## Code

```
library(ggplot2)
library(latex2exp)
<- function(x){
u log(x)
}
<- data.frame(
df x=seq(1,100,0.1),
y=NA
)
$y <- u(df$x)
df
#Variables for plot (may not match labels as not done to scale)
#Payoffs from gamble
<-3 #loss
x1<-90 #win
x2<-77 #expected value of gamble
ev<-70 #certain outcome
xc<-(ev-x1)/(x2-x1)
px2
ggplot(mapping = aes(x, y)) +
geom_line(data = df) +
geom_vline(xintercept = 0, linewidth=0.25)+
geom_hline(yintercept = 0, linewidth=0.25)+
labs(x = "x", y = "U(x)")+
# Set the theme
theme_minimal()+
#remove numbers on each axis
theme(axis.text.x = element_blank(),
axis.text.y = element_blank(),
axis.title=element_text(size=14,face="bold"),
axis.title.y = element_text(angle=0, vjust=0.5))+
#limit to y greater than zero and x greater than -8 (need -8 so space for y-axis labels)
coord_cartesian(xlim = c(-8, 100), ylim = c(0, 5))+
#Add labels W, U(W) and line to curve indicating each
annotate("text", x = x2, y = 0, label = "W", size = 4, hjust = 0.4, vjust = 1.5)+
annotate("segment", x = x2, y = 0, xend = x2, yend = u(x2), linewidth = 0.5, colour = "black", linetype="dotted")+
annotate("segment", x = 0, y = u(x2), xend = x2, yend = u(x2), linewidth = 0.5, colour = "black", linetype="dotted")+
annotate("text", x = 0, y = u(x2), label = "U(W)", size = 4, hjust = 1.1, vjust = 0.4)+
#Add labels W-R, U(W_R) and line to curve indicating each
annotate("text", x = xc, y = 0, label = "W-R", size = 4, hjust = 0.5, vjust = 1.5)+
annotate("segment", x = xc, y = 0, xend = xc, yend = u(xc), linewidth = 0.5, colour = "black", linetype="dotted")+
annotate("segment", x = 0, y = u(xc), xend = xc, yend = u(xc), linewidth = 0.5, colour = "black", linetype="dotted")+
annotate("text", x = 0, y = u(xc), label = "U(W-R)", size = 4, hjust = 1.05, vjust = 0.45)+
#Add expected utility line
annotate("segment", x = x2, xend = x1, y = u(x2), yend = u(x1), linewidth = 0.5, colour = "black", linetype="dotdash")+
#Add labels W-H, U(W_H) and line to curve indicating each
annotate("text", x = x1, y = 0, label = "W-H", size = 4, hjust = 0.4, vjust = 1.5)+
annotate("segment", x = x1, y = 0, xend = x1, yend = u(x1), linewidth = 0.5, colour = "black", linetype="dotted")+
annotate("segment", x = 0, y = u(x1), xend = x1, yend = u(x1), linewidth = 0.5, colour = "black", linetype="dotted")+
annotate("text", x = 0, y = u(x1), label = "U(W-H)", size = 4, hjust = 1.05, vjust = 0.45)+
#Add labels E[not I], E[U(not I)] and curve indicating each
annotate("text", x = ev, y = 0, label = TeX("E[$\\neg$ I]", output='character'), parse=TRUE, size = 4, hjust = 0.4, vjust = 1.4)+
annotate("segment", x = ev, y = 0, xend = ev, yend = u(x1)+(u(x2)-u(x1))*px2, linewidth = 0.5, colour = "black", linetype="dashed")+
annotate("segment", x = 0, y = u(x1)+(u(x2)-u(x1))*px2, xend = ev, yend = u(x1)+(u(x2)-u(x1))*px2, linewidth = 0.5, colour = "black", linetype="dashed")+
annotate("text", x = 0, y = u(3)+(u(x2)-u(x1))*px2, label = TeX("E[U($\\neg$ I)]", output='character'), parse=TRUE, size = 4, hjust = 1.05, vjust = 0.45)
```