Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
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Reasons for why slutsky matrix may be non symmetric
In demand system estimation, theoretically we require this matrix to be symmetric. This unfortunately is not the case most of the time.
What are some reasons for why symmetry of the slutsky matrix may ...
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Convexity preferences
What is the difference between convexity and strict convexity preferences? What is the difference between quasi-concavity and quasi-convexity? And is MRS still true in concave preferences?
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Utility Maximization of a quasi-linear utility function
I am dealing with a quasi-linear utility function. For example
$U=(x_1x_2)^{0.5}+cx_3$ with constrain $w\ge x_1+2x_2+px_3$.By taking c, w and p as constant, I function that by using Lagrange ...
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Competitive Equilibrium how to determine subject to functions
Consider a 1-commodity, 2-consumers, 2-periods economy with
S = 2, J = 1. The asset pays one unit (of the commodity) in state 1 and 2
units in state 2. q denotes the price of the asset at time 0. The ...
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Opportunity Cost effect on benefits
My question is the following:
Let's say a person has two career choices. He would be succesful in both, but in one of them he is slightly better and thus he will do better. So let's say career A will ...
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Calculate influence of absolute risk aversion on consumption decisions
Say I have the following setup:
A consumer chooses between two goods $x$ and $y$ (a numeraire) such that she maximises:
$$V(x,y)=u(x)+y$$
Under the constraint that her revenue $R$ is such that:
$$R\...
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Logarithmic Utility function Algebra
Question:
I'm told the following (by an exam mark scheme):
Using $a + b =1$
$a[ln(\frac{am}{p_1})] + b[ln(\frac{bm}{p_2})] = ln(m) - aln(p_1) - bln(p_2)$
I can't get this to hold without the ...
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Does an "optimal" MRS exist?
I was reading a case study in Hal Varian, where the author talks about essentially a surge pricing mechanism for incentivizing households to consume less electricity during peak hours (so as to not ...
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Preference relations based on Varian
I understand that there is no universally agreed terminology for preference relations. However I need to pin down a definitive way to think about them (both for my exam, and my own sanity). Please can ...
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Conflicting Definitions of Weak Monotnocity (preferences)
Strong Montonicity my sources seem to agree on Strong monotonicity, i state equivalent definitions below. But weak montonicity i keep finding what appear to be conflicting definitions. In the ...
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Should free market consumers have the maximum information easily available?
As far as I know, free markets rely on well-informed consumers. If this is the case, shouldn't an efficient free market provide consumers as much information as possible about a product so that the ...
CommunityBot
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Existence and uniqueness of demand, and symmetry implies equal demands given equal prices
Encountered the following problem during self study:
My take on the problem is that if we can show that the equation of the income expansion path is $x_1=x_2$ for all such $U(x_1,x_2)$ then we have ...
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Homothetic Functions and Monotonic Transformations
Using the following definition of a homotheic function (taken from my Mathematical Economics course pack).
A function $f: \mathbb{R^{n+}} \to \mathbb{R}$ is homothetic if it has the form:
$f(x,y) = q(...
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Homotheic Function Definitions
There are a number of different definitions of Homothetic functions i have come across. I have used each of them to prove that a function $f(x, y) = x^a y^b$ with $a+b > 0$ is homothetic. But i ...
CommunityBot
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Slutsy Equation and Income effect
Does the Slutsky equation always assume optimal levels of our variables, hence Marshellian demand = Hiscksian demand $x = h$ as indeed this is how the Slutsky is derived?
I originally thought this ...
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Convex Combination of pairs of points
Is it appropriate/meaningful to write vector/points $(a,b) \le (c,d)$, where i would mean component wise each component is $\le$
Specifically is my example below with reference to concavity ...
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What pricing strategies does Amazon use and how do they affect consumers' purchasing decisions?
As a frequent Amazon customer, I have noticed that the prices of products I am interested in buying often fluctuate over time. These changes could either be an increase or decrease in price, and I ...
