Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
322
questions
1
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2answers
342 views
What does price embody ? Do we constantly undervalue some type of products?
I'm not sure to fully get the meaning of prices. If I understand well, there
are two drivers of it :
The theory of demand and supply and thus prices are driven partly by the utility that agents get ...
2
votes
2answers
463 views
Does Modern Monetary Theory (MMT) provide a useful insight into how to manage the economy?
According to advocates of MMT, the primary risk once the economy reaches full employment is inflation, which can be addressed by gathering taxes to reduce the spending capacity of the private sector. ...
0
votes
0answers
29 views
Utility function parameters
I have the following utility function:
u($x_1$,$x_2$)=($x_1$+$b_1$)$^c$($x_2$+$b_2$)$^{1-c}$
I'm asked to explain what $b_1$, $b_2$ and $c$ stand for, maybe for c is like a weight of every good. but I'...
1
vote
1answer
38 views
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 ...
0
votes
1answer
54 views
max{x1,x2} where P1not=p2
I have seen min{x1,x2} functions representing perfect compliments but have never seen a max{x1,x2} function anywhere in my book or lectures, I also have never seen anything about p1 not equaling p2. ...
1
vote
1answer
80 views
General Equilibrium with Perfect Substitutes
I came across the following problem:
The quantities of an economy’s only two goods are denoted by $X$ and $Y$; no production is possible. Ann’s and Ben’s preferences are described by the utility ...
1
vote
0answers
30 views
graph of dependent income
I would need help with the following problem about consumer theory. Let us say that $X$ is the amount of days at the sea and $Y$ is the amount of days on the cottage. We have some utility function $u(...
-1
votes
0answers
35 views
Budget Set if quantity tax on consumption of ALL units beyond x_bar
Budget Set if quantity tax on consumption of ALL units and not just those in excess of x_bar when total quantity consumed is higher than x_bar?
Will it be 2 budget lines originating from M/p2
One at ...
2
votes
2answers
61 views
setting of Lagrangian function
Consider a simple consumer's problem:
Max $u(X)$ s.t. $\sum_i^l p_i x_i\leq \sum_i^l p_i w_i$
$w$ is initial endowment.
We can set the Lagrangian function to solve this problem.
$L=u(X)+\lambda ( \...
3
votes
1answer
81 views
How can I prove that a utility function does (or does not) satisfy diminishing MRS?
I have this CES utility function:
$$U(f, c) = (f^\alpha + c^\alpha)^{1/\alpha},$$
with $\alpha > 0$.
The problem set asks does it "satisfy the principle of diminishing marginal rate of ...
0
votes
1answer
105 views
Question on General Equilibrium: how to write offer curves?
QUESTION:
Consider simple two-person, two-good economy in which agents’ utility functions are given by
$U_1(x_{11}, x_{21}) = min\{x_{11}, x_{21}\} $, and $U_2(x_{12}, x_{22}) = min\{4x_{12}, x_{22}\}...
3
votes
1answer
49 views
Correct and complete characterisation of the Walrasian demand function
I would like to propose to you the following problem and my proposed solution. In particular, I am unsure in how to correctly characterize the Walrasian demand. Can you please have a look at it and ...
3
votes
2answers
92 views
Boundary solutions in the Utility Maximization Problem
I'm trying to find boundary solutions for the following utility maximization problem, but i'm unsure on how to proceed. Here is the problem and what I got so far:
$ \max x_1^\alpha + x_2 \qquad \text{...
1
vote
1answer
35 views
Budget Set- closed and boundedness
I am fairly new to economics, and we were introduced to budget sets,
The professor mentioned that the budget set $B(p,w) = \{x \in R^{l}_{+}: px \leq w\}$ is non empty and closed - I could prove the ...
0
votes
1answer
45 views
When is expenditure function non-decreasing?
I have to find parameters m and d for which expenditure function is non-decreasing and homogeneous of degree 1.
My expenditure function is:
I think that I should find ∂e/∂p which has to be >= 0 but ...
3
votes
2answers
416 views
Integral solution (or a simpler) to consumer surplus - What is wrong?
Problem
Given demand $D(p)=A-ap$, and $A,a>0$ and a fixed price $0<p_1<A/a$ by some company.
Calculate the consumer surplus and its derivative with respect to $p$. What is this number?
My ...
0
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0answers
24 views
Can someone help me prove that the CES function is also a Cobb-Douglass function [duplicate]
I would like some assistance with a problem that I have showing a CES function is also a Cobb-Douglass utility function.
Question: we have a CES function: $Y=A[\alpha K^{((1-\sigma)/\sigma))}+(1-\...
