manpreet Best Answer 2 years ago

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