16
There is a good Planet Money episode on ticket scalping; I recommend it.
The reason for banning ticket scalping has nothing to do with economic harm, and everything to do with making the arts (or sports, whatever) accessible to people of more-modest means. Consider the fact that artists could, if they wanted, just auction off all the seats to their shows, ...
14
Following up on the excellent MWG diagram in Amstell's answer, the fundamental observation needed is that holding $p$ fixed, $e$ and $v$ are inverses of each other. $e$ tells us the amount we need to spend to get a certain amount of utility $u$, while $v$ tells us the maximum amount of utility we can get from a certain expenditure $w$. Whenever we want to ...
13
Intuitively, a higher price for pears means that I have to give up more apples to be able to afford an extra pear (or, conversely, if I give up one pear then the number of extra apples that I can afford increases). This is going to make me want to reduce my pear consumption and increase my apple consumption (in orther words, to substitute away from pears ...
13
Not sure how much this will help, but the diagram in Mas-Colell p.75 is something I always have in mind when deriving these functions. I'm not sure what books you're using, but Microeconomics by Mas-Colell et al. is the go to graduate resource. But I prefer Microeconomic Analysis by Varian. Much easier to read and still has the important content needed ...
12
Since $a + b=1$ the equations are exactly the same. Substituting in for $a+b$ with $1$ in the third and fourth equations gives the first and second equations.
11
Yes, under some conditions. This is the classic integrability problem: for detailed discussion, see some excellent notes by Kim Border.
Several other technical conditions are required, but the most economically substantive condition is that the Slutsky matrix must always be symmetric and negative semidefinite. To be concrete, if we define the $ij$th element ...
11
Here's a figure to explain:
Starting from the old price line, where the optimal consumption bundle is point $A$, we increase the price of $y$ to get the new price line.
The Slutsky compensation says that we have to give the consumer enough extra income so that he can afford to old bundle ($A$) at the new price. Thus, we shift the new budget constraint out ...
10
Consider the Slutsky equation,
$$
\frac{\partial x}{\partial p} = \frac{\partial x^c}{\partial p} -
\frac{\partial x}{\partial I} x.
$$
A giffen good is the case where the income effect $\frac{\partial x}{\partial I} x$ is negative and large (in magnitude) enough so
that $\frac{\partial x}{\partial p} > 0$.
From Wikipedia:
There are three necessary ...
10
Quasilinear utility functions are useful in much of the demand estimation literature, particularly in discrete choice. For instance, check out Berry 1994,Berry Levinsohn Pakes 1995 and the many applications in Nevo's papers on demand estimation (here's a "practicioner's guide"). Ken Train's book on it is available for free here!
To summarize, they can lead ...
9
There is rather low probability for demand of a good to exhibit the Giffen property at market level, where averaging over heterogeneous preferences, different income levels and consequent differentiated behavior, will usually offset Giffen phenomena.
Looking at @jmbejara answer, goods that are likely to satisfy all three necessary conditions are drugs ...
9
You're right that it's a bit counterintuitive that the shape of the indifference curves shouldn't change when you transform the utility function. The reason is that you are transforming along an axis that is perpendicular to the plane where the indifference curve lives.
Let's imagine we have two goods, x and y, and let's say that the original utility ...
9
A good is normal if its demand is increasing in income. So let $p_x$ and $p_y$ be the price of the goods with quantities $x$ and $y$ and let $m$ be income.
Suppose $ax>by$. Then $\min\{ax,by\}=by$. By slightly reducing $x$ by and spending the saved money on $y$, one gets a better bundle. For an optimal bundle, this cannot be.
Similarly, it cannot be ...
9
It's called a Principal-Agent Conflict.
The RIAA/MPAA act as agents on behalf of the people who actually produce content (and consequently end-consumer value).
To maintain relevance to their principals', the RIAA/MPAA must signal value to them (i.e. claim loudly and repeatedly that they do something good for them [regardless of the validity of that claim])...
8
The primary literature concerned with this type of question (at least where classical results break down) is behavioral economics. There's a great general compilation of papers put together by the Russell Sage Foundation called the "Behavioral Economics Reading List" that includes, among other things, a General Introduction section with overview papers by ...
8
Consider a preference relation in $\mathbb{R}^2$ such that $x=(x_1,x_2)\succsim (y_1,y_2)=y$ $\iff$ $x_1\geq y_1$ and $x_2\geq y_2$.
1) You might like to argue whether this preference relation is strictly monotonic and continuous.
2) Is the relation defined above complete?
Then, as a side dish, you might also reconsider your claim that continuity is the ...
8
Here's a "no maths" explanation (including the inferior goods case, because I think it helps to understand what's going on):
Suppose we have a normal good, $x$, and we increase its price. Marshallian demand decreases thanks to two effects (i) consumers substitute away from $x$ towards cheaper alternatives; (ii) because prices are higher, consumers can ...
