How can I color the region bounded by two level curves of countour plots?

Hello! I think mine is a question about how the function surfc() works. I have very recently discovered to my surprise an easy way to create the Edgeworth Box of microeconomics using surfc. Here is an example (with green curves and red curves the countours of two superimposed surc() plots that ar ereoirented so you see just the contours (with colors of the two surfaces turned off).

Is there a way I can color the region bounded by one red countour and one green contour (the "eye" of a region in the Edgeworth Box)? I presume this is done with patch() but how does one identify the patch region using the contour curves?

My MatLab code follows below. Thank you in advance!

function Edgeworth_Box_Variable_Cobb_Douglas(alpha,beta)

%  This function plots an Edgeworth Box for two agents with
%  Cobb-Douglas utility functions. 
%  
%  Inputs are
%  alpha = the exponent of Agent 1's (Betty's) Cobb-Doulgas utility
%          function
%          u1(X1,Y1) = (X1^alpha)*(Y1^(1-alpha)) 
%  beta  = the exponent of Agent 2's (Alf's) Cobb-Doulgas utility
%          function
%          u2(X1,Y1) = (X1^beta)*(Y1^(1-beta)) 
%


% This block of code computes and plots the countours that are the
% indifference curves for Agent 1 and Agent 2.
[X1,Y1]=meshgrid(0:0.01:1,0:0.01:1) ;
[X2,Y2]=meshgrid(1:-0.01:0,1:-0.01:0) ; 

Z1 = (X1.^alpha).*(Y1.^(1-alpha)) ;
Z2 = (X2.^beta).*(Y2.^(1-beta)) ;

hold on
axis square
view(3)
view([0,90])

sbetty = surfc(X1,Y1,Z1) ;
sbetty(1).FaceColor = 'none' ;  
%sbetty(1).FaceColor = 'cyan' ;
%sbetty(1).EdgeColor = 'blue' ;
sbetty(1).EdgeColor = 'none' ;
sbetty(2).EdgeColor = 'green' ;
sbetty(2).LineWidth = 1 ;
sbetty(2).LevelStep = 1/10 ;

          
salf   = surfc(X1,Y1,Z2) ;
salf(1).FaceColor = 'none' ; 
%salf(1).FaceColor = 'yellow' ; 
%salf(1).EdgeColor = 'magenta' ;
salf(1).EdgeColor = 'none' ;
salf(2).EdgeColor = 'red' ;
salf(2).LineWidth = 1 ;
salf(2).LevelStep = 1/10 ;


%This next block of code plots the contrcat curve.
x = 0:0.01:1 ;
y = (1-alpha)*beta*x./((1-beta)*alpha + (beta-alpha)*x) ;
plot(x,y,'-b','LineWidth',2.0)

% This next block of code plots a boundary around the Edgeworth Box.

plot([0 1],[0,0],'-k','LineWidth',1)
plot([0 0],[0,1],'-k','LineWidth',1)
plot([1 1],[0,1],'-k','LineWidth',1)
plot([0 1],[1,1],'-k','LineWidth',1)

hold off

end

Answer 1

[darova]

• extract data from contour function
• use polyxpoly to find intersection segments

[Peter Vanderschraaf]

Hello, Thank you very much for responding and for your time. I'm afraid the code you have provided me did not run properly on my computer despite my repeated attempts to use it carefully and properly. (The get() command consistently somes up empty.)

In fact you program does something more complex than what I am after, in that it shades the intersections of every nearest pair of countours for each of the two agents. What I've been trying to do is shade the one "eye" bounded by the pair of two selected "opposing" contours. For example, I'd like to shade the intersection region of the one red curve and the one blue curve that intersect the point marked in black.

Just as a side comment, I think you are clearly right that the contour() command is a more straightforward approach to creating thises diagrams. But I've been using surfc() because in some circumstances I actually want to have a look at the two intersecting surfaces that define the level curves.

[darova]

Extract the data you want and make an intersection. There is no other way

[Peter Vanderschraaf]

Thank you, I will try this. And thank you again for your time and responses.

[darova]

im just doing my job