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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 40 "NelwinDecomp for Maple V.
4: Introduction" }}{PARA 19 "" 0 "" {TEXT -1 72 "24 Sep 1996 Ñ rev. 5 \+
Oct 1999\nEsben Sloth Andersen, esa@business.auc.dk\n" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT -1 48 "WARNING 1: The program do not work with
 Maple V!" }}{PARA 256 "" 0 "" {TEXT -1 338 "WARNING 2: You have to pr
ess <enter> on all procedures\nto allow the system to function properl
y.\nREMARK: In some cases you get an error message. If the\ntext follo
wing the error message includes \"oops!\" or\nsimilar expressions, the
n the errror message is the result\nof a deliberately wrong Maple stat
ement. See the text\nabout how to react.\n" }}}{SECT 0 {PARA 3 "" 0 "
" {TEXT -1 41 "The problem of decomposition in Maple V.4" }}{SECT 0 
{PARA 4 "" 0 "" {TEXT -1 12 "Introduction" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 585 "The basic heuristic in problem solving is \"divide and c
onquer\". Unless we divide a complex simulation model into simple and \+
relatively independent components, we are likely to run into serious t
rouble. Maple's primary means of decomposition are procedures (also ca
lled functions). In the following we see how a Nelson and Winter model
 can be defined by means of a fairly large number of procedures (in co
ntrast to SimpleNelwin where everything was included in a single proce
dure). The procedure that (directly and indirectly) reintegrates all t
he components is called StructuredNelwin." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 587 "One problem with this decomposition is that at the begin
ning of a Maple procedure, we have to declare which global variables w
e want to change. All other variables that are changed within the proc
edure are assumed to be local.  This means that Maple makes a distinct
ion between items that can only be accessed from within a given proced
ure (local or private items) and items that can be accessed without re
strictions (global or public items). Global items survive during a who
le Maple session while local items disappear when control is returned \+
from the procedure in which they existed." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 165 "In the present worksheet we shall make a compromise betw
een decomposition of programs and easy access to simulation data by pl
acing most variables in a single table." }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 61 "We start by setting the overall system in an adequate man
ner:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "restart;\ninterface
(prettyprint=1);\nprintlevel := 3;" }}{PARA 2 "" 1 "" {TEXT -1 53 "   \+
                                   printlevel := 3" }}}}{SECT 0 {PARA 
4 "" 0 "" {TEXT -1 42 "A (huge) table as a single global variable" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 372 "In an evolutionary model like Nel
win and extensions thereof there is a very large number of variables, \+
constants, etc. that we want to access and/or modify from different pr
oceduress. We also want to have access to these items for data analysi
s and for saving to the harddisk (so that we can later inspect the dat
a without having to do time consuming reruns of the model)." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 423 "To simplify these uses of global \+
items we shall try out the following solution: all global items are st
ored in a (huge) table declared as global. Maple tables can be conside
red as a generalisation of the array structure. It holds an indexed co
llection of elements. When we create an item, we give its indexes and \+
its value. Later the element can be retrieved by referring to its inde
xes. Many types of indexes can be used. " }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 112 "The table is controlled by a table monitor (# 1) that st
ores the data in the table and administers access to it." }}}{EXCHG 
{PARA 0 "> " 0 "`index/monitor`" {MPLTEXT 1 0 339 "`index/monitor1` :=
 proc(indices,table) \nif not (type(op(1,indices),string) or type(op(1
,indices),indexed))    then ERROR(`wrong first part of the index`); \n
fi;\nif (nargs = 2) then \n   if (assigned(table[op(indices)])) then t
able[op(indices)];\n   else ERROR(`not assigned`); \n   fi;\nelse tabl
e[op(indices)] := op(args[3..nargs]); \nfi;\nend:" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 245 "Since the names of most of the variables and cons
tants have to be enhanced with the name of the global table, we want t
his name to be as invisible as possible and not to be confured with an
y other names. We shall apply the name \"_\" (underscore)." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 147 "We now define a procedure for initialisi
ng the table with the name \"_\" and the index function \"monitor\". T
hen we call the initialisation procedure." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 58 "CreateTable := proc()\nglobal _;\n_ := table(monito
r1);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "CreateTable()
;" }}{PARA 2 "" 1 "" {TEXT -1 25 "table(monitor1, [\n\n    ])" }}}}
{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "The functioning of the global tab
le" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 196 "We now see how we can store
 and retrieve information. The first part of the index has to be a nam
e (letter or mix of letters and integers). Only information that has b
een stored can be retrieved. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "_[1,1,1] := 89.7;" }}{PARA 8 "" 1 "" {TEXT -1 56 "Error, (in ind
ex/monitor1) wrong first part of the index" }}{PARA 9 "" 1 "" {TEXT 
-1 60 " executing statement: ERROR(`wrong first part of the index`)" }
}{PARA 9 "" 1 "" {TEXT -1 63 " index/monitor1 called with arguments: [
1, 1, 1], table, [89.7]" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Oops!
 The problem here was that the first part of the index was not a name.