5
votes
0answers
94 views
Certainty equivalence when the utility is semi-continuous instead of continuous
Let $U:\mathbb R^2\to\mathbb R$ be a utility function.
If $U$ is strictly increasing and continuous, then it is well known that for any $(x_1,x_2)$ there exists a certainty $(c,c)$ such that $$U(x_1,...
0
votes
1answer
48 views
A question from MWG 2F12
This question is from MWG
if walrasian demand function is generated by a rational preference relation then it must satisfy weak axiom.
I cannot prove this statement. How can I do?Thanks alot.
3
votes
0answers
67 views
Who were the first economists arguing that utility maximization is the core of rationality and economic behavior?
I am looking for the first economists arguing that maximizing utility function is the iff condition of rational behavior.
I've learned that neoclassical economics is founded on this argument. Is this ...
0
votes
1answer
31 views
Elasticity of intertemporal sustitution with composite CRRA function
In the usual CRRA $\frac{c^{1-\sigma}-1}{1-\sigma}$ function we have that the intertemporal elasticity of sustitution $\partial\frac{c_{t+1}}{{c_{t}}{\partial r}}$ is $\frac{1}{\sigma}$.
But how can ...
2
votes
1answer
49 views
Proof on weak axiom of revealed preferences
I read the following statement.
“ A utility maximizer with strictly convex and strongly monotonic preferences
satisfies weak axiom of revealed preferences.”
How can I prove or show this? I cannot ...
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votes
1answer
29 views
Does transitivity qualify as a reason for Indifference curves intersecting each other?
Transitivity in preferences seems as a flawed concept because there might be a situation where
A>B, B>C but A<C.
Going by this analogy it seems that it does not qualify as a reason for ...
2
votes
1answer
467 views
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 ...
3
votes
1answer
85 views
Understanding the Choice Rule in MWG
I am reading the Microeconomics Theory book by MWG, and I am having a tough time interpreting what things mean to a real life example, so any help would be appreciated.
For example, it gave this. ...
2
votes
2answers
373 views
Marginal Rate of Substitution for perfect complements
I have come across the following problem:
Determine the marginal rate of substitution MRS(x1, x2) at point (x1, x2) = (5,1) for the following function:
u(x1, x2) = min(x1, x2).
The solution is that ...
1
vote
1answer
44 views
Why doesn't Nintendo fire up the old factories and re-produce *exact* copies of many of their most popular games, controllers and consoles?
Let's suppose that Nintendo announce tomorrow that they are going to create exact re-releases of the American and European NES, SNES and Nintendo 64 consoles, exactly the same as when they were ...
3
votes
1answer
40 views
Question about Strict Preference Relation
Strict Preference usually states that
x is strictly preferred to y if : < x is weakly preferred to y and not y is weakly preferred to x >.
Let me split the < > part into two segments:
x ...
2
votes
1answer
47 views
Question about an interpretation of the MRS
Given the marginal rate of substitution of $x$ for $y$ : $\frac{u'(x)}{u'(y)} $
I know one can interpret this as the amount of $y$ one is willing to give up for an additional unit of $x$, or the ...
1
vote
1answer
62 views
Proving that Marshallian demand is of the form: $x_i^*(p,I) = \hat{x}_i^*(p)I$ with certain conditions
Can I please have some feedback/help proving the following. My proof is below but I am quite uncertain as to whether my solution is efficient. Thank you.
If $u(x)$ is a homothetic utility, then show ...
0
votes
0answers
20 views
What is the relationship between Marshallian demand and Two-Stage Least Squares Estimation Procedure
I was reading Varian, and he gives an example of how to find the quantities demanded using a CobbDouglas utility function with observable data, and a question arose: what is the relationship between ...
3
votes
0answers
65 views
Continuous logit models - random utility with uncountable choice set
This question is about the mathematical foundations of the continuous logit model, as derived in McFadden (1976) (https://eml.berkeley.edu/reprints/mcfadden/math_theory.pdf) and Ben-Akiva et al (1985) ...
2
votes
1answer
58 views
When the global optimal is outside of the constraint set, what will be the demand?
$u:\mathbb R^n\to\mathbb R$ is a quasi-concave utility function so the indifference curves are convex.
$a,b\in\mathbb R^n$ are two points. Our budget set is the (one-dimensional) segment $[a,b]$ that ...
1
vote
1answer
229 views
Can implicit costs make every option not worth doing?
I'm new to microeconomics so sorry if this is simplistic, but if an action should only be taken when benefits > costs and opportunity costs are included in cost calculations, how would one deal ...
