CES indifference curves with different elasticities

ces_elas.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_elas.png"

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

set title "Implicit plot of CES functions (different subst. elasticities)"

set xrange [0:10]
set yrange [0:10]


sigma_1 = 2
rho_1   = 0.5
f(x,y)=0.25*(0.5*x**rho_1 + 0.5*y**rho_1)**(1/rho_1)


sigma_2 = 4  
rho_2   = 0.75 
g(x,y)=0.25*(0.5*x**rho_2 + 0.5*y**rho_2)**(1/rho_2)


sigma_3 = 1  
rho_3   = 1  # linear function
h(x,y)=0.25*(0.5*x**rho_3 + 0.5*y**rho_3)**(1/rho_3)


sigma_4 = 10  
rho_4   = 0.9  
i(x,y)=0.25*(0.5*x**rho_4 + 0.5*y**rho_4)**(1/rho_4)

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