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3

"If the new bundle was affordable at old prices, and the new and old bundles aren't equal, then the old bundle must not be affordable at the new prices". In other words, the Weak Axiom of Revealed Preference (WARP) refers to consistent (rational) decision-making. I think the proof is in terms of an 'if then' direct method: The Marshallian demand ...

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Suppose $c_t$ is some composite function of interest rate $r$, e.g. $c_t(G(r_t))$. First the intertemporal elasticity of substitution is actually (IES) given by $\frac{\partial \ln(c_{t+1}/c_{t})}{\partial r}$ (or also $\frac{\partial \ln(c_{t+1}/c_{t})}{\partial \ln( u'(c_{t+1})/u'(c_t))}$). You can take the derivative above using chain rule for composite ...

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As far as I can see this comes just from definitions: As given in MWG definition 1.C.1: The choice structure $(\mathscr{B},C(\cdot))$ satisfies the weak axiom of revealed preference if the following property holds: If for some $B \in \mathscr{B}$ with $x,y \in B$ we have $x\in C(B)$, then for any $B'\in \mathscr{B}$ with $x,y\in B'$ and $y\in C(B')$, we ...

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Just because there might be instances where transitivity is not satisfied does not mean that the entire concept is flawed. The concept of the color blue is not flawed just because things can exist that have a different color. Generally, preferences that are both complete and transitive are called rational, and I believe such preferences make a lot of sense. ...

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The word monotonic means "always moving in the same direction", in our case, always going up. Monotonic preferences mean that the customer always prefers more of a good. This comes in two flavors: Strictly monotonic: More of one good is always preferred to less of that good. Weakly monotonic: More of one good is always equivalent or better than ...

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