Questions tagged [consumer-theory]

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

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43 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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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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68 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 $$p_x x_a+p_y y_a=e_a.$$ ...
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123 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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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
212 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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38 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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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 ...
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157 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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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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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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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
78 views

Approaches in demand analysis

What is the difference between Engel Curve and the system approach of demand analysis?
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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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39 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 ...
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1answer
254 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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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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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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363 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 ...
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551 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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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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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 ...
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73 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. ...
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320 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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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(...
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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
136 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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131 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}\}...
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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 ...
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149 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
78 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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49 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 ...
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2answers
442 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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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-\...
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108 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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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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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
38 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 ...
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116 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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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
2k 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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102 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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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90 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 ...
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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 ...
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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) ...
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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 ...

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