;I define global variables globals [ ticks n_d n_s numb demand1 supply1 demand2 supply2 a_aggregate b_aggregate c_aggregate d_aggregate p_equilibrio q_equilibrio ] ;I define 2 breeds : buyers and sellers breed [buyers buyer] breed [sellers seller] turtles-own [ choice ] ; I define turtles own variables buyers-own [a b] ; I define buyers own variables sellers-own [c d] ; I define sellers own variables to setup ; I define setup function clear-all ; clear all set ticks 0 ; set counter 0 setup-turtles ; execute the function "setup-turtles" setup-function end to setup-turtles create-turtles number ; it creates a number of turtles equal to the one assigned by the slider "number" ask turtles [ setxy random-xcor random-ycor ; I set the position of the turtles in a random way set shape "person"] ; I set the shape of turtles end to setup-function ask turtles[ set choice random-float 1] ;I use variable "choice" to define if a turtle is "buyer" or "seller" end to go if ticks >= number-of-steps [ stop ] ; simulation stops if the number of steps is >= than slider value called "number-of-steps" set ticks ticks + 1 ; add 1 to the counter setup-function move-turtles do-mean do-plots if limit-speed? [ wait 0.6 ] ; wait the given number of seconds (if the switch is "on") end to move-turtles ask turtles [ if choice < 0.5 [ set breed buyers ; if variable "choice" is < 0,5 turtle is buyer and takes green color, otherwise turles is seller and takes red color set a (alfa + ((random-float 1) - 0.5)* w ) ; in this way "a" depends from "alfa" + a random variable (-0,5,0,5) with mean 0, that is multiplied by w, ;w defines the range of variation set b (-10 + ((random-float 1) - 0.5)* k ) set shape "person" set color green ] if choice > 0.5 [ set breed sellers set c (gamma + ((random-float 1 )- 0.5)* z) set d (10 + ((random-float 1 )- 0.5)* j) set shape "person" set color red ] move ] end to move rt ((random-float 1 )- 0.5)* 50 end to do-mean set n_d count buyers ; "n_d" counts the number of turtles that are buyers set n_s count sellers ; "n_s" counts the number of turtles that are sellers set numb n_s * n_d ask turtles [ set demand1 (sum values-from buyers [a + (b * 10)]) set demand2 (sum values-from buyers [a + (b * 20)]) set supply1 (sum values-from sellers [c + (d * 10)]) set supply2 (sum values-from sellers [c + (d * 20)]) set a_aggregate (demand1 - 10 * (demand2 - demand1)/(20 - 10)) set b_aggregate (demand2 - demand1)/(20 - 10) set c_aggregate (supply1 - 10 * (supply2 - supply1)/(20 - 10)) set d_aggregate (supply2 - supply1)/(20 - 10) if numb > 0 [ set p_equilibrio ((c_aggregate - a_aggregate)/(b_aggregate - d_aggregate)) set q_equilibrio (a_aggregate + b_aggregate * p_equilibrio) ] if numb = 0 [set q_equilibrio 0 set p_equilibrio 0] ] end to do-plots set-current-plot "Equilibrium price" plot p_equilibrio set-current-plot "Equilibrium quantity" plot q_equilibrio end @#$#@#$#@ GRAPHICS-WINDOW 285 529 757 696 35 10 6.522 1 10 1 1 1 0 1 1 1 -35 35 -10 10 CC-WINDOW 5 710 769 805 Command Center 0 BUTTON 3 10 66 43 NIL setup NIL 1 T OBSERVER T NIL BUTTON 83 10 146 43 NIL go\n T 1 T OBSERVER T NIL MONITOR 99 424 173 473 NIL count sellers\n\n 3 1 SLIDER 185 41 277 74 number number 1 500 85 1 1 NIL SLIDER 40 144 132 177 alfa alfa 120 200 150 1 1 NIL SLIDER 143 144 235 177 gamma gamma 60 100 80 1 1 NIL MONITOR 191 424 263 473 NIL count buyers\n 3 1 MONITOR 27 423 77 472 NIL ticks\n 3 1 SLIDER 5 372 151 405 number-of-steps number-of-steps 0 50000 30000 100 1 NIL PLOT 286 10 760 243 Equilibrium price Time Price 0.0 700.0 0.0 50.0 true false PENS "p_equilibrio" 1.0 0 -2674135 true MONITOR 30 547 80 596 a* a_aggregate 3 1 MONITOR 91 547 141 596 b* b_aggregate 3 1 MONITOR 153 547 203 596 c* c_aggregate 3 1 MONITOR 216 547 266 596 d* d_aggregate 3 1 MONITOR 29 633 130 682 Equilibrium Price p_equilibrio 3 1 SWITCH 161 372 281 405 limit-speed? limit-speed? 