You can use logical indexing for this:
beta=0.9;
r=(1-beta)/beta;
i2=4;
sigma1=0.1;
sigma2=0.2;
sigma3=0.7;
v=0.5;
i1 = 0:0.1:10;
q = NaN(size(i1));
if sigma1 == 0
q(:) = 0;
elseif sigma2 == 0 || v == 0
q(:) = 1-(i1-1/beta)/(sigma1+sigma3);
else
% idx is an array of logical type (i.e., each element is true or
% false) which is the same size as i1.
% each element of idx tells you whether or not the corresponding
% element of i1 satisfies the condition (i1 == (1+r)*...):
idx = i1 == (1+r)*(1-sigma3/(sigma3+v*sigma2))+sigma3/(sigma3+v*sigma2)*(i2-v*sigma2);
% now set the elements of q where idx is true (i.e., that condition is
% true) to 1:
q(idx) = 1;
% idx is another logical array, this time based on a different
% condition (i1 >= sigma1*...):
idx = i1 >= sigma1*((i2-1/beta)/v*sigma2 -1)-1/beta;
% set the elements of q where this second condition is true to
% the values calculated from the expression below.
% (note that i1(idx) is used - only using the elements of i1 where the
% condition is true)
q(idx) = 1-(i1(idx)-1/beta)/sigma1;
% final condition to check (i1 < sigma1*...)
idx = i1 < sigma1*((i2-1/beta)/v*sigma2 -1) -1/beta;
% set the corresponding elements of q, again based on i1(idx)
q(idx) = 1-(i1(idx)-r-1)/sigma1*(1-(sigma3/sigma1)*(1+sigma3/sigma1+sigma3/(sigma2*v))^(-1))+(sigma3/sigma1)*(1+sigma3/sigma1+sigma3/(sigma2*v))^(-1)*((i2-r-1)/v*sigma2-1);
end
plot(i1,q);
References:
https://www.mathworks.com/company/newsletters/articles/matrix-indexing-in-matlab.html (scroll down to near the bottom for the logical indexing section)
