 * (step (1,43) + step (-1, 49)) + B4 * (step (1, 56) + step (-1, 60)))
	~	Subscriptions/Year
	~	This is the rate of trial subscriptions that the company sells and is calculated \
		using a regression
		         equation.
	|

Production Expense Rate = 
Editing Printing and Distrib Expense Rate
	~	Dollar/Year
	~		|

Total Expense = 

INTEG (Production Expense Rate + Selling Expense Rate + Depreciation Charge Rate + General and Admin Expenses Rate
 - Expense Closing Balance,Initial Total Expense)
	~	$
	~	This is the total expense of the company
	|

Regular Subscription Selling Rate = 

A0 + (A1 + A2 * Subscription Rate + A3 * Magazine Volume Page Rate) * Regular Subscription Expiring Pipeout
 + (A4 + A5 * Subscription Rate + A6 * Magazine Volume Page Rate) * Trial Subscription Expire Pipeout
	~	Subscriptions/Year
	~	This is the number of regular subscriptions we sell every year
	|

Selling Expense Rate = 

Circulation Promotion Expense Rate + Advertising Selling Expense
	~	$/Year
	~	Those are the expense we incur to sell the magazines
	|

Total Revenue = INTEG (Circulation Revenue Rate + Advertising Revenue Rate - Revenue Closing Balance
,Initial Total Revenue)
	~	$
	~	This the total revenue of the company which is flushed out every \
		accounting period
	|

Advertising Rate = 

INTEG (Advertising Rate Change, Initial Advertising Rate)
	~	$/page
	~	$ charged per page of advertising
	|

Commission on Advertising Sales = 0.15
	~	Dimensionless
	~	This is the comission we pay on advertising sales to others
	|

Potential Subscribers =

INTEG (Regular Subscription Expiration Rate + Trial Subscription Expiration Rate - Regular Subscription Selling Rate
 - Trial Subscription Selling Rate, 1e+008)
	~	Subscriptions
	~	This is the potential market for the company.  We set the initial value as a big \
		number assuming
		         that the market is huge.
	|

Subscription Rate = 

INTEG (Subscription Rate Change, Initial Subscription Rate)
	~	$/Subscriptions/Year
	~	This is how much the company charges for a yearly subscription
	|

Total Readers = 

INTEG (Trial Subscription Selling Rate + Regular Subscription Selling Rate - Regular Subscription Expiration Rate
 - Trial Subscription Expiration Rate, Initial Total Readers)
	~	Subscriptions
	~	This is the total number of readers (subscriptions) that the company sold
	|

********************************************************
	.Control
***************************************************