powerUtilities = function()
{
x = seq(.01,3,.01)
lwd = 2
y = log(x)
ylim = c(min(y),max(y))
plot(x,y,type = "l",ylim =c(-8,2),lwd = lwd,xlim = c(0,3.01),
xlab = "WEALTH V",ylab = "U(V)")
gamma = -1
y = (x^gamma - 1)/gamma
lines(x,y,lty = 8,lwd = lwd)
gamma = .5
y = (x^gamma - 1)/gamma
lines(x,y,lty = 3,lwd = lwd)
abline(v = 0)
legend(1.2,-5.5,c("Gamma = .5", "Log Utility","Gamma = -1"),
lty = c(3,1,8),lwd = 2)
}
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