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Testing for Concavity - Local Maximum & Global Maximum
My question is under which contexts Negative Definitness (ND) vs Negative Semi-Definitness (ND) is required for classifying a global maximiser. And also Global vs Local.
I also want to understand what ...
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Example of consumer preferences that switches from being concave to being convex
Question
Is there an example of consumer preferences over consumption bundles $(x,y)\in \Bbb R^2$ that would be concave when $x$ is abundant relative to $y$ and convex otherwise?
Are there known ...
CommunityBot
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Difference between 'ideal variety' and 'love of variety' - International trade
What really is the difference between the "ideal variety" (Lancaster) of a differentiated product approach and the "love of variety" (Dixit and Stiglitz) approach?
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CES in Slutsky matrix (weird results)
We have a Slutsky matrix:
\begin{bmatrix}
\partial x_{1}^H/\partial P_1 & \partial x_{1}^H/\partial P_2 & \dots & \partial x_{1}^H/\partial P_n \\
\partial x_{2}^H/\partial P_1 &...
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The formula for expansion path
Is there a way how to precisely compute the expansion path?
I know a consumer's utility function $U(\boldsymbol{x})$, I know the budget constraint $\sum P_i x_i \leq M$, I am able to compute the ...
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What is the difference between Impression Management and Signaling Theory?
I'm interested in theories on how organisations shape their stakeholders' (especially consumers' and investors') perceptions and decisions. I read about Impression Management and Signaling Theory. ...
CommunityBot
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Prove strict monotonicity of utility function
I have the following utility function: $$ u(x_1, x_2, x_3) = med(x_1, x_2, x_3) $$ Given that $UMG_{i}$ ≥ 0, the utility function represents a strictly monotonic preference. Does this assertion make ...
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Proving that strict convexity is violated
I am given a utility function $u(x)=x_1^2+x_2^2$ and I am asked to see whether this function satisfies strict convexity. The answer is saying this:
We see that $u(3,0) = 9$, $u(0,3) = 9$, $u(1.5,1.5) =...
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Does local non-satiation hold for this problem?
I am getting some confusing results solving this problem:
$max_{c_0\geq0, c_1\geq0} \bigg\{EU = R(1-c_0) [p t_1 + (1-p) c_1^{-2} t_2] \bigg\} ~ s.t. ~c_0+c_1 \leq 1$
where $p$ is the probability of $...
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FOC greater than 0
I couldn't get my head around this part. Basically, I have to prove that a consumer has to hold a positive amount of assets, i.e. $x > 0$.
A hint suggested to find take the FOC, and then set $x = 0$...
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Composite good and preferences
Usually in economics, we could see some versions of multiplicative utility:
$$U(\boldsymbol{x}) = x*y$$
The thing is that most of the time an additional statement is given that $y$ is some composite ...
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How to create a composite good?
Let's say I would like to create some composite score for multiple of goods...
EDIT: More concise version based on @BrsG comments... I would come up with the following scenario. I have a consumer with ...
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Do Aggregated consumers make sense?
Aggregated consumers as a biased concept (in case of cross-price elasticity)?
I try to approach aggregated consumption data as if it was a new consumer (similarly to approaching average data as if it ...
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Solving Lagrangian FOCs: a few difficulties
I have an optimization problem from microeconomics that yields me the following first-order conditions based on a Lagrangian:
$ p_1 = \lambda \qquad(1)$
$ p_2 - \lambda (x_2^2+x_3^2)^{-1/3}x_2=0 \...
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Why do we not stick to utilities in calculating supply and demand?
Common microeconomics models give that MC must equal MR in the optimal position for the consumer, therefore, the marginal utility must equal its price. But this is where a mistake has been made, what ...
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Expenditure min problem
The typical expenditure min. problem wants to minimize expenditure under the constraint $u(x) \ge u^{\ast}$.
Why the solution of this problem is such that $u(x^{\ast})=u^{\ast}$ and not $u(x^{\ast})&...