 Let us make it correctly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
17 "_[K,1,1] := 89.7;" }}{PARA 2 "" 1 "" {TEXT -1 55 "                \+
                     _[K, 1, 1] := 89.7" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 61 "That was OK. But let us now try to make the error indirec
tly:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "K := 1;" }}{PARA 2 "
" 1 "" {TEXT -1 49 "                                           K := 1
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "_[K,1,1];" }}{PARA 8 "" 
1 "" {TEXT -1 56 "Error, (in index/monitor1) wrong first part of the i
ndex" }}{PARA 9 "" 1 "" {TEXT -1 60 " executing statement: ERROR(`wron
g first part of the index`)" }}{PARA 9 "" 1 "" {TEXT -1 55 " index/mon
itor1 called with arguments: [1, 1, 1], table" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 138 "Still the problem is that the first part of the index
 received by the Maple engine is not a name. Let us, therefore, restor
e the name \"K\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "K := 'K
';" }}{PARA 2 "" 1 "" {TEXT -1 49 "                                   \+
        K := K" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "_[K,1,1] \+
:= 89.7;" }}{PARA 2 "" 1 "" {TEXT -1 55 "                             \+
        _[K, 1, 1] := 89.7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
9 "_[K,1,1];" }}{PARA 2 "" 1 "" {TEXT -1 48 "                         \+
                   89.7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "_
[K,2,1];" }}{PARA 8 "" 1 "" {TEXT -1 39 "Error, (in index/monitor1) no
t assigned" }}{PARA 9 "" 1 "" {TEXT -1 43 " executing statement: ERROR
(`not assigned`)" }}{PARA 9 "" 1 "" {TEXT -1 55 " index/monitor1 calle
d with arguments: [K, 2, 1], table" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "_[K,2,1] := 89.7;" }}{PARA 2 "" 1 "" {TEXT -1 55 "   \+
                                  _[K, 2, 1] := 89.7" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "_[K,2,1];" }}{PARA 2 "" 1 "" {TEXT -1 48 "
                                            89.7" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 17 "_[K,1,2] := 93.8;" }}{PARA 2 "" 1 "" {TEXT 
-1 55 "                                     _[K, 1, 2] := 93.8" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "for i from 1 to 2 do\nprint(
_[K,1,i]);\nod;" }}{PARA 2 "" 1 "" {TEXT -1 48 "                      \+
                      89.7" }}{PARA 2 "" 1 "" {TEXT -1 48 "           \+
                                 93.8" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 80 "Now we can write a procedure that initialises the variabl
es K and A for N firms:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 
"Initialise := proc(N)\nglobal _;\nlocal i;\nfor i from 1 to N do\n   \+
_[A,i,1] := 0.16;\n   _[K,i,1] := 89.70;\nod;\nlprint(`Initialisation \+
OK`);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Initialise(4
);" }}{PARA 6 "" 1 "" {TEXT -1 17 "Initialisation OK" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 9 "print(_);" }}{PARA 2 "" 1 "" {TEXT -1 223 
"table(monitor1, [\n\n    (K, 4, 1) = 89.70\n\n    (A, 2, 1) = .16\n\n
    (K, 1, 2) = 93.8\n\n    (K, 3, 1) = 89.70\n\n    (A, 3, 1) = .16\n
\n    (K, 2, 1) = 89.70\n\n    (A, 4, 1) = .16\n\n    (K, 1, 1) = 89.7
0\n\n    (A, 1, 1) = .16\n\n    ])" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 187 "Remark that one value has survived from our earlier definition
 ((K, 1, 2) = 93.8). If we want to avoid such surprises, we have to cl
ear the table (by a redefinition: _ := table(monitor);)" }}}{PARA 0 "
" 0 "" {TEXT -1 18 "                  " }}}}{SECT 0 {PARA 3 "" 0 "" 
{TEXT -1 26 "A little on random numbers" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 926 "Let us look at the results of this procedure as an examp
le of random number generation. To secure that the result can be repro
duced, we start by setting the \"_seed\", i.e. the system variable gov
erning the outcome of the (pseudo) random number generation. The _seed
 is normally set to the last random number that has been generated by \+
Maple's internal system. But the user can define an initial value for \+
_seed. This initial value generates at deterministic sequence of numbe
rs that behave as if they were produced randomly. This means that alth
ough the sequence can be taken to represent the behaviour of a random \+
variable, the sequence can also be reproduced by giving the original _
seed to Maple's engine. In other words, since Maple's generation of ra
ndom numbers is strictly deterministic, each run with the same initial
 _seed value will give exactly the same result, ceteris paribus (i.e. \+
with no parameter change, etc.)." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "rand();" }}{PARA 2 "" 1 "" {TEXT -1 52 "              \+
                          427419669081" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "rand();" }}{PARA 2 "" 1 "" {TEXT -1 52 "              \+
                          321110693270" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "rand();" }}{PARA 2 "" 1 "" {TEXT -1 52 "              \+
                          343633073697" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "_seed := 2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "rand();" }}{PARA 2 "" 1 "" {TEXT -1 52 "                         \+
               854839338162" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
