Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
344
questions
0
votes
1answer
42 views
What utility function represents an agent with a time-discount factor?
Consider an agent who has a fixed budget, and should decide how to split it between consumption today and consumption tomorrow. For simplicity, suppose there is no interest, and no borrowing/lending, ...
3
votes
1answer
76 views
Solve for the Walrasian demand, Utility of three variables, and Convexity of Preferences?
I am given $U(x,y,z) = x^\frac{2}{3}y^\frac{1}{3} + z$. I am asked to solve the following:
(i) Prove the convexity of these preferences (convex, strictly convex or neither?)
(ii) Solve for the ...
1
vote
1answer
40 views
MRS not invariant under monotonic transformation
Consider U(x, y) = ln(x)ln(y). Is it quasi-linear?
My response was no, since applying an exponential would yield exp(ln(x)ln(y))= exp(ln(x+y)) = x+y.
However, the original MRS was (y/x)(ln(y)/ln(x)). ...
2
votes
2answers
200 views
Violation of Monotonicity of preferences
Hi I am reading Jehle and Reny in my master's course and I have come across a problem in one of the exercises. My instructor herself was a bit confused when a student gave her a counter-example and ...
1
vote
1answer
75 views
Binary choices in consumer theory
Back when I was a teaching assistant, we were teaching utility theory and how it relates to price determination. So we were looking at continuous goods (e.g. "food") so as to get marginal ...
1
vote
3answers
174 views
Graphing indifference curves to visualize solutions?
I am having trouble with being able to graph indifference curves. This is a particularly important skill to have especially when trying to visualize corner solutions, and when the Lagrangian method ...
1
vote
1answer
66 views
Marshallian demand for Cobb douglas function [closed]
would like to just check how one can obtain the Marshallian demand for Cobb Douglas function such as u(x1,x2) = x1^a x2^(1-a) ?
Was attempting the question but got somewhat stuck trying to ...
3
votes
1answer
50 views
Existence of maximal element in a compact choice set
I have a compact subset of $\mathbb{R}$, $X$. An agent has a continuous, transitive and complete preference relation $\succsim$ over $X$. I am wondering whether there exists a $y\in X$ such that $y\...
1
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1answer
49 views
Optimal consumption for infinite number of periods and exogenous income
I have the following optimization problem:
$\max_{\{c_t, s_{t+1}\}} \Pi_{t=0}^\infty c_t^{\beta^t}$
$\text{subject to } \space c_t + s_{t+1} = y_t + (1 + r) s_t \text{ and } s_0 = 0$
How do I find ...
0
votes
1answer
84 views
Calculate income and sustitution effect from utility funcion
Utility function $U(x_1 , x_2) = x_1 + 4 * x_2 $
$ p_1 = 3, p_2 = 8, m =120 $
$p_2$ changes from $8$ to $10 $
How can I calculate the income and substitution effect.
I first thought about calculating ...
5
votes
1answer
73 views
Pigouvian tax with general utility function
Suppose person a's consumption of good $y$ imposes a negative externality on person b. Person a's utility maximisation problem is
$$\max_{x_a,y_a} \ u_a(x_a,y_a),$$
subject to
$$p_x x_a+p_y y_a=e_a.$$
...
3
votes
1answer
133 views
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. ...
0
votes
0answers
18 views
Finding the pigou tax that supports a pareto efficient allocation as walrasian equilibrium
I have a two consumer economy with utility functions $u_1=x_{12}-x_{21}$ and $u_2=x_{21}x_{22}$. I am asked to find the Pigou tax $t>0$ on agent 2's consumption of good 1, such that the allocation $...
2
votes
2answers
216 views
Proving local non-satiation in arbitrary metric space
I have a pure exchange economy where every consumption set $X_i$ is non-empty and convex and every preference relation $\succeq_{i}$ is strictly convex. I am asked to show that preferences are locally ...
0
votes
1answer
40 views
How come a representative consumer with quasilinear utility need not economize?
Suppose a representative consumer has the following quasilinear utility function:
U_i(x_1,x_2)=ax_1+ax_2-(1/2)*[(x_1)^2+(x_2)^2] + k
where a>0 is a utility parameter, x_1 and x_2 are the goods, and ...
-1
votes
1answer
50 views
Why do companies and stores never seem to take into consideration the fact that few people want ugly colours of the same product?
In 1997, I traveled far and wide to hunt down an original Tamagotchi. Whereas everyone else had one of the numerous clones, often with many more features, I had to have the real Tamagotchi. When I ...
4
votes
1answer
270 views
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 ...
0
votes
2answers
42 views
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
votes
0answers
39 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
74 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
votes
1answer
82 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
65 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
votes
0answers
42 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
401 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_+...
7
votes
1answer
165 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
votes
0answers
129 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
364 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 ...
4
votes
2answers
571 views
Does Modern Monetary Theory (MMT) provide a useful insight into how to manage the economy?
According to advocates of [Modern Monetary Theory][MMT] (MMT), the primary risk once the economy reaches full employment is inflation, which can be addressed by gathering taxes to reduce the spending ...
0
votes
0answers
36 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'...
2
votes
1answer
82 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
90 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
490 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
33 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(...
3
votes
2answers
110 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
196 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
159 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
80 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
177 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
132 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
57 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
452 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
votes
0answers
28 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
112 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
63 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
72 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
47 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
185 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
44 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
4k 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
103 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. ...