2
votes
3answers
108 views
Relation between demands of $x, y$ and $z$
Question: Consider a consumer with utility function $U(x,y,z)=y\min\{x,z\}$. The prices of all three goods are the same. The consumer has $100 to spend on these three goods.The demands will be such ...
1
vote
1answer
103 views
Generalizing demand for perfect substitutes utility function
I have the utility function:
$U(x_1,...,x_n)=a_0+\sum_{i=1}^{n}a_ix_i\;\;\;\;\;\;\;\;\;a_j\in\mathbb{R}_+ \;\;\forall j=\{0,...,n\}$ (maybe $a_0$ could be zero)
$\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...
3
votes
3answers
558 views
Are Cobb-Douglas preferences monotone according to the marginal utility condition?
I understand that Cobb-Douglas preferences represented by $U(x,y)=x^ay^b$ are strictly monotonic, because increasing at least one of the goods in the bundle increases utility.
However, another ...
2
votes
2answers
105 views
In an intertemporal (2-period) consumption model, why is the investment rate independent of discount factor?
In lecture, my professor defined the following 2-period consumption model:
$c_i = $ consumption in period $i$.
$y =$ endowed income in period 1.
$r = $ interest rate in perfect credit markets.
$h = $ ...
3
votes
1answer
52 views
Lotteries = probability distribution?
Are "lotteries" in the model for choice under uncertainty not just probability distributions?
3
votes
1answer
46 views
Binary-continuous choice model in empirical consumer choices
There are quite a lot empirical research based on discrete choice models, in which the consumer selects one of J alternative goods to maximize her indirect utility. The key assumption of these models ...
0
votes
1answer
27 views
Expenditure function. Prove that this set is bounded
I need to prove that the following set is bounded in order to derive the expenditure function:
$e(p,v)=min_x px$
ST
$\{x \in R^n_+$ such that $U(x)\geq v\}$.
Knowing that $U(x):R^n \longrightarrow R$ ...
2
votes
2answers
90 views
Prove that budget constraint is Lower Hemi Continuos (LHC)
I need to prove that the following constraint is LHC.
$B=\{x \in R^n : px\leqslant pw)$
But Im not capable of finding and sequence $\{x_n\}$ such that $x_n \in B(p_n,w_n) \forall n$ and that $x_n\...
2
votes
1answer
22 views
Does anybody knows where I should look for a proxy for consumption to estimate a two factor C-CAPM?
Has anybody seen, any textbook recommendation that refers to the proper proxy for consumption. I am trying to estimate a two factor consumption CAPM, namely we I add a second factor apart from ...
0
votes
1answer
52 views
Does the duality of utility maximization and cost minimization hold in practice?
I recently learned about the relationship between utilization maximization and cost minimization.
Are there studies on whether this duality holds in real life?
Any information on this topic for a ...
1
vote
1answer
36 views
Whether a good is a Giffen good should be based on circumstance?
The textbook example of a Giffen good is the potato during the Irish Potato Famine. It is characterised by a positive income effect that is larger than the negative substitution effect when the price ...
1
vote
1answer
146 views
Mathematics of the income and substitution effects
I have recently been learning about the concept of utility and the indifference curve. I am having some problems understanding the effects on consumption of two goods $X$ and $Y$ of a change in the ...
4
votes
1answer
235 views
Price-consumption curve
Suppose a consumer whose income is $b$ has a utility function given by $U(x,y) = 2xy+y^2$ with the price of $x$ being $p_x$ and the price of $y$ being $p_y$.
Draw the price-consumption curve assuming ...
0
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0answers
9 views
Why is the demand, supply and Engel curves plotted with the dependant variable in the X axis and the independent variable in the Y axis?
I am new to economics and have read the first 7 chapters in Intermediate microeconomics by Hal R Varian. Throughout the text, graphs are drawn with the dependent variable (Quantity) in X and ...
3
votes
1answer
158 views
Marshalian and Hickisian Demands and Slutsky Equation
everyone.
I have the following question:
A consumer has the following indirect utility function:
$ V(p_1,p_2,b) = (p_2k-b)p_1^{-1} \left[ \frac{2p_2k - 2b}{p_2} \right]^{-2}, x_2 < k$
a) Find ...
0
votes
0answers
20 views
Aggregate CES Cobb-Douglas utility over different individuals
Suppose I have a CES Cobb-Douglas Utility function:
$$U_i=X^{\alpha_i} Y^{1-\alpha_i}$$
Can I add utilities of different individuals meaningfully? I.e, where people have different $\alpha_i$.
$$\...
