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Questions tagged [consumer-theory]

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

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Equivalence of two definitions of monotone preference

In MWG, the definition of weak preference is for all $x,y \in X$, $y>>x$ implies $y\succ x$ . But I have read some other articles that define weak preference as $y\geq x\implies y\succeq x$. ...
Nonenicht's user avatar
1 vote
1 answer
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Trying to find a proof for Strong Axiom of Revealed Preference with general choice set

Note this is question is not about consumer demand with price and income data. This is a question about general choice theory. For reference, see: https://www.jstor.org/stable/2550390 See Debreu's ...
High GPA's user avatar
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Prove a preference preserved under limits if and only if its upper and lower contour is closed

I'm concerned with the reverse direction, that upper and lower contour is closed implies the preference is continuous, that is for any sequence $x_n$ and $y_n$, $x_n\succcurlyeq y_n$ for all $n$, ...
Nonenicht's user avatar
1 vote
2 answers
57 views

Does duality hold for u(x, y) = x^2 + y^2? (Corner solution)

Could you please help me evaluate this logic? I've been told that "if preferences are strongly monotonic, duality holds." In the case of utility u(x,y) = x^2 + y^2, we will get a corner ...
Martin's user avatar
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Equivalence of two definitions of revealed preference

Given a choice structure $(\mathscr{B},C(.))$ we can construct a preference align with this structure, write it as $\succcurlyeq^C$ defined as $$x\succcurlyeq^C y\Leftrightarrow \exists B \in \mathscr{...
Nonenicht's user avatar
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20 views

consumption, income and utility

Question Description: Consider an economy populated by a large number of Farmers (F) and Computer Scientists (CS). Each person divides his 24-hour day into labour and leisure. If a Farmer decides to ...
ZZZ's user avatar
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2 votes
1 answer
409 views

How do I measure well-being without Utility function?

This is a question from a test: "A consumer with \$1000 income spends \$200 on good X per month. His income increases to \$1100, and price of good X increases 50%, with no other price changes. In ...
calavera's user avatar
3 votes
1 answer
88 views

Consumer surplus calculation

Suppose $P(Q) = 10-0.5Q$. If a firm is producing $q_1$ and $q_2$ units from its two different machines such that $Q = q_1 + q_2$, what is the consumer surplus at $(q_1, q_2)$? I think the consumer ...
consumer-surplus's user avatar
3 votes
1 answer
53 views

When are marginal rates of substitution consistent with a utility function?

Is it known when a marginal-rate-of-substitution function can be rationalized by some utility function? More precisely, and focusing on the case of two goods, what conditions are required on $M: (\...
John Sturm's user avatar
1 vote
1 answer
48 views

Finding Utility Function for Optimal Allocation in Consumer Choice Model

I'm working on a consumer choice model involving a consumer with one good and a numeraire. In this model, the price of the numeraire is assumed to be one. My objective is to identify the utility ...
lucas_vivier's user avatar
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Why do revenue neutral taxes result in a change in behaviour

Suppose we have the following utility function defined over two commodites, $c_{1}$ and $c_{2}$. The function is: $$ U\left(c_{1},c_{2}\right)=\ln\left(c_{1}\right)+\ln\left(c_{2}\right) $$ subject to ...
ChinG's user avatar
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1 vote
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Monotonicity of Concave Indifference Curves

I'm doing an intermediate micro course, and we've been given a problem asking to draw curves that correspond to the utility function with the expression of a circle centred at (3,4). I understand that ...
mayu's user avatar
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1 answer
32 views

Simultaneously a substitute and a complement (validity of a claim)

I have read the following claim: Sometimes the relationship between products can be both substitute and complement; that is, two products may be complements for one purpose but substitutes for ...
Athaeneus's user avatar
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How to aggregate goods with different units of measurement to reduce the economy with a Cobb Douglas utility function?

I want to model a economy where consumers have a Cobb Douglas utility function and where X1 = goods that pay a value added TAX (VAT), and X2 = goods that are exempt from this tax. I am working with ...
Santiago Valdivieso's user avatar
0 votes
1 answer
45 views

Confusion regarding the Slutsky equation

I'm reading Henderson and Quandt's Microeconomic Theory textbook and in the derivation process of the slutsky equation the final formula confused me a bit. The first term on the right of the equation ...
Adnan's user avatar
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4 votes
1 answer
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Prove: The law of demand holds if WA, Walras' law, homogeneity of degree 0, and homogeneity of degree 1 in wealth hold for Walrasian demand functions

Problem I am asked to prove the following result (MWG Exercise 2.F.5): The law of demand always holds if the walrasian demand function $x(\mathbf{p},w)$ satisfies the weak axiom of revealed ...
Beerus's user avatar
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Varian Analysis Non satiation question

Consider preferences defined over the nonnegative orthant by (xl,x2)> (yl,y2) if X1 + X2 < y1+ y2. Do these preferences exhibit local nonsatiation? If these are the only two consumption goods ...
Chavi Dusad's user avatar
2 votes
1 answer
59 views

Proof for Marshallian Demand function

If you have a Marshallian demand function that is strictly convex, then it satisfies WARP. How to prove this?
babededeeptido's user avatar
5 votes
1 answer
90 views

Question on Isolating The Wealth Effect in Analysis of Changes in Price-Wealth Combinations - MWG Exercise 2.F.3 Parts (e) and (f)

I am doing exercises in Chapter 2 of MWG. I feel I got completely lost in exercise 2.F.3 parts (e) and (f). $\textbf{Exercise}$ Here is the question: I have solved parts (a) to (d). In particular, I ...
Shenron's user avatar
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Does money illusion suggest Hicksian demand curves are more accurate?

