Simple Linear First-Order Difference Equations for Cobweb Model (Shiny App)

server.R

library(shiny)

# s(k) = s(0) + b*p(k-1)
# d(k) = d(0) - a*p(k)
# p(k) = -b/a*p(k-1) + (d0-s0)/a

cobweb = function(params){
  # Create data frame of prices, and supply and demand stocks
  
  s0 = params[1]
  d0 = params[2]
  a  = params[3]
  b  = params[4]
  p0 = params[5]
  k  = params[6]
  
  # Initialize data frame as model
  model = data.frame(p = p0, s = s0, d = d0)
  
  # Iteratively calculate price and supply and demand for k iterations
  for(i in 1:k){
    # Calculate price at p(i+1)
    p_next = -b/a*model[i,'p'] + (d0 - s0)/a
    
    # Calculate demand at time i+1 from price at p(i+1)
    d_next = d0 - a * p_next
    
    # Calculate supply at time i+1 from price at p(i)
    s_next = s0 + b * model[i, 'p']
    
    # Add new values to our model data
    model = rbind(model, c(p_next, d_next, s_next))
  }
  return(model)
}


plot_cobweb = function(params){
  s0 = params[1]
  d0 = params[2]
  a  = params[3]
  b  = params[4]
  p0 = params[5]
  k  = params[6]
    
  # Create the model data up to k iterations
  model = cobweb(params)
  
  # Initialize plot
  plot_max = round((max(model)+5)/5)*5
  plot(c(0, plot_max), c(0, plot_max), ann=F, bty='n', type='n')
  title(xlab='Price', ylab='Units')
  
  # Plot supply-price curve
  abline(s0, b, col='blue', lwd=2)
  text(0, s0, 'Supply', col='blue', pos=3)
  
  # Plot demand-price curve
  abline(d0, -a, col='orange', lwd=2)
  text(0, d0, 'Demand', col='orange', pos=3)
  
  # Add cobweb
  for(i in 1:k){
    # Line segment from [p(i), s(i+1)] to [p(i+1), d(i+1)]
    segments(x0 = model[i,   'p'], y0 = model[(i+1), 's'], 
             x1 = model[i+1, 'p'], y1 = model[(i+1), 'd'],
             col=ifelse(i==k, 'red', 'black'))
    
    # Line segment from [p(i+1), d(i+1)] to [p(i+1), s(i+2)]
    segments(x0 = model[i+1, 'p'], y0 = model[i+1, 'd'],
             x1 = model[i+1, 'p'], y1 = model[i+2, 's'])
  }
}


# Shiny server functions that capture user input
# and call the functions above when user changes inputs
shinyServer(function(input,output) {
  sliderValues <- reactive({
    c(input$s0, input$d0, input$a, input$b, input$p0, input$k)
  })
  
  output$cobwebPlot <- renderPlot({
    plot_cobweb(sliderValues())
  })
  
  output$cobwebTable <- renderTable({
    cobweb(sliderValues())
  })
})

ui.R

library(shiny)

# Define UI for dataset viewer application
shinyUI(pageWithSidebar(
  
  # Application title
  headerPanel("Cobweb Model"),
  
  sidebarPanel(
    sliderInput('s0', 'Initial Supply s(0):',
                min = 0, max = 25, step = 1, value = 1),
    
    sliderInput('d0', 'Initial Demand d(0):',
                min = 0, max = 25, step = 1, value = 12),
    
    sliderInput('a', 'Demand price sensitivity (a):',
                min = 0, max = 2, step = 0.01, value = 1, ticks=F),
    
    sliderInput('b', 'Supply price sensitivity (b):',
                min = 0, max = 2, step = 0.01, value = 0.7, ticks=F),
    
    sliderInput('p0', 'Initial price p(0):',
                min = 0, max = 25, step = 0.25, value = 14),
    
    sliderInput('k', 'Iterations',
                min = 1, max = 15, step = 1, value = 1,
                animate=animationOptions(interval = 500, loop=T)),
    
    helpText('Based on the discrete-time cobweb model.',
             'Seems to work best if you set iterations to ~10',
             'and then explore parameters. Press the play triangle',
             'under iterations to cycle through each step.')
    ),
  
  mainPanel(
    tabsetPanel(
      tabPanel('Plot',  plotOutput('cobwebPlot')),
      tabPanel('Table', tableOutput('cobwebTable'))      
      )
    )
))

To run this app, first make sure that you have R installed.

Then, at the command line (using Terminal.app on Mac or by running cmd on Windows), type R and hit enter to start R.

Once in R, make sure you have Shiny installed by running

install.packages("shiny")
library(shiny)

To start up a local web sever so that you can view the Cobweb Model shiny app, just run

runGist(8670772)

If you happen to get a download has nonzero exit status when you run the runGist command, then run the following and try again.

options('download.file.extra' = '--no-check-certificate')

As mentioned here