bundling: Profitability of bundling strategies

#' Demands, Profits, Consumer Surpluses, Cost for Mix Bundling strategy
#' @param r1.r2 N valuations of good 1 and 2  - reserversion prices r1, r2
#' @param price.pc Monopoly price of good 1 , good 2 and bundle [price.pc <- c(p.1, p.2, p.b)]
#' @param c.1  Parameter of production cost of good 1
#' @param c.2  Parameter of production cost of good 1
#' @param alfa Parameter of scale economics alfa = 0 --> CRS, alfa < 0 --> IRS, alfa < 0 --> DRS
#' @param beta Parameter of sope economics  beta = 0 --> neutral, beta > 0 complementary in proiduction, beta < 0 substitution in production
#' @param teta Parameter of complementary and substitution of goods beta = 0 --> neutral, beta > 0 complementary in consumption, beta < 0 substitution in consumption
#' @param FC Fixed Cost of production
#'
#' @return For a given: i. N valuations of r1 ,r2 ii. Monopoly prices p1, p2 iii. Technology
#'  profit  - profit for Pure Bundle strategy
#'  c.s     - Consumer surplus for Pure Componenets strategy
#'  t.c     - cost of production
#'  no.buy  - number of consumers which do not buy any good
#'  buy.b   - number of consumers which buy bundle of good 1 and good 2
#' @examples
#' c.1  <-  0.5   # parametr of cost of y1 (MC1 for beta = 0, alfa = 0)
#' c.2  <-  0.5   # parametr of cost of y2 (MC1 for beta = 0, alfa = 0)
#' beta <-  0     # parametr of scope economics
#' alfa <-  0     # parametr of scale economics
#' teta <-  0     # parametr of degree of contingency
#' FC <- 250      # Fix Costs
#' r1.r2      <- r1.r2.cable  # Valuations of TV and Internet
#' price.mb   <- c(20,40,50)  # monopoly prices of TV, INTERNET and  bundle TV and Internet
#' demand.m.b <- Profit.MB(r1.r2,price.mb, c.1, c.2, alfa, beta, teta, FC)
#' plot(r1.r2, type = "p", col="transparent", xlab="r1", ylab="r2", main = "MB" )
#' points(demand.m.b$no.buy , pch = 8, col  = "gray80" )
#' points(demand.m.b$buy.1 , pch = 19,    col  = "gray50")
#' points(demand.m.b$buy.2 , pch = 18,    col  = "gray50")
#' points(demand.m.b$buy.1.2 , pch = 17,    col  = "gray10")
#' legend("topright", col = c("transparent","gray80","gray50 ", "gray50 ","gray10"),
#' pch=c(1,8,19,18,17), legend=c("", "no buy","buy y1", "buy y2" , "buy bundle"), bty="n")
#' abline(a=demand.m.b$p.b, b= -1, lty = 2)
#'
#' @export
Profit.MB <- function(r1.r2,prices.mb,c.1,c.2,alfa,beta,teta,FC){

  p.1 <- prices.mb[1]
  p.2 <- prices.mb[2]
  p.b <- prices.mb[3]


  no.buy <- as.matrix(r1.r2[(r1.r2[,1] <  p.1) & (r1.r2[,2] <  p.2) &
                     (1+teta)*(r1.r2[,1]+r1.r2[,2]) < (p.1 + p.2)&
                     (1+teta)*(r1.r2[,1]+r1.r2[,2]) < p.b, ])


  buy.1 <-  as.matrix(r1.r2[(r1.r2[,1] > p.1) &
                   ((r1.r2[,1] - p.1) > (1 + teta)*(r1.r2[,1]+r1.r2[,2]) - p.b) &
                   ((r1.r2[,1] - p.1) > (r1.r2[,2]- p.2 )),])

  buy.2 <-  as.matrix(r1.r2[(r1.r2[,2] > p.2) &
                    ((r1.r2[,2] - p.2) > (1+teta)*(r1.r2[,1]+r1.r2[,2]) - p.b) &
                    ((r1.r2[,2] - p.2 )>(r1.r2[,1]- p.1 )),])

  buy.1.2 <- as.matrix(r1.r2[((1+teta)*(r1.r2[,1]+r1.r2[,2]) > p.b) &
                     ((1+teta)*(r1.r2[,1]+r1.r2[,2]) - p.b > r1.r2[,1] - p.1) &
                     ((1+teta)*(r1.r2[,1]+r1.r2[,2]) - p.b>(r1.r2[,2]-p.2)),])


  n.1     <-  dim(buy.1)[1]
  n.2     <-  dim(buy.2)[1]
  n.1.2   <-  dim(buy.1.2)[1]
  n.n.b   <-  dim(no.buy)[1]

  t.c     <- Cost.Bundle((n.1  + n.1.2),(n.2 + n.1.2),c.1,c.2,alfa,beta,FC)
  profit <- p.1*(n.1) +  p.2*(n.2) +  p.b*n.1.2 - t.c


  c.s <- ifelse(n.1==0, 0, apply(buy.1, 2, sum)[1]) +
    ifelse(n.2==0, 0, apply(buy.2, 2, sum)[2]) +
    ifelse(n.1.2==0, 0, apply(buy.1.2, 2, sum)[1]) +
    ifelse(n.1.2==0, 0, apply(buy.1.2, 2, sum)[2])

  output.MB <-
    list(
         profit = profit,
         c.s    =  c.s,  ################
         t.c    = t.c,
         p.1    = p.1,
         p.2    = p.2,
         p.b    = p.b,
         no.buy = no.buy,
         buy.1  = buy.1,
         buy.2  = buy.2,
         buy.1.2  = buy.1.2)

  return(output.MB)}