7
The concept of "marginal utility" (and therefore of decreasing such) has meaning only in the context of cardinal utility.
Assume we have an ordinal utility index $u()$, on a single good, and three quantities of this good, $q_1<q_2<q_3$, with $q_2-q_1 = q_3-q_2$.
Preferences are well behaved and satisfy the benchmark regularity conditions, so
$$u(q_1)&...
7
This post shows clearly why in the world of "standard" ordinal utility, concavity of a utility function cannot obtain an economically meaningful interpretation, although it may be useful as a mathematical property.
But "standard" ordinal utility is not compatible with Econometrics, because Econometrics deal inherently with situations where there exists ...
7
Yes it is:
If direction
$$
x \succ y \Rightarrow x \not \precsim y \Rightarrow u(x) > u(y).
$$
Only if direction:
For all $x, y \in X$,
$$
x \succsim y \iff u(x) \geq u(y)
$$
implies
$$
x \sim y \iff u(x) = u(y).
$$
Also
$$
u(x) > u(y) \Rightarrow u(x) \geq u(y) \Rightarrow x \succsim y ,
$$
$$
u(x) > u(y) \Rightarrow u(x) \not = u(y) \...
7
Here a short answer: Homothetic, identical preferences have the modelling advantage that the distribution of income across individuals does not matter for aggregate demand. That is, if you want to study, let's say, monetary policy where you do not expect changes in the distribution of income to affect your policy recommendations, then this is a reasonable ...
7
Looking more closely at your question, I think things should not be overly complicated. From Mas-Colell et.al.
Definition 3.C.1:
The preference relation $\succsim$ on X is continuous if it is preserved under limits. That is, for any sequence of pairs $\{(x^n, y^n)\}^\infty_{n=1}$ with $x^n \succsim y^n$ for all $n$, $x = \lim_{n \rightarrow \infty} x^n$, ...
7
The problem is that there are no indifference "curves" but indifference "areas". Consider the following graph:
For a reference bundle $A$ (equivalent to $\{2,3\}$), the gray regions indicate the areas of indifference, based on your definition of preferences (the black lines are part of the indifference areas).
Thus, by selecting any bundle, you can find ...
7
Not really, you're right in that (loosely speaking) the MRS is the amount of one good someone is willing to give up in order to get an additional unit of another good. However, the slope of the budget line measures the amount of one good someone has to give up in order to get an additional unit of another good.
In the first case, only preferences matter, ...
6
Yes.
We know that a monotonic transformation of a utility function still represents the same preferences and as the old utility function represented homothetic preferences the new one does, too.
As an easy example you could look at Cobb-Douglas utility functions of the form $u(x,y) = a\left(x y\right)^\alpha$. For $\alpha = \frac12$ the utility function is ...
6
The usual textbook example of a Giffen good (i.e. a good whose demand curve slopes upwards) is the Irish potato famine. The idea is that as potatoes (a staple food) became more expensive, people could no longer afford expensive foods such as meat and so ended up buying more potatoes! However, this example has come in for criticism, not least of all because a ...
6
It all depends on whether you treat the budget constraint as an equality or inequality constraint. These are two different problems, with two different solutions in this case.
One version of the problem (rewriting the objective in the form suggested by denesp, and dropping the constant, for clarity) is
\begin{align}
\max~&-4(x-4.5)^2 -2(y-1.5)^2\\\text{...
6
The simple answer is that they don't think they would make as much money.
In many countries illegally downloading music or movies is getting harder and harder. The recording industry has achieved this by persuading governments to instruct the ISPs to block torrent sites, torrent proxy sites and sites that list proxy sites completely so no one can access ...
6
I am assuming that the following facts do not require proofs for the purposes of this question.
Fact 1: Let $h_n$ be a sequence in $\mathbb{R}^K$ such that $\lim_{n\rightarrow \infty} h_n =h\in \mathbb{R}^K$. Then, for each $i\in \{1,2,\ldots,K\}$, we have $h^i_n\rightarrow h^i$.
Fact 2: Let $z_n$ and $q_n$ be sequence in $\mathbb{R}$ such that $\lim_{n\...
6
Let me answer the question by following @HRSE's explanation and recommending a good reading. Eaton and Kortum (Ecta, 2002) use homothetic preferences, a convenient assumption to get a tractable general equilibrium Ricardian model of trade. However, there is exhaustive evidence that the income elasticity of demand varies across goods and that this variation ...
6
To begin with, I think the question is wrongly stated. For if the defininition of a thin indifference curve is such that continuity of a consumer's preferences implies thin indifference curves, then, surely, continuity implies thin indifference curves... This answers your question.
However, if we are to make a suitable definition of a thin indifference ...
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