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Expected utility maximization question
If the utility function of an individual is $u(w) = 10 \sqrt{w}$ and the individual starts with $w = 100$ (where $w$ denotes the wealth available to him). If he buys a lottery that costs him $51$ and ...
CommunityBot
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Why do we need Complementary Slackness Condition for Karush-Kuhn-Tucker Conditions
Complementary slackness condition (CSC) state that
$\lambda_j[g_j(x) − c_j] = 0 \hspace{5pt} \text{for} \hspace{5pt} j = 1, ..., m.$ Therefore, every constraint either needs to be an equality ...
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Nonlinear budget constraints (for quantity discounts)
I was thinking about quantity discounts and if there is a possibility to model them not as bundles (as is typical for second price discrimination) but rather as prices being some continous functions ...
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Finding consumed quantity using marginal utilities
I was asked the following problem : for an individual, the ratio between the marginal utility of orange juice and marginal utility of apple juice is constant and equal to $0.5$. The two goods cost 3\$ ...
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Does consumer demand in the secondhand market actually affect the firsthand market for high-cost goods
In the 21st Century, there is an increasing consumer awareness of the externalities of manufacturing and along with it a stronger consumer preference to buying used goods rather than new.
My question ...
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Concave preferences have negative SE [Proof]
Question from Intermediate Microeconomics by Hal Varian: Suppose that preferences are concave. Is it still the case that the substitution effect is negative? This is my point: If preferences are ...
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what is monotonicity and strict monotonicity in preferences?
I am really confused between monotonic preferences and strictly monotonic preferences, I saw some video and read certain answer where it is mentioned that the
When preferences are monotone / weak ...
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Is the Hicksian demand curve steeper or flatter than Slutsky demand?
Putting price on the vertical axis and quantity on the horizontal axis, is the Slutsky demand steeper or flatter than the Hicksian demand curve? If I calculate the Slutsky and Hicksian substitution ...
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Are the goods in additively separable utility functions normal goods?
Inspired by this answer.
To make it a bit more precise, by normal good I mean demand is (not necessarily strictly) increasing in income, and by additively separable utility function I mean that a ...
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Looking for a term I'm pretty sure exists
Let me describe the situation:
Company is selling a product; they buy it at x, sell it at some % over for profit. Taken on a monthly scale, you can see the profit of that particular object by ...
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Why is isoelastic utility function so prevalent?
An isoelastic utility function is used in both simple and advanced models. I understand that it is fairly convenient to work with mathematically and that there are empirical estimations of its ...
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Low fees government provided elderly nursing houses- private or public goods or quasi public?
I am really confused on how to classify low fees government nursing home services that are provided to elderly people. Is it public good or private good or quasi-public?
My reasoning is that it is a ...
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Is the preference relation represented by $u(x)=min(x_1, x_2, x_3)$ convex? True or False [closed]
Taking two bundles $x$ and $y$,
$x = (x_1, x_2, x_3)$ and $y = (y_1, y_2, y_3)$,
I understand I have to consider three cases to prove convexity, when $x\sim y$, $x\succ y$, $y\succ x$.
I understand ...
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Is the leontief utility function homogeneous of degree zero? And if that is true, how can that be prove? [closed]
I have not been able to find a mathematical prove is such statement.
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$\{\text{Giffen goods} \} \subsetneq \{\text{Inferior goods}\}$
I was asking myself why is a Giffen good an inferior good and I read the following post : Difference between Giffen and inferior goods. Why aren't all inferior goods Giffen goods?.
The 2nd comment ...
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More direct way to derive indirect utility function from expenditure function
I have this general form for a expenditure function $e(p,u)=f(u)\cdot g(p)$ where $f(u)$ is increasing monotonic. How can I derive a functional form for an indirect utility function from this ...
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Why is internet piracy decreasing?
As an ex-user of pirated content (before I had so much discretionary income), I observe that overall content piracy over the internet is much less prevalent nowadays than only a few years ago. For ...
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