11 "_seed := 2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "rand();" 
}}{PARA 2 "" 1 "" {TEXT -1 52 "                                       \+
 854839338162" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "_seed := 2
7:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "rand();" }}{PARA 2 "" 
1 "" {TEXT -1 52 "                                        540331065308
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "_seed := 27:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "rand();" }}{PARA 2 "" 1 "" 
{TEXT -1 52 "                                        540331065308" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 396 "Apart from the rand function, Map
le's functions for producing random numbers are placed in the random p
ackage within the stats package. This means that you can either call t
hese functions by a long name or - after calling the package - by a sh
ort name. Let us consider Maple's function for generating a sequence o
f random numbers distributed according to a normal distribution with d
efined mean (" }{XPPEDIT 18 0 "mu=2" "/%#muG\"\"#" }{TEXT -1 26 ") and
 standard deviation (" }{XPPEDIT 18 0 "sigma=.5" "/%&sigmaG$\"\"&!\"\"
" }{TEXT -1 104 ").  We start by the long name. Then we load the rando
m package and make a few tries with the short name." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 31 "stats[random,normald[2,0.5]]();" }}{PARA 
2 "" 1 "" {TEXT -1 51 "                                        2.44053
6751" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(stats[random])
;" }}{PARA 2 "" 1 "" {TEXT -1 198 "[beta, binomiald, cauchy, chisquare
, discreteuniform, empirical, exponential, fratio, gamma,\n\n    lapla
ced, logistic, lognormal, negativebinomial, normald, poisson, students
t, uniform,\n\n    weibull]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
17 "normald[2,0.5]();" }}{PARA 2 "" 1 "" {TEXT -1 51 "                \+
                        2.155756361" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "_seed := 27:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "normald[2,0.5]();" }}{PARA 2 "" 1 "" {TEXT -1 51 "              \+
                          1.513856966" }}}{PARA 0 "" 0 "" {TEXT -1 2 "
  " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "_seed := 27:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "normald[2,0.5]();" }}{PARA 
2 "" 1 "" {TEXT -1 51 "                                        1.51385
6966" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 165 "Finally we ask for five \+
random numbers determined by the same _seed. Remark that the first is \+
the same as before, while the others are (pseudo) randomly distributed
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "_seed := 27:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "normald[2,0.5](5);" }}{PARA 
2 "" 1 "" {TEXT -1 77 "              1.513856966, 1.732695730, 1.24721
1154, 2.270571276, 2.961489731" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
111 "We also need random numbers distributed according to the Poisson \+
distribution (with the parameter lambda, here " }{XPPEDIT 18 0 "lambda
=3" "/%'lambdaG\"\"$" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "poisson[3](5);" }}{PARA 2 "" 1 "" {TEXT -1 56 "      \+
                             5.0, 3.0, 2.0, 1.0, 0" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 117 "Finally we try in vain to obtain a series of uni
formly distributed random numbers from 1 to 6 (like throwing a dice).
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "uniform[1..6](5);" }}
{PARA 8 "" 1 "" {TEXT -1 62 "Error, (in stats/parms/functions/uniform)
 invalid types in sum" }}{PARA 9 "" 1 "" {TEXT -1 30 " executing state
ment: b := a+1" }}{PARA 9 "" 1 "" {TEXT -1 63 " locals defined as: a =
 1. .. 6., b = b, status = status, x = x" }}{PARA 9 "" 1 "" {TEXT -1 
72 " stats/parms/functions/uniform called with arguments: 5, [1 .. 6],
 false" }}{PARA 9 "" 1 "" {TEXT -1 86 " stats/functions/random called \+
with arguments: [uniform[1 .. 6]], [5], uniform[1 .. 6]" }}{PARA 9 "" 
1 "" {TEXT -1 81 " stats[random,uniform[1 .. 6]] called with arguments
: 5, topname(uniform[1 .. 6])" }}{PARA 9 "" 1 "" {TEXT -1 41 " uniform
[1 .. 6] called with arguments: 5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
190 "Oops! Here we encountered a grave error in the Maple system. Luck
ily most of Maple's system is accessible to users, so we can correct t
he error immediately (do not think about the details!)." }}}{SECT 0 
{PARA 4 "" 0 "" {TEXT -1 42 "Correcting a bug in Maple's random packag
e" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 404 "Unfortunalely there is a bug
 in the Maple function for creating a uniform distribution. Therefore,
 we have to include a corrected version of a helping procedure relatin
g to the uniform function. The new version of the procedure (`stats/pa
rms/functions/uniform`) secures that the uniform distribution in Maple
's random function package works correctly. Just press <enter>. Do not
 bother about the details." }}}{EXCHG {PARA 0 "> " 0 "`stats/parms/fun
ctions/uniform`" {MPLTEXT 1 0 1167 "`stats/parms/functions/uniform` :=
 proc(xvalue, given, xcheck)\nlocal a, b, status, x;\noption system, r
emember, \n`Copyright (c) 1993 by Waterloo Maple Inc. \nBug corrected \+
by ESA, 1 Sep 1996. Another bug concerning one real argument is still \+