I interpret "money illusion" to mean that consumers tend to falsely equate their nominal income or wealth to their objective utility level. If that is the correct interpretation, it seems to ...
UtilityMaximiser's user avatar
3 votes
1 answer
150 views

Question on The Weak Axiom of Revealed Preference and The Definition of Revealed Preference Relation

I am solving the following problem (from Exercise 2.F.3 (b) in MWG) and I got confused by the weak axiom of revealed preference and the definition of the revealed preference relation. Here is the ...
Shenron's user avatar
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2 votes
1 answer
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MWG Exercise 2.E.5

Exercise Suppose that $x(\mathbf{p},w)$ is a demand function which is homogeneous of degree one with respect to $w$ and satisfies Walras' law and homogeneity of degree zero. Suppose also that all the ...
Shenron's user avatar
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0 answers
79 views

substitution effect in slutsky equation

We know Slutsky equation decomposes the price effect into substitution effect and income effect, where the substitution effect is the partial derivative of Hicksian demand function against the change ...
Nonenicht's user avatar
1 vote
1 answer
54 views

Does utility representation theorem need locally-nonsatiated as a condition?

I'm reading MWG's Microeconomics, and I'm a bit confused about the utility representation theorem. It states that a rational and continuous preference relation can be represented by a continuous ...
Nonenicht's user avatar
1 vote
2 answers
99 views

Negative marginal utility and negative marginal product

In microeconomics, we usually 'allow' utility functions with negative partial derivatives, indicating a 'bad' commodity, such as $u(x,y)=x^2-y$. Naturally, a utility-maximising consumer with a usual ...
AcadEconInd's user avatar
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0 answers
24 views

What does GARP in revealed preferences mean and how to regocnize it graphically?

I have a froblem understanding GARP in revealed preferences. I know what WARP means, and that SARP adds transivity such that it allows for indirect preferences, but what about GARP? How can you ...
EcoSTUD233's user avatar
1 vote
0 answers
20 views

Calculate consumers WTP for product attributes

I have a large panel on the city level of how many cars of each {model, fueltype} combination were newly registered in each year. This panel also includes a large variety of characteristics for each ...
rösti23's user avatar
2 votes
0 answers
32 views

Substitutable preferences vs. gross substitutes over indivisible items

I don't really have a background in economics. I'm trying to understand the relationship between these two terms, if they are related at all. The definitions that I understand are here: Substitutable ...
AWhite's user avatar
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1 answer
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Vertical income expansion path: explanation?

On the horizontal axis we have good x, on the vertical axis good y. The income expansion path is vertical. Which of the following assumptions is wrong? no homotheticity no strong monoticity ...
EcoSTUD233's user avatar
1 vote
1 answer
78 views

Example of a utility function which yields inelastic demand function

I am looking for a example of a utility function which, when the utility maximisation problem is solved, results in an inelastic demand. The standard examples in textbooks always seem to have unitary ...
Anthony's user avatar
  • 215
1 vote
1 answer
152 views

Utility function for a combination of a normal good and necessary good

I am trying to formulate a decision problem for an agent involving their heating-energy consumption $c$. Let $x$ denote all other consumption. What would be a reasonable utility function to employ ...
Anthony's user avatar
  • 215
0 votes
1 answer
40 views

Showing UMP and EMP do not exhibit duality if the assumption of local non-satiation is absent

I have been trying to use the contradiction method to prove this, but it does not seem to be working. Suppose $x^*$ is optimal in both EMP and UMP. Then $u(x^*) \geq u(x')$ for all $x'$ in $B_pw$. And ...
pacmanscuriousbloob's user avatar
1 vote
2 answers
281 views

Marshallian demand for x^2+y^2

My question is regarding a simple marshallian demand calculation. Given a utility function $u(x,y)=x^2+y^2$ and a budget constraint $p_1x+p_2y=m$. What are the Marshallian demand functions for each x ...
Neil B's user avatar
  • 13
1 vote
1 answer
41 views

Change in Hicksian Demand of an Inferior Good when changing Utility

How can you rigorously show that Hicksian demand for an inferior good will decrease when utility increases? Thanks,
Peter Luu's user avatar
0 votes
1 answer
76 views

