breed [firms firm] breed [consumers consumer] consumers-own [ price_list purchases ] firms-own [ capacity quantity price profits quantity_left quantity_sold best_profits best_price profits0 future_price_correction0 future_price_correction cartel? ] to setup ca reset-ticks create-firms firms_number create-consumers consumers_number ask firms [ set capacity precision (random 100 + 1.5 * random-float 1 * consumers_number) 0 set price precision (random-float (max_reservation_price)) 2 set best_price price set quantity random (consumers_number) set profits 0 set best_profits 0 set cartel? false set shape "factory" setxy random-xcor random-ycor ] ask consumers [ set shape "person" set color blue set purchases (random max_quantity_purchased) + 1 set price_list n-values purchases [precision (2 * a + b + random-float max_reservation_price) 2] ;this condition is needed in order to have that the variable costs for one unit are covered setxy random-xcor random-ycor] run_consumers compute_profits end to go create_demand ifelse ex-post_price_revision [ex-post_correct_price] [correct_price] if ticks = 100 [create_cartel] cartel_quantity run_consumers compute_profits graph tick if ticks = 200 [stop] end to create_demand ; This procedure creates a decreasing reservation price vector which randomly evolves over time ask consumers[ let random_list n-values purchases [precision (random-float demand_growth ) 2] set price_list (map + price_list random_list) set price_list sort-by [?1 > ?2] price_list ] end to run_consumers ask consumers[ let counter 0 while [counter < purchases and count ((firms in-radius consumer_radius) with [quantity_left > 0]) != 0] [set heading random 360 fd random 2 set counter counter + 1 let counterparts (firms in-radius consumer_radius) with [quantity_left > 0] let counterparts1 counterparts with-min [price] let counterpart one-of counterparts1 if counterpart != nobody[ if [price] of counterpart <= item (counter - 1) price_list [ ask counterpart [ set quantity_left quantity_left - 1 set quantity_sold quantity_sold + 1 ] ] ] ] ] end to correct_price ask firms with [cartel? = false] [ set best_profits 0 let j 0 while [j < firms_number][ let p1 item j [price] of firms - random-float(1) - 0.5 if p1 <= 0 [set p1 0.01] let d1 (count consumers in-radius consumer_radius with [item 0 price_list >= p1]) / count firms in-radius consumer_radius let profits1 (d1 * p1 - a * d1 ^ 2 - b * d1 - c) if profits1 > best_profits [ set best_price p1 set quantity d1 set best_profits profits1] set j j + 1 ] if quantity > capacity [set quantity capacity] set quantity_left quantity set quantity_sold 0 set price precision (best_price)2 ] end to ex-post_correct_price ask firms with [cartel? = false] [ set future_price_correction0 precision (future_price_correction)2 if profits = profits0 [ set future_price_correction random-float 1 - 0.5] if profits > profits0 [ if future_price_correction0 >= 0 [set future_price_correction precision (random-float 10)2] if future_price_correction0 < 0 [set future_price_correction precision ( -1 * random-float 10)2] ] if profits < profits0 [ if future_price_correction0 >= 0 [set future_price_correction precision ( -1 * random-float 10)2] if future_price_correction0 < 0 [set future_price_correction precision (random-float 10)2] ] set price precision (price + future_price_correction) 2 let p price set quantity count consumers in-radius consumer_radius with [item 0 price_list >= p] / count firms in-radius consumer_radius if quantity_sold = 0 [ set price p - 10 set future_price_correction -10] set quantity_left quantity set quantity_sold 0 if quantity > capacity [ set quantity capacity ] ] end to compute_profits ask firms [ set profits0 profits set profits precision (quantity_sold * price - a * quantity ^ 2 - b * quantity - c)2 ] end ;;;collusion part;;; ;creation of the cartel to create_cartel ask firms[ let % capacity * 100 / (sum [capacity] of firms) if % >= minimum_% [set cartel? true]] ask firms with [cartel? = false] [ set color red ] let p [] ;this condition is needed in order to know what is the higher price between the cartel firms ask firms with [cartel? = true] [ set color green set p lput price p set p sort-by [?1 > ?2] p ] let reservation [] ;I need also to know what's the highest reservation price in order to be able to check that the cartel price is below it. ask consumers [ set reservation lput item 0 price_list reservation set reservation sort-by [?1 > ?2] reservation ] ask firms with [cartel? = true] [ ;I ask to the cartel firms to set the same price equal to the higher price among them plus a surcharge set price item 0 p * (1 + cartel_%_surcharge / 100) if price > item 0 reservation [ set price item 0 reservation ] ] end to cartel_quantity ask firms with [cartel? = true] [ let p price set quantity count consumers in-radius consumer_radius with [item 0 price_list >= p] set quantity_left quantity set quantity_sold 0] end ;;;graphs;;; to graph plot_average_cartel_profits plot_avaragae_non_cartel_profits plot_number_of_cartellist plot_non_cartel_avarage_price plot_cartel_price plot_average_reservation_price end to plot_average_cartel_profits set-current-plot "profits" set-current-plot-pen "cartel firm avarage profits" let f count firms with [cartel? = true] if ticks > 40 [ ifelse f > 0 [plot sum [profits] of firms with [cartel? = true] / (1 * f)] [plot 0] ] end to plot_avaragae_non_cartel_profits set-current-plot "profits" set-current-plot-pen "non cartel firm avarage