Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
308
questions
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23 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
78 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
41 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
61 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
26 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
38 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 ...
-2
votes
1answer
27 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
104 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
79 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
66 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
41 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
30 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
44 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
39 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
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0answers
18 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
63 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
228 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
105 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
66 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
433 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
100 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 = $ ...
2
votes
1answer
51 views
Lotteries = probability distribution?
Are "lotteries" in the model for choice under uncertainty not just probability distributions?
3
votes
1answer
41 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
25 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
84 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
45 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
34 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
120 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
226 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
126 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
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0answers
17 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}$$
Can I add utilities of different individuals meaningfully? I.e, where people have different $\alpha_i$.
$$\...
0
votes
0answers
24 views
Soft Question: Econometric model recommendation - covid situation and supermarket sales
I am interested in modelling the impact of the current covid pandemic on supermarket sales (in a specific country in Europe) as part of my bachelor's thesis (next year), however, I am having a hard ...
0
votes
1answer
25 views
How has decreasing quality (or the need to pay more for the same quality) tracked with inflation?
I'm trying to identity a missing variable that could affect poor and middle class consumers more than more wealthy/resourceful individuals.
Assuming that there are decisions regarding cost reductions ...
0
votes
0answers
42 views
Relationship between strictly convex preference and convex preference
Let X be a convex subset of linear topological space and let binary relation >=
be a complete preordering.
prove: If preference relation is strictly convex and continuous, then it is convex.
Since ...
0
votes
0answers
15 views
Optimising behaviour for labour supply
Suppose someone has an uncompensated labour supply schedule h(w,m)=A+Bw+Cm where h is hours of work, w is real wage rate and m is real unearned income. What are the requirements for optimising ...
-2
votes
1answer
76 views
Cobb-Douglas function homotheticity
I've been given the Cobb-Douglas utility function:
$\ u(q_1, q_2)=a\ln q_1+b\ln q_2=q_1^aq_2^b \ $
If I want to prove homothetic preferences, I use the following condition:
$\ u(\lambda q_1, \...
0
votes
1answer
81 views
How do I derive the aggregate demand function given two utilities functions?
Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$.
...
3
votes
1answer
35 views
Empirical tests for symmetry of cross-price elasticities
It is a well known fact in consumer theory that for a Hicksian demand curve the cross-price elasticity of good $i$ with respect to the price of good $j$ equals the cross-price elasticity of good $j$ ...
0
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0answers
35 views
On Demand Functions and Engel Curves
A consumer has utility function $U(x,y)=(x−2)y$, where $x≥2$ and $y≥0$. The price of $x$ is $P_x$, the price of $y$ is $P_y$ and the consumer's income is $I>2P_x$. ($x$ and $y$ do not have to be ...
-1
votes
1answer
49 views
Minimizing consumption in a single market( Partial Equilibrium)
Let there be a good X where the optimal consumption is 0; i.e the social costs for any unit provided would always be greater than the utility surplus of the market.
We know that prohibiting it( ...
1
vote
1answer
106 views
Example of a utility maximization problem with a non-binding budget constraint
Given a utility function $U(x,y): \mathbb{R}^{2} \to \mathbb{R}$, the general utility maximization can be stated as follows:
$$
\max_{x, y} U(x,y) \text{ s.t. } p_{x}x + p_{y}y \leq m
$$
where the $...
1
vote
1answer
66 views
Why can utility functions be continuous, and what does this imply for marginal utility?
I am studying microeconomics at the introductory undergraduate level and two related but distinct questions are puzzling me.
First, my textbooks express utility functions as continuous functions by ...
1
vote
0answers
42 views
Shortcuts for elasticity of substitution
How can I find the elasticity of substitution (I know the definition) if I know the utility function $u(x,y)$? I know its increasing in $x$ and $y$, etcetera, and has everything else you want from a ...
0
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0answers
155 views
On shapes of indifference curves
I encountered this question in Microeconomics by Pindyck and Rubinfeld.
The question says that "Suppose Jones and Smith have each decided to
allocate $1000 per year to an entertainment budget
in the ...
0
votes
1answer
83 views
Budget Constraint in Utility Maximisation Problem with Lagrange Multipliers
Lets say we have a utility function $U: \mathbb{R}^{2} \to \mathbb{R}$ given by $U(x,y)$ and a binding budget constraint $p_{x} x + p_{y} y = m$, where $p_{x}, p_{y}$ are prices of goods $x,y$ and $m$ ...
0
votes
1answer
28 views
Optimizing Lagrangian Function Subject to 4 Input/Output Constraints:
The objective function:
$$\text{utility}=U\left(x_{c}, y_{c}\right)$$
subject to,
$x_{o}=f\left(y_{i}\right)$
$y_{o}=g\left(x_{i}, x_{o}\right)$
$x_{c}+x_{i}=x_{o}+x^{*}$
$y_{c}+y_{i}=y_{o}+y^{*}$
...
1
vote
1answer
83 views
How to find Marshallian demand of $u(x,y,z)=x+y^2+2z^2$?
Consider the utility function $u(x)=x+y^2+2z^2$. How to derive Marshallian demand for a consumer with these preferences?