present. In the one-argument case, only integers can be used`;\n\nif n
ops(given) = 0 then a := evalf(0); b := evalf(1)\nelif nops(given[]) =
 2 then \n   a := evalf(op(1, given[])); b := evalf(op(2, given[]))\ne
lif nops(given) = 1 then a := evalf(op(1, given[])); b := a + 1\nelse \+
\n   status := 'abort';\n   RETURN(status, \n   [`requires two paramet
ers (no parameters defaults to 0,1),       received`, given])\nfi;\nif
 not type([a, b], list(numeric)) then\n   status := 'FAIL';\n   RETURN
(status, [`unable to find evalf() of the bounds `, a, b])\nfi;\nif not
 (a < b) then\n   status := 'abort';\n   RETURN(status, [`right bound \+
must be greater than left bound,    received`, a, b])\nfi;\nif not xch
eck then x := xvalue\nelse\n   x := evalf(xvalue);\n   if not type(x, \+
numeric) then\n       status := 'FAIL';\n       RETURN(status, [`unabl
e to find evalf() of argument, \n              received`, xvalue])\n  \+
 fi\nfi;\nstatus := 1;\nstatus, [x, a, b]\nend:" }}}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 31 "Now we try again with our dice:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 17 "uniform[1..6](5);" }}{PARA 2 "" 1 "" 
{TEXT -1 77 "              2.860190768, 3.619231213, 1.287895212, 2.93
8127176, 5.667342603" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 28 "The ele
ments of NelwinDecomp" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 "Introduc
tion" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 255 "In the following formulat
ion of functions and procedures, the classic Nelson and Winter model f
amily has been formulated according to the paradigm of decomposed prog
ramming that combines elements of structured programming and object-or
iented programming. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 143 "The core
 of the program (or system of functions and procedures) is the transfo
rmation of the state variables of a firm - its physical capital (" }
{XPPEDIT 18 0 "K" "I\"KG6\"" }{TEXT -1 37 ") and its (reciprocal) prod
uctivity (" }{XPPEDIT 18 0 "A=Q/K" "/%\"AG*&%\"QG\"\"\"%\"KG!\"\"" }
{TEXT -1 3 "). " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 246 "The mechanism
 of transformation from one state to the next includes both elements w
ithin and beyond the individual firm, and the state transformation inc
ludes both deterministic and probabilistic elements. Let us start to e
xplore these elements. " }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 46 "Crea
ting a global table and an individual firm" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 144 "We start by making a slight change in the functions for \+
monitoring a table and for creating the global table. Then we call Cre
ateTable function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 253 "`ind
ex/monitor2` := proc(indices,table) \nif not (type(op(1,indices),strin
g) or type(op(1,indices),indexed)) then ERROR(`wrong first part of the
 index`); fi;\nif (nargs = 2) then table[op(indices)];\nelse table[op(
indices)] := op(args[3..nargs]); \nfi;\nend:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 95 "CreateTable := proc()\nglobal _;\n_ := table(mon
itor2);\n_[newFirm] := 0;\nRETURN(`Table OK`);\nend:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 14 "CreateTable();" }}{PARA 2 "" 1 "" {TEXT 
-1 50 "                                          Table OK" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(_);" }}{PARA 2 "" 1 "" {TEXT 
-1 42 "table(monitor2, [\n\n    newFirm = 0\n\n    ])" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 70 "Then we define a procedure for creating f
irms and make our first firm:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 221 "CreateFirm := proc(capital,productivity)\nglobal _;\nlocal firm
Key;\nfirmKey := _[newFirm] + 1;\n_[newFirm] := firmKey;\n_[K,firmKey,
1] := capital;\n_[A,firmKey,1] := productivity;\nRETURN(`Firm created.
 FirmKey`, firmKey);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "CreateFirm(91.33,.16);" }}{PARA 2 "" 1 "" {TEXT -1 58 "           \+
                       Firm created. FirmKey, 1" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 9 "print(_);" }}{PARA 2 "" 1 "" {TEXT -1 86 "table
(monitor2, [\n\n    (K, 1, 1) = 91.33\n\n    (A, 1, 1) = .16\n\n    ne
wFirm = 1\n\n    ])" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "We now mak
e another firm to allow for Schumpeterian competition:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "CreateFirm(91.33,.16);" }}{PARA 2 "
" 1 "" {TEXT -1 58 "                                  Firm created. Fi
rmKey, 2" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 15 "Output decision" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 124 "The firm is now ready for making \+
its first decision. This concerns output. The decision-making rule is \+
simply that the firm " }{XPPEDIT 18 0 "i" "I\"iG6\"" }{TEXT -1 51 " pr
oduces as much as possible in any given period (" }{XPPEDIT 18 0 "t" "
I\"tG6\"" }{TEXT -1 17 "). The output is " }{XPPEDIT 18 0 "Q[i,t]" "&%
\"QG6$%\"iG%\"tG" }{TEXT -1 47 " or, in relation to the global table, \+
_[Q,i,t]." }}}{EXCHG {PARA 0 "> " 0 "FirmOutput" {MPLTEXT 1 0 69 "Firm
Output := proc(i,t)\nglobal _;\n_[Q,i,t] := _[A,i,t]*_[K,i,t];\nend:" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "FirmOutput(1,1);" }}
{PARA 2 "" 1 "" {TEXT -1 49 "                                         \+
 14.6128" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "FirmOutput(2,1)
