CES indifference curves with different value shares

ces_shares.plt

#
# GNUPLOT script to draw CES functions with different parameters
#

# script based on the implicit function plotting trick from:
# http://gnuplot-surprising.blogspot.de/2011/09/assume-three-is-equation-fxygxy-and-we.html


# uncomment in case you want to save it to a file
#set term png enhanced lw 2 font "Times,18"
#set output "ces_share.png"

set contour
set cntrparam levels discrete 1
set view map
unset surface

set title "Implicit plot of CES functions (different value shares)"

set xrange [0:5]
set yrange [0:5]

sigma = 2
rho   = 0.5    # 1-(1/sigma) 


f(x,y)=(0.5*x**rho + 0.5*y**rho)**(1/rho)
g(x,y)=(0.4*x**rho + 0.6*y**rho)**(1/rho)
h(x,y)=(0.3*x**rho + 0.7*y**rho)**(1/rho)
i(x,y)=(0.2*x**rho + 0.8*y**rho)**(1/rho)

splot f(x,y),g(x,y),h(x,y),i(x,y)