## Code

```
library(ggplot2)
<- function(x){
u ifelse (x >= 0, x^0.5, -(-x)^0.5)
}
<- data.frame(
df x = seq(-25, 25, 0.1),
y = u(seq(-25, 25, 0.1))
)
#Variables for plot (may not match labels as not done to scale)
#Payoffs from gamble
<- -20 #loss
x1<- 0 #win
x2<- -10 #expected value of gamble
ev<- -10 #certain outcome
xc<-(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 = "v(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, 25), ylim = c(-5, 5))+
#Add labels -10, v(sell) and line to curve indicating each
annotate("text", x = xc, y = 0, label = "-10", size = 4, hjust = 0.6, vjust = -0.5)+
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 = "v(sell)", size = 4, hjust = -0.1, vjust = 0.3)+
#Add labels -20, v(-20) and line to curve indicating each
annotate("text", x = x1, y = 0, label = "-20", size = 4, hjust = 0.5, vjust = -0.5)+
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 = "v(-20)", size = 4, hjust = -0.1, vjust = 0.6)+
#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 v(hold) and curve indicating position
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 = "v(hold)", size = 4, hjust = -0.1, vjust = 0.45)
```