Questions tagged [consumer-theory]

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

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25 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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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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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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35 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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27 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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28 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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45 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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1answer
49 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
51 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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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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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
45 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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23 views

Optimizing Lagrangian Function Subject to 4 Input/Output Constraints:

The objective function: $$\text{utility}=U\left(x_{c}, y_{c}\right)$$ subject to, $x_{o}=f\left(y_{i}\right)$ $y_{o}=g\left(x_{i}, x_{o}\right)$ $x_{c}+x_{i}=x_{o}+x^{*}$ $y_{c}+y_{i}=y_{o}+y^{*}$ ...
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1answer
51 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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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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33 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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1answer
85 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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58 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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27 views

Change in Consumer Surplus with two goods

Suppose we have two goods, price changes in the two are independent; having seen this question I am considering why the change in total Consumer Surplus is the sum of the change in Consumer Surplus ...
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2answers
198 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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140 views

Are there any other rational preference relations without utility function representations, besides Lexicographic?

It seems like lexicographic isn't that "special". Like yes it is special in that supposing it has a utility function gives you a bijection from the rationals to the reals, but I mean unique in some ...
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279 views

Finding demand functions for an unusual utility function

I have a utility function: $U = x + \min\{x,y\}$ I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements? Also, what preferences ...
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20 views

Would households rather live in a world with or without the unemployment insurance?

Would households rather live in a world with or without the unemployment insurance? What is a good example of world in which unemployment insurance is seen as a benefit, and not a hindrance?
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59 views

Consumer Theory question [closed]

You plan to use the following specification for an empirical study: $$e_i = \alpha_i + \sum_{j=1}^{n} \beta_{ij}p_i + \gamma_iy +\delta_i, i=1,...,n$$ where $e_i$ is the consumer's expenditure on ...
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39 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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63 views

Log Utiliy Function Trick

I am watching Lecture 3 of Yale's Financial Theory Lecture (by John). At about minute 50 he explains something along this line (with reference to log utility functions). MUx/Px=MUy/Py And ...
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2answers
175 views

Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x1, x2\} + x3$

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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17 views

Index Theorem for Regular Infinite-Agent Economies

A formulation of the Index theorem states that for a regular economy: $\sum_{p | z(p) = 0, p_L = 1} index p = +1$ Does this hold for models with uncountably many agents?
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1answer
39 views

Prove that $h(p,u) = \nabla_p e(p,u)$ is implied by Roy's identity

I am struggling a bit with the math in my first graduate microeconomics course. I'm not sure if this belongs here. If it doesn't, please direct me to a more appropriate place. Below is one question ...
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CPI Bias with consumers using computers extensively

I was studying Microeconomics from Microeconomics by Pindyck and Rubinfeld where it was written that CPI calculated on Laspeyres index has overstated the cost of living for consumers who use computers ...
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1answer
87 views

Identifying utility function

I recently came across a utility function with min written at the start. I assumed that it was a case of a leontief utility function, and only after going ahead with the problem I found out that it is ...
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2answers
67 views

Indifference Curves and Preferences

Why are averages preferred to extremes on the same indifference curve? Doesn't everything along an indifference curve have the same preference?
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570 views

Difference between Engel curve and income expansion path

I was scrolling through many questions on this site about income offer path and it appeared to me that income offer path, income expansion path, engel curve all are different terms with same meaning, ...
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2answers
149 views

Set Theory Properties of the Budget Constraint

In Microeconomic theory, the budget constraint is defined by 4 distinct properties: It is Bounded Closed Convex Non-empty The 1. 2. and 4. are very straight forward and the benefits in terms of ...
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28 views

Difficulty Understanding CPI (Consumer Price Index)

Here's a question about CPI in my microeconomics text (Pindyck), which I don't seem to understand: The price of computers has fallen substantially over the past two decades. Use this drop in price ...
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1answer
40 views

Opportunity Cost effect on benefits

My question is the following: Let's say a person has two career choices. He would be succesful in both, but in one of them he is slightly better and thus he will do better. So let's say career A will ...
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2answers
100 views

Assumption of sufficient wealth in quasi-linear preferences

Whenever we talk about quasi-linear preferences, we assume that the consumer is sufficiently wealthy. As far as I understand is that we need that assumption in order to obtain an interior solution. ...
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1answer
153 views

Is there a proof for composite commodity theorem?

I have been reading Economics and Consumer Behavior by Angus Deaton and John Muellbauer, specifically reading up on Composite Commodity Theorem, which states: if prices move in parallel to each ...
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1answer
44 views

Asymmetric (in sign) cross-price derivatives in consumer-theory problem

I'm puzzled why, in the following optimal-choice problem, good $x$ depends on price $p_y$ but the opposite is not true. Should not the sign of $\frac{\partial x}{\partial p_y}$ be the same of $\frac{\...
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122 views

The mathematical proof of a monotonic utility transformation does not restrict the use of strictly decreasing monotonic functions. Why bar them?

I understand from an intuitive sense that decreasing monotonic transformations will skew the choices and ordinality. But mathematically the $F'(U(x,y))$ just cancels out each other out in numerator ...
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1answer
61 views

A weaker definition of local non-satiation can also imply indifference “curve”

Let $u$ be a continuous utility function on $\mathbb R^2_+\setminus\{0\}$. Consider the following three conditions: Local non satiation says that for any $x \in X$ and $\epsilon > 0$, there exists ...
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83 views

What is the iff condition for a preference with linear Engel curves (all Engal curves are linear)?

If we restrict the consumption at $\mathbb R_+^n$, then it seems like we are implicitly assuming that the Engel curve pass through the origin, so the iff condition would be homothetic preference. ...
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54 views

Household utility functions

In basic consumer theory, there is an individual consumer who has a utility function, this function induces the individual's demand (given budget and prices), and this in turn determines the ...
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56 views

Finding the optimal consumption bundle given the strictly concave utility function $v(x,y) = U(x) +y$?

I am also finding it difficult to understand what are the fundamental differences between analysing optimal bundles between concave and convex functions ? Does it also happen that the optimal bundle ...
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How can i determine the homogeneity degree of Stone Gaery function? [closed]

I dont know how to demonstrate homogeneity degree of this function $(X-\alpha)^{\beta}(Y)^{1-\beta}$ Any idea? Thanks.
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Do you know any paper that discuss the effect of the deterrence of fines of individuals' behaviours? What is the difference between a fine a fee?

According to Gneezy and Rustichini the presence of an extrinsic reward in activities with a level of intrinsic motivation (e.g. volunteering) reduces intrinsic motivation, thus it may determine ...
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2answers
71 views

Market baskets: cross-border comparisons

The concept of a market or consumer basket is quite intuitive. I assume a market basket for a given country tells for which goods an average person spends how much of her money. To be able to compare ...
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3answers
100 views

Is the price-quantity diagram fundamentally wrong?

I have wondered about the following diagram: which shows a relationship between Price (Preis) and quantity (Menge). The supply (Angebot) curve is rising with the amount; the demand (Nachfrage) is ...
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1answer
26 views

Substitution effect when price of both goods change by the same percentage

I am trying to grasp the concept of income- and substitution effects. The way, I've understood it, the decomposition bundle is found, at the original indifference curve, where the slope equals that ...
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21 views

How are preferences related to relative prices?

For instance, across regions of a country or between countries. Is that different preferences for food lead to distinct relative prices in different regions or countries? Or is it the other way ...

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