Re: Indifference curves for utility functions of form min(ax+by, cx+dy)

Posted by vikram on Jun 07, 2012; 3:50pm
URL: http://discussion-forum.276.s1.nabble.com/Indifference-curves-for-utility-functions-of-form-min-ax-by-cx-dy-tp7577527p7577553.html

This is a brilliant thread. To continue the discussion, I have a query on similar line. On another thread, Amit Sir has explained that for a utility function like U(x,y)=min{x+y,2y} the demand function is as given below.
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I generally explain this using graph but since i cannot do so here. Let me give you the demand correspondence for x.
x = M/(p(x)+p(y))  if p(x) < p(y)
   = [0, M/(p(x)+p(y))]  if p(x) = p(y)
   = 0 if p(x) > p(y)
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But how does one arrive at such a distribution using the optimization technique (Max U(x,y) and budget constraint)? One only touches upon the first result i.e. x = M/px+py. Please explain!!