;" }}{PARA 2 "" 1 "" {TEXT -1 49 "                                    \+
      14.6128" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 38 "Industry-level
 supply and market price" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 291 "Let u
s now consider what happens in the short run at the market level. In t
he Nelson and Winter model this is quite simple (because our analytica
l interest is concentrated on other issues). First we find total suppl
y. Then we find the market price in a market with unit elasticity of d
emand:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "Supply := proc(t)
\nglobal _;\nlocal i;\n_[TQ,t] := add(_[Q,i,t], i=1.. _[newFirm]);\nen
d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Supply(1);" }}{PARA 
2 "" 1 "" {TEXT -1 49 "                                          29.22
56" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Price := proc(t)\nglo
bal _;\n_[P,t] := _[Revenue]/_[TQ,t];\nend:" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 72 "Before we can find the price, we need to define the par
ameter \"Revenue\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "_[Re
venue] := 67;" }}{PARA 2 "" 1 "" {TEXT -1 54 "                        \+
              _[Revenue] := 67" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 9 "Price(1);" }}{PARA 2 "" 1 "" {TEXT -1 51 "                     \+
                   2.292510676" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 
18 "Firm-level profits" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "We can n
ow calculate the firm's profits per unit of capital." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 149 "Profit := proc(i,t)\nglobal _;\nlocal co
sts, revenue;\ncosts := _[c] + _[r_in] + _[r_im];\nrevenue := _[P,t]*_
[A,i,t];\n_[pi,i,t] := revenue - costs;\nend:" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 211 "This function depends on three parameters. We give th
em values taken from Nelson and Winter - but not adapted to the two-fi
rm case. This means that we should not expect the model to be in an in
itial equilibrium." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "_[c] \+
:= .16;\n_[r_in] := 0.00112;\n_[r_im] := 0.0223;" }}{PARA 2 "" 1 "" 
{TEXT -1 51 "                                        _[c] := .16" }}
{PARA 2 "" 1 "" {TEXT -1 54 "                                     _[r_
in] := .00112" }}{PARA 2 "" 1 "" {TEXT -1 54 "                        \+
              _[r_im] := .0223" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "Profit(1,1); Profit(2,1);" }}{PARA 2 "" 1 "" {TEXT -1 51 "    \+
                                    .1833817082" }}{PARA 2 "" 1 "" 
{TEXT -1 51 "                                        .1833817082" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 187 "We see that each firm makes a pro
fit in the initial period. However, let ud make a couple of new firms \+
of the same size as the two pervious ones, and consider the consequenc
e for profits:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "CreateFir
m(91.33,.16); CreateFirm(91.33,.16);" }}{PARA 2 "" 1 "" {TEXT -1 58 " \+
                                 Firm created. FirmKey, 3" }}{PARA 2 "
" 1 "" {TEXT -1 58 "                                  Firm created. Fi
rmKey, 4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "FirmOutput(3,1)
; FirmOutput(4,1);" }}{PARA 2 "" 1 "" {TEXT -1 49 "                   \+
                       14.6128" }}{PARA 2 "" 1 "" {TEXT -1 49 "       \+
                                   14.6128" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 10 "Supply(1);" }}{PARA 2 "" 1 "" {TEXT -1 49 "        \+
                                  58.4512" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "Price(1);" }}{PARA 2 "" 1 "" {TEXT -1 51 "          \+
                              1.146255338" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 37 "for i from 1 to 4 do Profit(i,1); od;" }}{PARA 2 "
" 1 "" {TEXT -1 52 "                                        -.00001914
59" }}{PARA 2 "" 1 "" {TEXT -1 52 "                                   \+
     -.0000191459" }}{PARA 2 "" 1 "" {TEXT -1 52 "                    \+
                    -.0000191459" }}{PARA 2 "" 1 "" {TEXT -1 52 "     \+
                                   -.0000191459" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 146 "With the set-up of new firms, the capacity of the i
ndustry fits the fixed level of revenue in a way that profits become p
ractically equal to zero." }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 35 "Se
arch for and choice of technology" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
123 "The simulation of innovation and imitation depends on Maple's ran
dom nummer generators (see the section on random numbers)." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 53 "A firm can obtain a new level of producti
vity (a new " }{XPPEDIT 18 0 "A" "I\"AG6\"" }{TEXT -1 166 ") either in
 a direct (innovative) or in an indirect (imitative) way. The chances \+
of obtaining success depends on the firm's level of innovative R&D and
 imitative R&D." }}}{EXCHG {PARA 0 "> " 0 "Innovate" {MPLTEXT 1 0 137 
"Innovation := proc(i,t)\nglobal _;\nlocal innoResearch;\ninnoResearch
 := _[r_in]*_[K,i,t];\n_[A_in,i,t] := InnoResult(i,t,innoResearch);\ne
nd:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 138 "The Innovation procedure \+