1 1 -1000 MONITOR 149 633 272 682 Equilibrium Quantity q_equilibrio 3 1 PLOT 286 251 759 511 Equilibrium quantity Time Quantity 0.0 700.0 0.0 0.0 true false PENS "q_equilibrio" 1.0 0 -13791810 true SLIDER 68 272 160 305 w w 1 500 1.0 0.25 1 NIL SLIDER 68 306 160 339 z z 1 500 1.0 0.25 1 NIL SLIDER 175 272 267 305 k k 1 15 1.0 0.25 1 NIL SLIDER 175 307 267 340 j j 1 15 1.0 0.25 1 NIL TEXTBOX 38 115 263 135 Constant of demand and supply intercept: TEXTBOX 121 234 230 252 Control parameters: TEXTBOX 92 253 155 271 Intercepts TEXTBOX 195 253 256 271 Slopes TEXTBOX 188 10 285 38 Number of turtles TEXTBOX 33 522 268 541 Coefficients of aggregate supply and demand: TEXTBOX 14 287 55 315 Demand TEXTBOX 16 317 55 335 Supply @#$#@#$#@ WHAT IS IT? ----------- In a generic market the interactions between buyers and sellers can be simulated by observing single supply and demand functions and then aggregating them. This project simulates a simple market constituted by agents with linear single demand and supply functions. Aggregate demand and supply functions are then generated. The model evaluates equilibrium price and quantity at every step. HOW IT WORKS ------------ For every turtles (agents) a single linear demand or supply function is generated. Step by step every agent randomly choses to be either buyer or seller. Linear functions are generated according to the equation: y=a+bx : demand function y=c+dx : supply function where y is the quantity and x is the price. Single demand (supply) function is defined choosing values a,b (c,d) representing intercept and slope of the line. These values are random for every agent, and they are generated through uniformly distributed shocks in the parameters: set a (alfa + ((random-float 1) - 0.5)* w ) set b (-10 + ((random-float 1) - 0.5)* k ) for demand function, and set c (gamma + ((random-float 1 )- 0.5)* z) set d (10 + ((random-float 1 )- 0.5)* j) for supply function. To aggregate the functions, given two prices p1 and p2, single quantities are added up obtaining two points of the aggregate demand (supply): given these points of the aggregate demand (supply) the curve is obtained by interpolation. Setting aggregate demand equal to aggregate supply we obtain equilibrium price and quantity. HOW TO USE IT ------------- 1) Before SETUP it is possible to modify the following parameters with the appropriate sliders: NUMBER: number of agents ALFA: constant of demand function intercept GAMMA: constant supply function intercept W: to increase range of variation in single demand intercept K: to increase range of variation in single demand slope Z: to increase range of variation in single supply intercept J: to increase range of variation in single supply slope NUMBER-OF_STEPS: number of steps LIMIT-SPEED?: wait the given number of seconds (if the switch is "on") Except the slider NUMBER all others can be changed while the simulation is running. 2) Playing SETUP turtles are created. 3) Playing GO it will start the simulation. Equilibrium price and quantity are plotted at every step. THINGS TO NOTICE ---------------- Modifying parameters which influence intercepts, the equilibrium price and quantity have an increase in volatility, and a major increment in quantity is noticed. This parameter has been kept intentionally high to have variability in prices (but intercepts of some buyers or sellers could be negative). In the volume graph, instead, the increment of volatility is easily noticed even with many agents, and more clear with few ones. Hence, during the simulation, the variation of parameters alfa and gamma could be interpreted as a "shock" in aggregated demand and aggregated supply, which modify the equilibrium price. Increasing gamma, the main component for single supply functions, the function of aggregated supply is shifted up generating a decerease in the equilibrium price and an increase in equilibrium quantity. In the same way increasing alfa the aggregated demand function is shifted up, generating an increase in equilibrium price and equilibrium quantity. THINGS TO TRY ------------- Hence, during the simulation, the variation of parameters alfa and gamma could be interpreted as a "shock" in aggregated demand and aggregated supply, which modify the equilibrium price. Increasing gamma, the main component for single supply functions, the function of aggregated supply is shifted up generating a decerease in the equilibrium price and an increase in equilibrium quantity. In the same way increasing alfa the aggregated demand function is shifted up, generating an increase in equilibrium price and equilibrium quantity. EXTENDING THE MODEL ------------------- The model can be improved in different ways in order to show a more accurate and realistic market, for example, using agents with non-linear demand and supply function or using intelligent adaptive agents. [see "Terna, 2002A"]. RELATED MODELS -------------- This simulation is based upon the general concept in [Terna, Boero, Morini, Sonnessa "Modelli per la complessità. La simulazione ad agenti in economia". Ed. 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