## Code

```
library(ggplot2)
<- function(x){
u ^(1/2)
x
}
<- data.frame(
df x=seq(0,220,0.1),
y=NA
)
$y <- u(df$x)
df
#Variables for plot (may not match labels as not done to scale)
#Payoffs from gamble
<-0 #loss
x1<-200 #win
x2<-100 #expected value of gamble
ev<-80 #certain outcome
xc<-50 #certainty equivalent
ce<-(ev-x1)/(x2-x1)
px2
ggplot(mapping = aes(x, y)) +
#Plot the utility curve
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(-25, 220), ylim = c(0, 16))+
#Add labels 4, U(4) and line to curve indicating each
annotate("text", x = xc, y = 0, label = "4", size = 4, hjust = 0.6, 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(4)", size = 4, hjust = 1.05, vjust = 0.3)+
#Add expected utility line
annotate("segment", x = x1, xend = x2, y = u(x1), yend = u(x2), linewidth = 0.5, colour = "black", linetype="dotdash")+
#Add labels 10, U(10) and line to curve indicating each
annotate("text", x = x2, y = 0, label = "10", 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(10)", size = 4, hjust = 1.05, vjust = 0.45)+
#Add labels E[A]=5, E[U(A)] and curve indicating each
annotate("text", x = ev, y = 0, label = "E[A]=5", size = 4, hjust = 0.4, vjust = 1.5)+
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(x1)+(u(x2)-u(x1))*px2, label = "E[U(A)]", size = 4, hjust = 1.05, vjust = 0.45)+
#Add vertical line indicating certainty equivalent and labelled "CE"
annotate("segment", x = ce, xend = ce, y = 0, yend = u(ce), linewidth = 0.5, colour = "black", linetype="dotted")+
annotate("text", x = ce, y = 0, label = "CE", size = 4, hjust = 0.4, vjust = 1.5)
```