depends on a procedure (InnoResult) that we have not defined yet. Furt
hermore, we have not specified the size of " }{XPPEDIT 18 0 "r[n]" "&%
\"rG6#%\"nG" }{TEXT -1 126 ". Therefore, it is still too early to call
 the procedure. Or, rather, we obtain a symbolic result instead of a n
umeric result:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Innovatio
n(1,1);" }}{PARA 2 "" 1 "" {TEXT -1 59 "                              \+
   InnoResult(1, 1, .1022896)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "
Before we define the missing procedure and parameter, we define how a \+
firm makes an Imitation:" }}}{EXCHG {PARA 0 "> " 0 "Imitate" {MPLTEXT 
1 0 131 "Imitation := proc(i,t)\nglobal _;\nlocal imiResearch;\nimiRes
earch := _[r_im]*_[K,i,t];\n _[A_im,i] := ImiResult(i,t,imiResearch);
\nend:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 174 "Whether the results of
 the firm's innovative and imitative search are successful or unsucces
sful, they can be used in determinining the technology applied in the \+
next period." }}}{EXCHG {PARA 0 "> " 0 "TechnoChoice" {MPLTEXT 1 0 95 
"TechnoChoice := proc(i,t)\nglobal _;\n_[A,i,t+1] := max(_[A,i,t], _[A
_in,i,t], _[A_im,i,t]);\nend:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 
58 "\"Techno space\" for innovation and industry-level imitation" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 127 "To determine innovations and imit
ations we need to be sure that the random package is loaded. Furthermo
re, we define the _seed:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 
"with(stats[random]): _seed := 1;" }}{PARA 2 "" 1 "" {TEXT -1 51 "    \+
                                     _seed := 1" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 247 "The space in which firms search for innovations can
 be constructed in different ways. Major alternatives depict science-b
ased search and cumulative-technology search. Let us put both alternat
ives into the definition of the procedure \"InnoResult\". " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 458 "InnoResult := proc(i,t,effort)\ngl
obal _;\nlocal lambda, draws, mean,lnResult;\nlambda := _[d_in]*effort
;\ndraws := poisson[lambda]();\nif draws > 0 then\n   if _[searchType]
 = cumulative then\n      mean := ln(_[A,i,t]);\n      lnResult := nor
mald[mean,_[sigma_in]]();\n      _[A_in,i,t] := exp(lnResult);\n   els
e\n      mean := ln(_[A_mean,t]);\n      lnResult := normald[mean,_[si
gma_in]]();\n      _[A_in,i,t] := exp(lnResult);\n   fi;\nelse _[A_in,
i,t] := 0;\nfi;\nend:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "The imit
ation procedure is simpler:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
194 "ImiResult := proc(i,t,effort)\nglobal _;\nlocal lambda, draws;\nl
ambda := _[d_im]*effort;\ndraws := poisson[lambda]();\nif draws > 0 th
en\n   _[A_im,i,t] := _[A_max,t];\nelse _[A_im,i,t] := 0;\nfi;\nend:" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "We need to specify some paramet
ers before these procedures can be called by the firms:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "_[searchType] := cumulative;" }}
{PARA 2 "" 1 "" {TEXT -1 59 "                                _[searchT
ype] := cumulative" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "_[d_i
n] := 0.3;" }}{PARA 2 "" 1 "" {TEXT -1 52 "                           \+
            _[d_in] := .3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "_[d_im] := 0.3;" }}{PARA 2 "" 1 "" {TEXT -1 52 "                  \+
                     _[d_im] := .3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "_[sigma_in] := 0.2;" }}{PARA 2 "" 1 "" {TEXT -1 54 " \+
                                    _[sigma_in] := .2" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 58 "We also need to find the firm with the le
ading technology:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "Maximu
m := proc(t)\nglobal _;\n_[A_max,t] := max(seq(_[A,i,t], i=1.._[newFir
m]));\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Maximum(1);
" }}{PARA 2 "" 1 "" {TEXT -1 47 "                                     \+
       .16" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 31 "Firms' innovation
 and imitation" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "The firms can no
w try the innovative and imitative lotteries. We start with firm #1 in
 period 1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Innovation(1,
1);" }}{PARA 2 "" 1 "" {TEXT -1 46 "                                  \+
           0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "We were unlucky. \+
However, with another seed we obtain an innovation:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "_seed := 21: Innovation(1,1);" }}{PARA 2 
"" 1 "" {TEXT -1 51 "                                        .18600565
42" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Imitation(1,1);" }}
{PARA 2 "" 1 "" {TEXT -1 47 "                                         \+
   .16" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Innovation(2,1); \+
Imitation(2,1);" }}{PARA 2 "" 1 "" {TEXT -1 46 "                      \+
                       0" }}{PARA 2 "" 1 "" {TEXT -1 47 "             \+
                               .16" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "Innovation(3,1); Imitation(3,1);" }}{PARA 2 "" 1 "" 
{TEXT -1 46 "                                             0" }}{PARA 
2 "" 1 "" {TEXT -1 46 "                                             0
