globals [ price num-adopted prev-num-adopted ] breed [agents agent] agents-own [ a-threshold tech ] to setup clear-all setup-pop setup-environment make-decisions update-plots update-histogram end to setup-pop create-agents Population-Size [ if Threshold-Method = "Normal" [ set a-threshold random-normal Thres-Param1 Thres-Param2 while [(a-threshold < 0) or (a-threshold > max-pxcor)] [set a-threshold random-normal Thres-Param1 Thres-Param2] ] if Threshold-Method = "Log Normal" [ set a-threshold exp ( random-normal Thres-Param1 Thres-Param2 ) while [(a-threshold < 0) or (a-threshold > max-pxcor)] [set a-threshold exp ( random-normal Thres-Param1 Thres-Param2 )] ] setxy a-threshold random-ycor set tech 0 ] end to setup-environment set price max-pycor set num-adopted 0 set prev-num-adopted 0 end to update-histogram set-current-plot "Thresholds-Histogram" set-plot-x-range 0 int (0.5 + max [a-threshold] of agents) histogram [a-threshold] of agents end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to go if Tech-Dynamics-Method = "Exponential Decay" [ set price max-pxcor * exp (- TD-Param1 * ticks) ] if Tech-Dynamics-Method = "Linear Decay" [ set price max-pxcor - (TD-Param2 * ticks) ] if Tech-Dynamics-Method = "Fixed" [ set price max-pxcor / 2 ] make-decisions if price < 0 [stop] tick update-plots if ((num-adopted = Population-Size) and (num-adopted = prev-num-adopted)) [stop] end to make-decisions ask agents [ if-else price > a-threshold [ set tech 0 set color red ] [ set tech 1 set color green ] ] set num-adopted count agents with [tech = 1] end to update-plots set-current-plot "Environment" plot price set-current-plot "Adoption" plot num-adopted if ticks mod Output-Every-n-Ticks = 0 [ set-current-plot "Adoption-Rate" set-plot-pen-interval Output-Every-n-Ticks plot ((num-adopted - prev-num-adopted) / Output-Every-n-Ticks) set prev-num-adopted num-adopted ] end @#$#@#$#@ GRAPHICS-WINDOW 210 10 482 303 -1 -1 2.6 1 10 1 1 1 0 0 0 1 0 100 0 100 0 0 1 ticks INPUTBOX 5 55 160 115 Population-Size 1000 1 0 Number CHOOSER 5 119 143 164 Threshold-Method Threshold-Method "Normal" "Log Normal" 1 INPUTBOX 5 168 84 228 Thres-Param1 2 1 0 Number INPUTBOX 86 168 165 228 Thres-Param2 1 1 0 Number CHOOSER 5 278 159 323 Tech-Dynamics-Method Tech-Dynamics-Method "Exponential Decay" "Linear Decay" "Fixed" 0 INPUTBOX 5 327 84 387 TD-Param1 0.1 1 0 Number INPUTBOX 86 327 165 387 TD-Param2 1 1 0 Number TEXTBOX 7 8 202 56 Probit Model of Technological Diffusion 16 0.0 1 BUTTON 209 318 273 351 Setup setup NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 209 357 272 390 Go (Once) go NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 209 396 272 429 Go go T 1 T OBSERVER NIL NIL NIL NIL PLOT 487 10 687 160 Environment Time (ticks) Price 0.0 10.0 0.0 10.0 true false PENS "Cost" 1.0 0 -2674135 true PLOT 487 164 687 314 Adoption Time (ticks) # Adopters 0.0 10.0 0.0 10.0 true false PENS "default" 1.0 0 -16777216 true PLOT 487 319 687 469 Adoption-Rate Time (ticks) # New Adopters 0.0 10.0 0.0 10.0 true false PENS "default" 1.0 0 -16777216 true INPUTBOX 690 319 845 379 Output-Every-n-Ticks 4 1 0 Number PLOT 281 319 481 469 Thresholds-Histogram Adoption Thresholds Frequency 0.0 10.0 0.0 10.0 true false PENS "default" 1.0 1 -16777216 true MONITOR 5 231 129 276 Exp (Thres-Param1) exp Thres-Param1 17 1 11 TEXTBOX 5 391 155 409 Expon. only 11 0.0 1 TEXTBOX 86 389 236 407 Linear only 11 0.0 1 @#$#@#$#@ WHAT IS IT? ----------- A "Probit" or "Rank" model of diffusion of a innovation or new technology. Unlike an epidemic model of diffusion, in the Probit model agents are all aware of the innovative technology at the start, but differ in their adoption because of differences in their own attributes. E.g. firms differ in size, and larger firms may learn how to use a technology earlier. Agents make decisions concerning whether or not to adopt the technology. The technology starts off expensive, but over time its price falls. Each agent has its own threshold value for the technology's cost below which the agent will decide to adopt the technology. HOW IT WORKS ------------ Agents are initialised with threshold values sampled at random from a given distribution. Each time tick all agents renew their decision to adopt or not. Each time tick the cost of the technology changes according to some given function. On the World screen, agents' x-coordinates are used to represent their adoption threshold. HOW TO USE IT ------------- Select the methods for threshold setting and technology dynamics, and choose suitable parameters. THINGS TO NOTICE ---------------- For some combinations of threshold distribution and technology dynamics the number of adopters over time may form an s-shaped curve, and the rate of adoption may form a bell-shaped curve. THINGS TO TRY ------------- In particular, try "Normal" for thresholds and "Linear" for technology dynamics. Then try "Log Normal" and "Exponential". (Don't forget you may need to change the parameters for the thresholds method!) What happens if you have log normal thresholds, but linear change? EXTENDING THE MODEL ------------------- This model considered only one changing factor - price. What about the benefits of adopting technology? (Use an agent's y-coordinate to represent this visually.) Agents adopt if the technology is profitable - i.e. benefits > costs. What methods should we use for benefits as opposed to costs? NETLOGO FEATURES ---------------- RELATED MODELS -------------- Compare with diffusion models based on the notion of diffusion as an epidemic, or adoption because of word-of-mouth advertising. CREDITS AND REFERENCES ---------------------- For more on Probit models, and other models of technological diffusion, see chapter 3 in: Stoneman, Paul (2002) "The Economics of Technological Diffusion" Blackwell Publishers: Oxford. @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 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