plot indifference curves of non-homothetic CES variants

non_homothetic_isoquants.plt

# plot the indifference curves of non-homothetic CES variants


# 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 "Non-homothetic isoquants (modified CES)"

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


sigma = 2                 # elasticity of substitution
rho   = 0.5               # 1-(1/sigma)
mu    = 0.5               # commitement term
t     = 2                 # homotheticity parameter (wealth effect)  




#    
# gradual increase in wealth for the standard CES
# plotted as a set of indifference curves    
#
#f(x,y)=(0.5*x**rho + 0.5*y**rho)**(1/rho)                   # standard CES
#h(x,y)=(0.5*(t*x)**rho + 0.5*(t*y)**rho)**(1/rho)           # standard CES doubled consumption
#t1 = 0.5
#g(x,y)=(0.5*(t1*x)**rho + 0.5*(t1*y)**rho)**(1/rho)        
#t2 = 1.5
#i(x,y)=(0.5*(t2*x)**rho + 0.5*(t2*y)**rho)**(1/rho)       




#    
# gradual increase in wealth for the commitment version
# plotted as a set of indifference curves    
#    
g(x,y)=(0.5*(x-mu)**rho + 0.5*y**rho)**(1/rho)              # commitment version
i(x,y)=(0.5*(t*x-mu)**rho + 0.5*(t*y)**rho)**(1/rho)        # commitment version
t1 = 0.5
f(x,y)=(0.5*(t1*x-mu)**rho + 0.5*(t1*y)**rho)**(1/rho)        
t2 = 1.5
h(x,y)=(0.5*(t2*x-mu)**rho + 0.5*(t2*y)**rho)**(1/rho)       


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