Do the slope of a linear demand function and the elastisicy of demand coincide when we use specific preferences for pricing. As a paradigm, if we consider the case of CARA normal preferences, by solving the proble of the represenative conumer, we know that the demand function is a linear one. In this case the slope and the elasticity of the demand function coincide, but is this the case in general?
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3$\begingroup$ No, the elasticity varies along linear demand curves. Because the slope of such demand curves is constant, it cannot always be equal. $\endgroup$– BayesianNov 19, 2020 at 10:54
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No, slope of a demand function is $\frac{\partial q(p)}{\partial p}$ elasticity of demand is $\frac{\partial q(p)}{\partial p} \frac{p}{q(p)}$. So they cannot be same except in some special cases.
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$\begingroup$ I think that this is what I want to know. One of such speacial cases is when we have CARA preferences. $\endgroup$ Nov 19, 2020 at 10:58
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$\begingroup$ However, I would be glad if someone could provde two paradigms with their correpsonding reasoning. One for the case they coincide and some other for the case that they are different $\endgroup$ Nov 19, 2020 at 11:00
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4$\begingroup$ @HungerLearn what do you mean by 2 paradigms? This is one paradigm + math. For example, if $q(p)=100$ then $\partial q(p)/ \partial p= 0$ and at the same time also $\partial q(p)/ \partial p *p/q(p)=0$. Or if $q(p) = p $ then $\partial q(p)/ \partial p= 1$ and $\partial q(p)/ \partial p *p/q(p)=1$ $\endgroup$– WilliamTNov 19, 2020 at 11:13
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