3

An indifference curve for perfect substitutes is a straight line. In fact it is the line defined by $y=const-x$, for a utility level of $const\in\Bbb R$. We maximize the utility when our budget line is tangent to the IC line. But they are both straight lines, so there are a few cases (considering a situation with only 2 goods): the prices are not equal ($...


2

It is almost true. There are examples of demand that have a negative definite Slutsky matrix but fails the Weak Axiom. However, if we ask that $$v \cdot S(p,w) v <0 $$ whenever $v \not = \alpha p$ for any scalar $\alpha$ (i.e. $S$ is negative definite for all vectors except those proportional to price), then the Weak Axiom holds.


2

The income effect is defined as $\mathbf{-\frac{\partial x_i}{\partial m}x_i}$. Let $x_i$ be a normal good; that is, a good whose Marshallian demand increases with an increase in income $\left(\frac{\partial x_i}{\partial m} > 0\right)$. Even if there was no substitution effect $\left(\frac{\partial h_i}{\partial p_i} = 0\right)$ from an increase in own-...


1

Although my teacher has yet to verify my solution for d) (which I believe is incorrect), he shared his answer and the condition $x_2<k$ derives from the positivity of $V(p_1,p_2,b)$ and from the budget inequality $p_1x_1+p_2x_2≤b$. The other answers are correct.


1

Why are we decomposing the effect of a change in price of one commodity into all these effects which are (as I have understood), all hypothetical. They're hypothetical, but they are nevertheless meaningful. We can easily imagine what it would be like if an agent had a larger budget while prices remain unchanged; we can also imagine what it would be like if,...


1

You interpreted the passage you read as essentially saying that "with log preferences, the Marshallian demand for the good does not depend on its price." That doesn't sound very plausible, don't you think? But the passage clearly refers to an intertemporal choice problem, it is about log-preferences over a single good and over time, it does not relate to ...


1

First of all: In general, for preferences that are quasi-linear in $x(y)$ it holds true that: Overall effect = Substitution effect, if in the initial situation both goods or if only good $y(x)$ are consumed. Overall effect = Income effect, if in the initial situation only good $x(y)$ is consumed. Substitution effect= $x( p(x)', m') - x( p(x), m)$ Income ...


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