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Innovation(4,1); Imitat
ion(4,1);" }}{PARA 2 "" 1 "" {TEXT -1 46 "                            \+
                 0" }}{PARA 2 "" 1 "" {TEXT -1 47 "                   \+
                         .16" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 175 "
In this sequence the are three firms that obtain an imitation (with a \+
boring value) and one firm that obtain an innovation. This is reflecte
d in the TechnoChoice of the firms:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 77 "TechnoChoice(1,1); TechnoChoice(2,1);\nTechnoChoice(3
,1); TechnoChoice(4,1);  " }}{PARA 2 "" 1 "" {TEXT -1 51 "            \+
                            .1860056542" }}{PARA 2 "" 1 "" {TEXT -1 
47 "                                            .16" }}{PARA 2 "" 1 "
" {TEXT -1 47 "                                            .16" }}
{PARA 2 "" 1 "" {TEXT -1 47 "                                         \+
   .16" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 11 "New Capital" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 330 "Now we come to the investment pro
cess. The ability to invest depends on the profits in the present peri
od. Banks can improve the situation but are also using profits as thei
r criteria. The willingness to invest depends on the expected mark-up \+
over costs in the next period (i.e. possibly using the new technology \+
in the estamate)." }}}{EXCHG {PARA 0 "> " 0 "MaxInvest" {MPLTEXT 1 0 
168 "MaxInvest := proc(i,t)\nglobal _;\nif _[pi,i,t] <= 0 then _[loans
,i] := 0;\nelse _[loans,i] :=  _[b]*_[pi,i,t];\nfi;\n_[I_max,i,t] := _
[delta] + _[pi,i,t] + _[loans,i];\nend:" }}}{EXCHG {PARA 0 "> " 0 "Des
iredInvest" {MPLTEXT 1 0 195 "DesiredInvest := proc(i,t)\nglobal _;\n_
[s,i,t] := _[Q,i,t]/_[TQ,t];\n_[rho,i] := _[c]/(_[P,t]*_[A,i,t+1]);\n_
[I_des,i,t] := _[delta] + 1 \n                 - _[eta]/(_[eta] - _[s,
i,t])*_[rho,i];\nend:" }}}{EXCHG {PARA 0 "> " 0 "ChangeCapital" 
{MPLTEXT 1 0 185 "ChangeCapital := proc(i,t)\nglobal _;\nlocal Inv;\n_
[constraint,i,t] := min(_[I_des,i,t], _[I_max,i,t]);\nInv := max(0, _[
constraint,i,t]);\n_[K,i,t+1] := _[K,i,t]*(Inv + 1 - _[delta]);\nend:
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Before we can run these proce
dures we need to define some new parameters:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "_[b] := 1.0;" }}{PARA 2 "" 1 "" {TEXT -1 51 "   \+
                                     _[b] := 1.0" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 17 "_[delta] := 0.03;" }}{PARA 2 "" 1 "" {TEXT 
-1 53 "                                      _[delta] := .03" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "_[eta] := 1;" }}{PARA 2 "" 
1 "" {TEXT -1 51 "                                        _[eta] := 1
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "MaxInvest(1,1); Desired
Invest(1,1); ChangeCapital(1,1);" }}{PARA 2 "" 1 "" {TEXT -1 51 "     \+
                                   .0299808541" }}{PARA 2 "" 1 "" 
{TEXT -1 51 "                                         .029421419" }}
{PARA 2 "" 1 "" {TEXT -1 51 "                                        9
1.27715820" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "MaxInvest(2,1
); DesiredInvest(2,1); ChangeCapital(2,1);" }}{PARA 2 "" 1 "" {TEXT 
-1 51 "                                        .0299808541" }}{PARA 2 
"" 1 "" {TEXT -1 51 "                                        -.1332079
60" }}{PARA 2 "" 1 "" {TEXT -1 49 "                                   \+
       88.5901" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 277 "For the first \+
firm the innovation means that the firm wants to invest, but investmen
t is smaller than depreciation so capital becomes smaller. In the seco
nd case mark-up is considered insufficient. Therefore no investment ta
kes place, and capital decreases by the depreciation." }}}}{SECT 0 
{PARA 4 "" 0 "" {TEXT -1 10 "Parameters" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 122 "We have defined the parameters successively. Here is a p
rocedure that contains them all. It makes parameter change easier:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 373 "Parameters := proc()\nglob
al _;\n_[b]         :=   1       ;\n_[c]         :=   0.16    ;\n_[del
ta]     :=   0.03    ;\n_[Revenue]   :=   67      ;\n_[d_im]      :=  \+
 0.3     ; \n_[d_in]      :=   0.3     ;\n_[eta]       :=   1       ;
\n_[phi]       :=   0.05    ; \n_[r_im]      :=   0.00112 ;\n_[r_in]  \+
    :=   0.0223  ;\n_[searchType]:= cumulative;\n_[sigma_in]  :=   0.2
     ;\nend:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 41 "The evolution o
f an industry in t periods" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 132 "Now
 we can define a procedure that uses the specification of the individu
al decisions etc. to simulate the evolution of an industry:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 511 "NelwinDecomp := proc(n,T,se
ed)\nglobal _, _seed;\nlocal i,t;\nwith(stats[random]);\n_seed := seed
;\n_[newFirm] := 0;\nCreateTable();\nParameters();\nfor i from 1 to n \+
do\n   CreateFirm(91.33,.16);\nod;\nfor t from 1 to T do\n   for i fro
m 1 to n do\n      FirmOutput(i,t);\n   od;\n   Supply(t);\n   Price(t
);\n   Maximum(t);\n   for i from 1 to n do\n      Innovation(i,t);\n \+
     Imitation(i,t);\n      TechnoChoice(i,t);\n      Profit(i,t);\n  \+
