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Note to solve percentage change of demand


To solve


We use total derivative


Divide both sides with



Multiply and divide and on relevant components on the RHS:


is the cross-price elasticity (unweighted, constant-output) of and , denote it as
is also the elasticity of and Q. From 1) to 3) in the note of restriction, we know is linear homogeneous in Q, or the percentage change of equals the percentage change of Q, so


Multiply 100 on both side and rewrite in percentage change form (lower case), we have: