When trying to fashion a gamma-shaped prior, I've found it more intuitive to start with the mode and standard deviation, instead of the mean and standard deviation as used in the book. The reason is that the gamma distribution is typically very skewed, and therefore the location of the mean is not very intuitive. Here I present how to compute the shape and rate parameters of the gamma distribution from a desired mode and standard deviation.
You can extract the mathematical formula for getting to shape and rate parameters from the R code I created:
# Specify desired mode and sd of gamma distribution:
mode = 10
sd = 20
# Here are the corresponding rate and shape parameter values:
ra = ( mode + sqrt( mode^2 + 4*sd^2 ) ) / ( 2 * sd^2 )
sh = 1 + mode * ra
# Graph it:
x = seq(0,mode+5*sd,len=1001)
plot( x , dgamma( x , shape=sh , rate=ra ) , type="l" ,
main=paste("dgamma, mode=",mode,", sd=",sd,sep="") ,
ylab=paste("dgamma( shape=",signif(sh,3)," , rate=",signif(ra,3)," )",
abline( v=mode , lty="dotted" )
The figure it creates looks like this (below). Notice that the mode is indeed as desired.
Hope that helps. Let me know.