Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
327
questions
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If I had a new economical theory, how could I share it with academical environments? I call it “algorythmic economy”
If I had a new economical theory, how could I share it with academical environments? I call it algorythmic economy.
I have made this same question on Quora.
https://www.quora.com/unanswered/If-I-had-a-...
0
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0answers
34 views
How to derive consumer expenditures in EMEA 14.2.5
I am working on a problem 14.2.5 from EMEA by Sydsaeter, Hammond and Strom.
Consider the consumer demand problem:
$$ \max_{x,y} U(x,y) = \alpha \ln(x-a) + \beta \ln(y-b) \text{ s.t. } px+qy=m \tag{*} ...
4
votes
1answer
61 views
Is an income tax always more favourable for consumers compared to ad valorem/quantity tax?
I'm studying the optimal choice of consumers with regards to taxation.
I read that for consumers, income tax is generally (for Cobb-Douglas preferences) preferred compared to ad valorem tax:
If the ...
2
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1answer
72 views
Approaches in demand analysis
What is the difference between Engel Curve and the system approach of demand analysis?
1
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1answer
54 views
Demand function for partially subsumable products
I am struggling with this question that should be simple for economists (I am not an economist at all):
There is a market with a limited number of (heterogenous) consumers with two firms, each ...
0
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0answers
34 views
How to calculate substitution and income effect when only 1 bundle is given?
I was given information of a consumer that initially consumed 4 units of both good x and good y with the initial price of $5 for both goods (px = py = 5).
The initial budget constraint is 40 = 5x +5y
...
2
votes
1answer
163 views
How to prove that a utility function U(x,y)=min(x,2y) is quasiconcave?
I have a question that asks:
"Let there be two goods 1 and 2.Let $x$ and $y$ denote their respective quantities.$(x,y)$ represents a bundle. Suppose a consumer’s preferences over bundles in $R^2_+...
6
votes
1answer
91 views
Interior Solution for profit maximisation problem
A function $c: \mathbb{R}^K_+ \xrightarrow{} \mathbb{R}_+$ is is said to be a cost function if
The value of function $c$ at $y = \textbf{0}$ is $0$: $c(\textbf{0}) = 0$
$c$ is continuous on the ...
4
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0answers
118 views
Looking for an universal utility function
I'm trying to build a computer simulation of an economy which separate simulation for each household and I'm trying to figure out what utility function should I use to model the households behavior. I ...
1
vote
2answers
362 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 ...
3
votes
2answers
510 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. ...
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31 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
57 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
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1answer
59 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
204 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
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0answers
31 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(...
2
votes
2answers
72 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
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1answer
97 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
115 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}\}...
4
votes
1answer
69 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
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2answers
120 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
39 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
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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
430 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
25 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
104 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
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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.
4
votes
0answers
68 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
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1answer
35 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
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1answer
77 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
30 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
1k 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
91 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
943 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
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1answer
45 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
50 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
67 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
21 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
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0answers
66 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
59 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
233 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
111 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
166 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
671 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
117 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 = $ ...
4
votes
1answer
52 views
Lotteries = probability distribution?
Are "lotteries" in the model for choice under uncertainty not just probability distributions?
3
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1answer
49 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
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1answer
30 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
96 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\...