Exponential Income Consumption Curve

From the Engel's Law we know that as income increases the share of income spent of foods decreases and the share of income spent on luxury goods increases. I wanted to represent this using Consumer ...
João Maria's user avatar
2 votes
0 answers
53 views

Estimating the form of a utility function on two or more commodities

I am looking for experiments for estimating the form a utility function of a consumer on two or more commodities. In particular, I would like to know e.g. if the utility function of a consumer is of ...
Erel Segal-Halevi's user avatar
1 vote
2 answers
127 views

Reservation price and demand curve

Q1: There are $25$ consumers with each demanding 1 unit and each consumers' valuation of the product is $10$. How would the demand curve look like. Q2: Now suppose there's a monopolist with $MC=8$ and ...
hr08's user avatar
  • 25
0 votes
0 answers
22 views

Consumer optimization problems with multiples cases

Does anyone know of any resources where the Lagrangian optimization of the consumer problem with one constraint has two cases for an answer? For example, when income is greater than x, the optimal ...
GraceLynn87's user avatar
1 vote
1 answer
395 views

The sufficient condition for unique interior solution in utility maximization problem

Suppose the utility function is continuous, differentiable, strictly increasing and strictly quasiconcave. Whether the utility maximization problem has unique interior solution? If not, is there any ...
23134's user avatar
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0 votes
0 answers
65 views

Cobb Douglas Indirect Utility/Expenditure continuity proofs

How should I go about proving that the general Cobb Douglas indirect utility function and expenditure functions are continuous? There are many ways to prove continuity, but which would be the easiest? ...
GraceLynn87's user avatar
0 votes
0 answers
41 views

Intertemporal consumption with heterogeneous/multiple goods

I'm currently trying to build a CGE, and I'm stuck at the household's problem which is about intertemporal utility maximisation. The household consumes multiple heterogeneous goods $C_i$ (I'm limiting ...
Meg's user avatar
  • 31
3 votes
1 answer
49 views

Consumer theory with subproblem

Say the agent's problem is $$\max_{c,\{h\}, N}\{U(c, v(\boldsymbol{h} ; \boldsymbol{\theta}))+\lambda(w N-c)\}$$, subject to $\sum_{i=1}^{I} h_{i}+N \leq 1, \quad N \in \mathcal{N}$. Assume $U(c, v(\...
Alalalalaki's user avatar
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3 votes
1 answer
56 views

$H$ is a constant? Maximizing: $\int _0^Te^{-t}f(x,u)dt$ st $x_t=g(t,x,u)$ and $g$ is independent of $t$

$\max_{x(t),u(t)}\int _0^Te^{-t}f(x(t),u(t))dt$, st derivative $x_t=g(t,x(t),u(t))$. Prove that $H$ is constant. My try2: consider the Hamiltonian $$ H(x(t), u(t)) = e^{-t}f(x(t), u(t)) + \lambda(t) g(...
dodo's user avatar
  • 293
1 vote
1 answer
48 views

Give bundles $x,y\in \mathbb R^n$, there must exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$?

For a problem in revealed preference. Give bundles $x,y\in \mathbb R^n$, must there exist a budget $B\supset\{x,y\}$ and a demand $D(B)\in[x,y]$? Intuitively, this mean that we have two bundles, and ...
dodo's user avatar
  • 293
1 vote
1 answer
218 views

Paradox of 'more quantity means greater satisfaction' in consumer behavior

I am trying to understand consumer behavior in microeconomics. Consider a market basket of food and clothing. Utility / Satisfaction of 200 gram food + 2 shirts is always supposed to be greater than ...
prabhas's user avatar
  • 11
0 votes
1 answer
34 views

Consumption with quantity discount

A consumer has the utility function: u(x,y) = x*y his initial budget constraint is: 12 = 2x+ 1y. He has a budget of $12 for the whole question, which has to be completely used. so that he consumes 3 x ...
AJl's user avatar
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0 answers
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Properties of Consumer Preferences - Monotonicity

Was reviewing topics and I came across this question. I am confused because there is no reference to strict or weak monotonicity in this case. I first thought that monotonicity is violated b/c an ...
Sperbs's user avatar
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2 votes
1 answer
244 views

Reasons for why slutsky matrix may be non symmetric

In demand system estimation, theoretically we require this matrix to be symmetric. This unfortunately is not the case most of the time. What are some reasons for why symmetry of the slutsky matrix may ...
EconJohn's user avatar
  • 8,405
0 votes
0 answers
29 views

Convexity preferences

What is the difference between convexity and strict convexity preferences? What is the difference between quasi-concavity and quasi-convexity? And is MRS still true in concave preferences?
Huy Lê Thanh's user avatar
2 votes
1 answer
420 views

Utility Maximization of a quasi-linear utility function

I am dealing with a quasi-linear utility function. For example $U=(x_1x_2)^{0.5}+cx_3$ with constrain $w\ge x_1+2x_2+px_3$.By taking c, w and p as constant, I function that by using Lagrange ...
Paul Huang's user avatar

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