profits" let f count firms with [cartel? = false] if ticks > 40 [ ifelse f > 0 [plot sum [profits] of firms with [cartel? = false] / f] [plot 0] ] end to plot_number_of_cartellist set-current-plot "profits" set-current-plot-pen "cartel firms number" let f count firms with [cartel? = true] if ticks > 40 [plot f] end to plot_non_cartel_avarage_price set-current-plot "prices" set-current-plot-pen "non cartel avarage price" let f count firms with [cartel? = false] if ticks > 40 [ ifelse f > 0 [plot sum [price] of firms with [cartel? = false] / f] [plot 0] ] end to plot_cartel_price set-current-plot "prices" set-current-plot-pen "cartel price" let f count firms with [cartel? = true] if ticks > 40 [ ifelse f > 0 [plot sum [price] of firms with [cartel? = true] / f] [plot 0] ] end to plot_average_reservation_price set-current-plot "prices" set-current-plot-pen "average reservation price" let cons_num count consumers if ticks > 40 [ let temp [] ask consumers [ let element item 0 price_list set temp fput element temp] let s sum temp ifelse cons_num > 0 [plot s / cons_num] [plot 0] ] end @#$#@#$#@ GRAPHICS-WINDOW 210 10 649 470 16 16 13.0 1 10 1 1 1 0 1 1 1 -16 16 -16 16 0 0 1 ticks 30.0 SLIDER 18 162 190 195 a a 0 20 1.11 0.01 1 NIL HORIZONTAL SLIDER 18 200 190 233 b b 0 100 3.69 0.01 1 NIL HORIZONTAL SLIDER 18 238 190 271 c c 0 100 7.64 0.01 1 NIL HORIZONTAL SLIDER 18 278 190 311 consumers_number consumers_number 0 1000 1000 1 1 NIL HORIZONTAL SLIDER 18 318 190 351 firms_number firms_number 0 10 10 1 1 NIL HORIZONTAL SLIDER 17 359 194 392 max_reservation_price max_reservation_price 0 100 100 1 1 NIL HORIZONTAL SLIDER 19 397 191 430 max_quantity_purchased max_quantity_purchased 0 10 10 1 1 NIL HORIZONTAL SLIDER 19 436 191 469 consumer_radius consumer_radius 0 23 7 1 1 NIL HORIZONTAL BUTTON 18 10 104 43 NIL setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 117 10 198 43 NIL go T 1 T OBSERVER NIL NIL NIL NIL 1 TEXTBOX 28 143 178 161 cost function a*q^2 + b*q + c 11 0.0 1 BUTTON 117 66 198 99 NIL go NIL 1 T OBSERVER NIL NIL NIL NIL 1 SWITCH 206 476 376 509 ex-post_price_revision ex-post_price_revision 0 1 -1000 SLIDER 19 475 191 508 demand_growth demand_growth -5 5 0 0.01 1 NIL HORIZONTAL SLIDER 658 44 832 77 minimum_% minimum_% 0 100 8 1 1 NIL HORIZONTAL TEXTBOX 666 14 816 42 Minimum % of total capacity to be part of the cartel 11 0.0 1 TEXTBOX 74 112 145 130 Setup options\n 11 0.0 1 BUTTON 19 67 103 100 NIL create_cartel NIL 1 T OBSERVER NIL NIL NIL NIL 1 SLIDER 658 85 833 118 cartel_%_surcharge cartel_%_surcharge 0 100 5 1 1 NIL HORIZONTAL PLOT 657 122 1338 347 Profits NIL NIL 0.0 10.0 0.0 10.0 true true "" "" PENS "cartel firm avarage profits" 1.0 0 -13840069 true "" "" "non cartel firm avarage profits" 1.0 0 -2674135 true "" "" "cartel firms number" 1.0 0 -16644859 true "" "" PLOT 657 349 1338 552 Prices NIL NIL 0.0 10.0 0.0 10.0 true true "" "" PENS "cartel price" 1.0 0 -8330359 true "" "" "non cartel avarage price" 1.0 0 -2139308 true "" "" "average reservation price" 1.0 0 -16514813 true "" "" TEXTBOX 903 72 1265 100 The graphs will be displayed after 40 ticks 11 0.0 1 @#$#@#$#@ ## WHAT IS IT? The model tries to study the effect of cartels on competition. In order to have a realistic model I did not use a demand curve, but the demand is given by consumers, each one with his/her own reservation price and with a range within he/she looks for a seller. ## HOW IT WORKS In the world there are two agents: consumers and firms. The former confront their own reservation price with the price of the firms within their range. Consumers go randomly around and choose the lower price if this is lower than thei reservation and they exchange with the firm. Firms can be part or not of the cartel. In order to be part of the cartel a firm must have a production capacity above a certain threshold At the setup no firm is in the cartel. Such firms firstly decide the price on the basis of past profits: they verify if an increase in the price has led to increasing profits and they act accordingly. Firms in the cartel set price in a different way: they set the price as a percentage recharge on the highest price of cartels firms. Both types (collusive and not) are assumed to know perfectly the demand within their range (i.e. they know the reservation price of every consumer) and they set the quantity produced counting the consumers with a reservation price lower than their prices. ## HOW TO USE IT Users of the model may choose through the sliders the parameters of the cost function, the consumers and firms number, the maximum reservation price, the maximum amount of goods that a consumer can buy, the radius within which consumers look for a firm, the demand variability over time, the surcharge of the cartel, and minimum percentage of the total production to be part of the cartel. Users also decide when the cartel is created by pressing the button "create_cartel". ## THINGS TO TRY The main thing to try is to move the sliders in the interface, especially the radius, the surcharge of the cartel, the variability of the demand, the threshold to be part of the cartel and see what are the effects on the model. ## EXTENDING THE MODEL The model can be extended in many ways: with different criteria for setting up the cartel, adding the possibility to exit the cartel if it's no longer profitable. ## CREDITS AND REFERENCES Iwan Bos & Joseph E. Harrington, Jr, 2010. 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