draw utility (or expectation) function

draw_utilityfun.R

Ut <- function(x,alpha,beta,lambda){
  ifelse(x>0, x^alpha, -lambda*((-x)^beta))
}

params <- list(
  list(alpha=1,beta=1,lambda=1),
  list(alpha=1,beta=1,lambda=2),
  list(alpha=1/2,beta=1/2,lambda=2),
  list(alpha=2,beta=2,lambda=1)
)

png("draw_u.png")
par(mfrow =c(2,2))
for(i in 1:4){
  with(params[[i]], curve(Ut(x,alpha,beta,lambda), -2,2, main=paste("scenario", i), ylab="U"))  
}
dev.off()

with(params[[1]], 0.5*Ut(1,alpha,beta,lambda)+0.5*Ut(-1,alpha,beta,lambda))
with(params[[2]], 0.5*Ut(1,alpha,beta,lambda)+0.5*Ut(-1,alpha,beta,lambda))
with(params[[3]], 0.5*Ut(1,alpha,beta,lambda)+0.5*Ut(-1,alpha,beta,lambda))
with(params[[4]], 0.5*Ut(1,alpha,beta,lambda)+0.5*Ut(-1,alpha,beta,lambda))

with(params[[1]], 0.5*Ut(2,alpha,beta,lambda)+0.5*Ut(0,alpha,beta,lambda))
with(params[[2]], 0.5*Ut(2,alpha,beta,lambda)+0.5*Ut(0,alpha,beta,lambda))
with(params[[3]], 0.5*Ut(2,alpha,beta,lambda)+0.5*Ut(0,alpha,beta,lambda))
with(params[[4]], 0.5*Ut(2,alpha,beta,lambda)+0.5*Ut(0,alpha,beta,lambda))