Questions tagged [consumer-theory]

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

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44 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) $\sum_{i=1}^{n}a_i\in (0,K)\;\;\;$ ...
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+200

Piracy/File sharing - Why aren't songs, movies or books given for free?

Question: Why aren't songs, movies or books given for free (+ads)? i. Sub-question Every minute, people are pirating and there is no stopping that. If people see 0.99 for a song on iTunes and 0.00 ...
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1answer
59 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 $y$. ...
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1answer
48 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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1answer
35 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 ...
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3answers
100 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 ...
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2answers
107 views

Is there any evidence for consumer utility-maximising behaviour, at individual or market level?

Even though utility maximisation is ubiquitous in economic textbooks to model consumer behaviour, its usefulness is rarely demonstrated by evidence. Is there any evidence that some consumers do ...
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1answer
223 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 ...
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3answers
208 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 ...
3
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1answer
33 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 $j$ ...
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2answers
92 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 = $ ...
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1answer
27 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 ...
2
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1answer
44 views

Lotteries = probability distribution?

Are "lotteries" in the model for choice under uncertainty not just probability distributions?
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1answer
21 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 $U(x):R^n \longrightarrow R$ ...
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2answers
68 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\...
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0answers
16 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 ...
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1answer
19k views

Gross substitutes vs. net substitutes

Wikipedia explains the difference between products that are "gross substitutes" and products that are "net substitutes". However, the mathematical explanation doesn't give much intuition about these ...
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1answer
92 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 ...
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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 ...
3
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1answer
108 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 ...
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1answer
21 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 ...
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1answer
214 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 ...
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2answers
213 views

Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x_1, x_2\} + x_3$

I know how to solve the two-good case with $u(x) = \min\{x1, x2\}$, but the addition of $x3$ confuses me. Problem Derive the demand function $x(p,w)$ from $u(x) = \min\{x1, x2\} + x3$ What I did ...
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2answers
7k views

How to derive utility possibility frontier?

I'm trying to derive the utility possibility frontier of a economy whose consumption contract curve is $$y_A = \frac {y} {x} x_A$$ and $$y_B = \frac {y} {x} x_B$$where $x_A + x_B = x$ and $y_A + y_B= ...
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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 ...
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0answers
14 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 $\alpha_i$. $$\...
3
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1answer
99 views

Consumer Utility Maximization equivalent of economies of scope

Economies of scope captures the idea of having efficiency in variety. I've come across this idea only in producer theory to capture the idea that companies may benefit from their ability to reduce ...
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1answer
219 views

Why is the marginal utility of money assumed to be constant in Marshallian Theory of Consumer Behaviour

While studying the Marshallian Theory of Consumer Behaviour, I came across the assumption that the marginal utility of money is assumed to be constant. Can someone please explain why is this so?
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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 ...
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0answers
33 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 ...
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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 ...
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1answer
45 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, \...
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0answers
30 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 ...
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1answer
47 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( ...
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2answers
109 views

Utility Functions: Implying endless consumption?

Do utility functions imply that if a consumer's income infinite, his consumption should also be infinite? The reason why I'd think this is the case is based on my basic understanding of utility ...
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1answer
70 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 $...
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1answer
59 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 ...
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2answers
630 views

Fast way to write out the utility optimization problem for a Cobb-Douglas function?

In my last problem set, I had to solve both the Utility Maximization Problem (UMP) and Expenditure Minimization Problem (EMP) for a Cobb Douglas utility function. Recall, Cobb Douglas is defined as $$...
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0answers
39 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 ...
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0answers
103 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 ...
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1answer
61 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 $m$ ...
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1answer
24 views

Optimizing Lagrangian Function Subject to 4 Input/Output Constraints:

The objective function: $$\text{utility}=U\left(x_{c}, y_{c}\right)$$ subject to, $x_{o}=f\left(y_{i}\right)$ $y_{o}=g\left(x_{i}, x_{o}\right)$ $x_{c}+x_{i}=x_{o}+x^{*}$ $y_{c}+y_{i}=y_{o}+y^{*}$ ...
3
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1answer
839 views

Intertemporal consumption question

This question is driving me nuts. Suppose, an individual lives for two periods. In each period she consumes only one good,which is rice. In period 2, she can costlessly produce 1 unit of rice, but ...
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0answers
208 views

MWG Example 3.E.1

I do not understand how Mas-Collel, Whinston, and Green derive the Hicksian demand functions in Example 3.E.1 in their textbook. Allow me to give further background regarding the problem: The ...
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1answer
56 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?
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25 views

weakly preferred consumer bundles

I am currently studying consumer choice and saw that weak preference refers to when an individual prefers or is indifferent to two bundles (such as bundle A and bundle B). I was wondering what is ...
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1answer
34 views

Is Buy Nothing Day a classist protest of Black Friday?

I hope this isn't off topic, it seems specifically economic to me even though it probably intersects with other fields of study. Black Friday is seen as an iconic hallmark of consumerism, and Buy ...
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2answers
220 views

Corner solution of the maximization problem

Answer Hello, I upload the actual question with my 8-pages answer. Please can you check it. Is there a corner dissolution for $c=\gamma$. Please share your ideas. Thanks.
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2answers
1k views

Utility function used to indicate bliss point

How does one create a utility function to indicate existence of a bliss point? what do the goods marshillian demands look like in such a situation?
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66 views

Special case for wealth allocation with quasilinear utility functions

Building on this question, regarding the answer from Bkay: Is it a general statement that when $m < \frac{p_y^2}{4 p_x}$, all income will be allocated to $x_M$? What about the case when the ...

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