November 30th, 2016, 02:34 AM  #1 
Member Joined: Sep 2013 Posts: 83 Thanks: 0 
So I took this off a course book I'm reading on microeconomics note: $\displaystyle {x_1} = \phi (\bar z + {y^h}  x_2^h)$ I tried using the chain rule: $\displaystyle {{dU} \over {dz}} = {{dU} \over {d{x_1}}}{{d{x_1}} \over {dz}} + {{dU} \over {d{x_2}}}{{d{x_2}} \over {dz}}$ where I got the same expression EXCEPT for the first term, so I don't understand where the ()sign come from: $\displaystyle  U_1^h({x_1},x_2^h)$ Last edited by skipjack; November 30th, 2016 at 06:15 AM. 
November 30th, 2016, 08:35 AM  #2 
Member Joined: Sep 2013 Posts: 83 Thanks: 0 
update: So instead of applying the normal chain rule, since: $\displaystyle \eqalign{ & z = U({x_1},x_2^h) \cr & {x_1} = g({x_2}) \cr & {{dz} \over {d{x_2}}} = {{\partial f} \over {\partial {x_1}}}{{d{x_1}} \over {d{x_2}}} + {{\partial f} \over {\partial {x_2}}}{{d{x_2}} \over {d{x_2}}} = {{\partial f} \over {\partial {x_1}}}{{d{x_1}} \over {d{x_2}}} + {{\partial f} \over {\partial {x_2}}} \cr} $ , since $\displaystyle {x_1}$ is function of $\displaystyle x_2^h$. This seems to yield the correct expression, or maybe I've missed something ? Last edited by Ku5htr1m; November 30th, 2016 at 08:41 AM. 
November 30th, 2016, 03:55 PM  #3 
Member Joined: Sep 2013 Posts: 83 Thanks: 0 
This is from F.A.Cowell  Microeconomics  Principles and Analysis p.452453


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