I have a CES utility function, in my class notes I have remark that when the CES is constant and less than one the demand in absolute terms remains unchanged when price of second commodity changes.

However, once I solve the lagrangian and derive demand I find that $$\partial D(p_1,p_2,I)/\partial p_2 <0$$ which implies that the demand should decrease when price of good 2 increases.

Did I made a mistake in my lecture notes or am I missing something? Thanks in advance for any insight


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