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Background of equation:

I'm trying to apply Agent-based Computational Economics on NetLogo. But I'm struggling with coding an integral equation (her: /int):

Yt = Ls ^1-ε · [/int between upper Qt+1 and lower Qt] x(qt)^ε dqt

Consider a country with Ls of high-skilled workers and a measure Lu of low-skilled workers. At any time t, a representative firm assembles an aggregate consumption good Yt by using high-skilled labor and a measure of size one of differentiated intermediate goods. Firms are ordered by the efficiency of automated processes in production. Specifically, let qt be the continuous firm-specific efficiency of automation in production and let x(qt) denote the quantity of an intermediate input in final goods production. Then, assuming a Cobb-Douglas technology final goods production function which is given by... (see: screenshot) ε ∈ (0, 1) is the elasticity of output with respect to intermediate inputs.

My question:

Is NetLogo able to solve this or do I need to use an extension such as R or Mathematica?

THANKS A LOT!

breed [ firm firms ]

globals [   
; defines global variables or parameters and are accessible anywhere in the model by all agents
  t     ; time
  Ls    ; high-skilled labour
  Lu    ; low-skilled labour
  Yt    ; representative firm assembles an aggregate consumption good
  qt    ; continous firm-specific efficiency of automation in production
  x-qt  ; quantity of an intermediate input in final goods production
  Qt    ; efficiency in automation of the least productive firm
  Qt+1  ; efficiency in automation of the most productive firm
]

to setup
  clear-all  
  clear-all-plots 
  ask patches [ set pcolor white ]   ;; creates blank background

  create-firms n-firms [   ; number of firms in slider
    setxy random-xcor random-ycor   ;; distributes the firms randomly
    set size 1
    set shape "house"
    set color grey
    set Yt   ; adds firm-specific variable of output  
    set qt   ; adds firm-specific variable of efficiency of automation
    set x-qt   ; adds firm-specific variable of input needed
  ]
  reset-ticks   ; resets the tick counter to zero
end
Community
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user11277648
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  • NetLogo cannot solve differential equations. I don't understand enough of what you are trying to do, but many problems that you might think of as solving differential equations are not 'solved' in NetLogo but are stepped through. That is, at each time step, you directly calculate the new value of something based on the current values of the contributing variables. – JenB Mar 30 '19 at 09:36
  • As a simple example, you would never calculate the cumulative sum of a variable, it is sufficient to simply add the value for the new time step to the sum calculated at the previous time step and stored in a variable. – JenB Mar 30 '19 at 09:37
  • Thank you for your comments. I'm relatively new to NetLogo but I'm trying to explain an economic phenomenon which has been conceptualised in an econometric equation by "translating" it into NetLogo. It seem that I'm lacking a handbook with rules of thumb for agent-based computational economics. – user11277648 Apr 01 '19 at 13:55
  • Could you recommend one by any chance? – user11277648 Apr 01 '19 at 13:55
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    I'm not an economist, but a simple google search gets you to https://www.amazon.co.uk/Agent-Based-Modelling-Economics-Lynne-Hamill/dp/1118456076 and it has Cobb-Douglas in the index – JenB Apr 01 '19 at 14:17
  • Thanks I have found the same already – user11277648 Apr 03 '19 at 10:03

0 Answers0