Questions tagged [consumer-theory]

the study of consumer choice and its fundamental underpinnings in preferences and constraints.

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30 views

Arguments of the Marshallian demand system of a Cobb-Douglas utility function

For a utility function of the form $U(x_1,x_2) = x_1^\alpha x_2^\beta$ and the standard budget constraint, the utility maximisation problem gives us a demand system characterised by: $x_1(\alpha, \...
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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, ...
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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 ...
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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)). ...
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2answers
201 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 ...
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1answer
76 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 ...
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3answers
176 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 ...
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1answer
68 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 ...
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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\...
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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 ...
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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 ...
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1answer
75 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
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1answer
134 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. ...
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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 $...
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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 ...
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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 ...
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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
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1answer
271 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 ...
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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-...
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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{*} ...
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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 ...
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1answer
82 views

Approaches in demand analysis

What is the difference between Engel Curve and the system approach of demand analysis?
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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 ...
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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
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1answer
407 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_+...
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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 ...
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0answers
130 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 ...
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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
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2answers
572 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 ...
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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'...
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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
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1answer
91 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
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1answer
506 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 ...
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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
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2answers
112 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 ( \...
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1answer
198 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 ...
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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
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1answer
81 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
179 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{...
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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 ...
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1answer
58 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
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2answers
453 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 ...
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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
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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,...
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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.
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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 ...
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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
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1answer
187 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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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 ...
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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 ...

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