    MaxInvest(i,t);\n      DesiredInvest(i,t);\n      ChangeCapital(i,
t);\n   od;\nod;\nend:" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 27 "Mode
l run and data analysis" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 40 "The ti
me-consuming simulation excersises" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
340 "We start by running the model for a relative low number of firms \+
and periods. The reason is that Maple is very slow compared to e.g. C+
+. Make the run and study the time it takes at your computer system. (
REMARK: At the moment the parameters are adapted to 4 firms.) In our f
irst call we use the arguments: firms = 4, periods = 4, seed = 1." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "NelwinDecomp(4,4,1);" }}
{PARA 2 "" 1 "" {TEXT -1 51 "                                        8
3.35282919" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 28 "Procedures for da
ta plotting" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 185 "To ease the analys
is of the results of evolutionary simulations, Andersen et al. (DRUIDI
C) have made a series of helping procedures. Here are  a couple for pl
otting of time series data." }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 60 "P
rocedure that plots a time series for a firm-level variable" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 337 "This procedure draws time series data fo
r the firms of the industry. In order to allow simple comparisons acro
ss time series for different variables, each firm is given a specific \+
colour that is the same in all plots. (The procedure can easily be ext
ended with new features, like plotting over specific ranges of firms a
nd periods, etc.)" }}}{EXCHG {PARA 0 "> " 0 "DrawVariable" {MPLTEXT 1 
0 626 "DrawVariable := proc(var,firmno,periods)\nglobal peri,plotdata,
text;\nlocal colour,tt,t,n,a,Num,Per;\noption `ES Andersen, Aalborg Un
iversity, 1 Sep 96`;\nif nargs = 3 then\n   Num := firmno;\n   Per := \+
periods;\nelse\n   Num := _[N];\n   Per := _[T];\nfi;\nperi := seq(t, \+
t = 1..Per);\ncolour := seq('COLOUR'(HUE,n/Num), n=1..Num);\na:=NULL;
\nfor n from 1 to Num do\n\011a := a, 'CURVES'([seq(MergeLists([peri[t
t]],\n      [_[var,n,tt]]),tt=1..Per)],colour[n],THICKNESS(2));\nod;\n
\ntext := cat(`Variable `,var,` for `, Num, ` firms and `, Per, ` peri
ods.`);\nplotdata := 'PLOT'(a, 'TITLE'(text), AXESSTYLE(NORMAL), AXEST
ICKS(5,5));\nplotdata;\n\nend:" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 
57 "Function that helps the creation of a PLOT data structure" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "This procedure performs a subtask \+
for the DrawVariable procedure, namely to create data points." }}}
{EXCHG {PARA 0 "> " 0 "MergeLists" {MPLTEXT 1 0 527 "MergeLists := pro
c(list1, list2)\nlocal LookUpItem,i;\noption `ES Andersen, Aalborg Uni
versity, 24 Aug 96`;\n\n\011LookUpItem := proc(list1, list2, seriesnum
ber)\n\011local listnumber;\n\011if type(seriesnumber, even) then\n
\011\011listnumber := seriesnumber/2;\n\011\011RETURN(list1[listnumber
]);\n\011else\n\011\011listnumber := (seriesnumber-1)/2;\n\011\011RETU
RN(list2[listnumber]);\n\011fi;\n\011end;\n\011\nif not nops(list1) = \+
nops(list2) then\n\011ERROR(`the number of elements in lists must be t
he same`);\nfi;\n[seq(LookUpItem(list1, list2, i), \n\011\011\011\011i
 = 2..nops(list1)*2 + 1)];\011\nend:" }}}}{SECT 0 {PARA 4 "" 0 "" 
{TEXT -1 16 "Legend for plots" }}{EXCHG {PARA 0 "> " 0 "Legend" 
{MPLTEXT 1 0 449 "Legend := proc(N)\nglobal periods,plotdata,text;\nlo
cal colour,i,n,a,b;\noption `ES Andersen, Aalborg University, 28 Aug 9
6`;\n\ncolour := seq('COLOUR'(HUE,n/N), n=1..N);\na:=NULL; b := NULL;
\nfor n from 1 to N do\n\011a := a, 'CURVES'([[0,N-n],[10,N-n]],\n    \+
colour[n],THICKNESS(2));\n b := b, 'TEXT'([11,N-n],`Firm `.n,FONT(TIME
S,ROMAN,12));\nod;\n\ntext := cat(`Legend for `,N,` firms`);\nplotdata
 := 'PLOT'(a, b, 'TITLE'(text), AXESSTYLE(NONE));\nplotdata;\n\nend:" 
}}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 28 "Plots of core firm variables
" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 135 "Let us make a new simulaton a
nd analyse the results. We call \"StructuredNelwin\" with the argument
s: firms = 4, periods = 16, seed = 17." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "NelwinDecomp(4,16,17):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 150 "We now use the plot procedures to draw core variables fo
r firms. To get a plot for all firms and all periods, simple give a va
riable name as argument." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 
"DrawVariable(A,4,16); DrawVariable(constraint,4,16);" }}{PARA 13 "" 
1 "" {INLPLOT "6)-%'CURVESG6%727$\"\"\"$\"#;!\"#7$\"\"#F)7$\"\"$F)7$\"
\"%F)7$\"\"&F)7$\"\"'F)7$\"\"($\"+(ed+s\"!#57$\"\")$\"+VkUu<F:7$\"\"*F
=7$\"#5F=7$\"#6F=7$\"#7F=7$\"#8$\"+X)p*\\=F:7$\"#9$\"+'\\i^'>F:7$\"#:F
M7$F*FM-%'COLOURG6$%$HUEG#F(F1-%*THICKNESSG6#F--F$6%72F'7$F-$\"+=$R'H;
F:7$F/Fhn7$F1$\"+0-qK>F:7$F3F\\o7$F5F\\o7$F7F\\o7$F<F\\o7$F@F\\o7$FBF
\\o7$FDF\\o7$FFF\\o7$FH$\"+>9'Qe#F:7$FLFgo7$FP$\"+6x$Q%HF:7$F*F[p-FS6$
FU#F(F-FW-F$6%72F'7$F-$\"+fe!R=#F:7$F/Fep7$F1Fep7$F3Fep7$F5Fep7$F7Fep7
$F<Fep7$F@$\"+O$R_[#F:7$FBF^q7$FDF^q7$FFF^q7$FHF^q7$FLF[p7$FP$\"+3j#Gv
$F:7$F*Ffq-FS6$FU#F/F1FW-F$6%72F'F,F.F0F2F47$F7F)7$F<F)7$F@F)7$FBF)7$F
DF)7$FFF)7$FHF)7$FLF)7$FPF)7$F*F)-FS6$FUF(FW-%&TITLEG6#%GVariable~A~fo
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