Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
464 questions
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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 ...
CommunityBot
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Consumption based asset pricing - covariance of consumption and returns impact on asset price
I'm reading about consumption based asset pricing model. I don't fully understand a basic equation below.
Let's start with the law:
$$
p_t = E_t\left[\beta \frac{u'(c_{t+1})}{u'(c_t)}p_{t+1}\right]
$$
...
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Walrasian demand from indirect utility
In chapter 3, Section 3.G(Page no.73, 2'nd paragraph) of Microeconomic Theory by Andreu Mas-Colell, Whinston and Green the author argued that unlike the Hicksian demand function that can be derived ...
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Difficulty understanding steps in optimal taxation derivations
I am replicating the derivations from the paper Environmental policy, public finance and the labour market in a second-best world (Bovenberg & van der Ploeg, Journal of Public Economics, 1994), ...
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Negation of WARP
I wanted to write the negation of WARP.
The following is the definition of WARP from Microeconomic Theory by Andreu Mas-Colell, Whinston and Green:
The Walrasian demand function $x(p,w)$ satisfies the ...
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Are weakly monotonic preference and strictly monotomic preference the same?
Recently I am reviewing preference theory and I found that I am confused about the difference between weakly monotonic preference and strictly monotonic preference.
Now, let us suppose $X$ is the ...
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Under what conditions would a quasilinear utility function in a function form exhibit diminishing marginal rate of substitution?
Let the utility function be: $U(x_1,x_2) = x_1 + x_2^\alpha$.
Diminishing MRS requires $\frac{dMRS}{dx_1} <0$, however, taking this derivative results in 0, as $MRS = \frac{1}{\alpha x_2^{\alpha -1}...
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How does a lack of incentive to purchase new stuff affect economics?
How does a lack of incentive to purchase new stuff affect economics?
I've perceived as if a lot of economics is rooted in the idea of continued innovation and consumption, but then I've realized that ...
CommunityBot
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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 ...
CommunityBot
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Marginal value curve is the inverse of demand function
From Introduction to Economic Analysis by McAfee and Lewis. They write that:
the marginal value curve is the inverse of the demand function, where the demand function gives the quantity purchased at ...
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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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Two-period two-good optimal consumption problem
I'm trying to solve a two-period two-good consumption problem. Endowment in the two periods is $w_1$ and $w_2$, the interest rate is $\rho$, and total utility is
$$
U(x_1, y_1) + \beta U(x_2, y_2)\ .
...
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If both goods are considered economic goods in the economy, then how can their demand be negatively sloped when in a state of satiation or bliss?
if both goods are economic bad, then we can say that they have a negatively sloped demand curve. But how can we say the same for economic goods in a state of satiation or bliss?
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Infinite marginal utility for vanishing consumption: Is this always true?
I am considering a utility function over a single good for an intertemporal allocation problem. The class of power utility functions
$$
u(x) = \frac{x^\gamma}{\gamma}
$$
where $\gamma < 1$, $\gamma ...
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What is the point of Slutsky and Hicksian Compensation. And What to they have to to with WARP?
I am currently working through a Advanced Microeconomics textbook by Muñoz-Garcia for a upcoming class. I am very confused about the idea of compensation in which we take away wealth in price ...
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Shape of the contract "curve"
In the edgeworth box model, is the pareto set / contract curve necessarily shaped like a monotonically increasing function? This seems to be stated / implied in various places (such as Wikipedia), but ...
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To what extent are people's preferences quasilinear?
In many economic models (e.g. in auction theory, as well as fair division), it is common to assume that the agents' preferences are quasilinear, that is, their utility to a bundle of items and money ...
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Proof that if the MRS is increasing in one good, then the other is normal
Osborne and Rubinstein (Models in Microeconomic Theory, p. 70) prove the proposition that, if the demand function of a rational consumer has the property that $\text{MRS}(x_1, x_2)$ is increasing in $...
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Implications of assuming quadratic utility; the search for an alternative
In this answer, I was pointed to the utility function
$$
U(c, y) = c - \frac{c^2}{2} + y
$$
with corresponding demand function
$$
c(p) = 1 -p
$$
which is inelastic for $p < 1/2$. Something that ...
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Can Giffen goods not be inferior goods?
I was asking myself why is a Giffen good an inferior good and I read the following post : Difference between Giffen and inferior goods. Why aren't all inferior goods Giffen goods?.
The 2nd comment ...
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Do standard consumer theory axioms rule out corner solutions?
By standard consumer theory axioms I mean (1) completeness, (2) transitivity, (3) continuity, (4) non-satiation, and (5) strict convexity of the indifference curves.
If these axioms are not sufficient ...
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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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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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Conflicting Definitions of Weak Monotnocity (preferences)
Strong Montonicity my sources seem to agree on Strong monotonicity, i state equivalent definitions below. But weak montonicity i keep finding what appear to be conflicting definitions. In the ...
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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$.
...
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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 ...
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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 ...
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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$, ...
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Continuous rational and monotone preference relation implies $x\succsim0$?
I updated my proof to a general version as follows: please share your thoughts & 2cent. Thanks
Show a monotone continuous complete preorder on $\mathbb{R}^L_+$ has $y\geq x\rightarrow y\succsim x$....
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(Preference Relation/Set) Continuous $\succsim$ imply closedness of upper and lower contour sets
[ADDED/MODIFIED] : I have put my proof where the commodity space is simply $\mathbb{R_+}$(e.g. nonnegative reals) for simplicity below. Please share your 2 cent. I have put words to aid my own ...
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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{...
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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 ...
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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 ...
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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: (\...
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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 ...
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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 ...
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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
...
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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 ...
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Equivalent of shephard's lemma in consumer theory
I'm studying micro from the Mas-Colell, and I'm trying to understand the proof 2 of proposition 3.G.1. It is about proving that the derivative of the expenditure function w.r.t. the price of a ...
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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 ...
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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 ...
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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 ...
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1
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Proof for Marshallian Demand function
If you have a Marshallian demand function that is strictly convex, then it satisfies WARP.
How to prove this?
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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 ...
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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 ...
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4
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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 $u(x) = \min\{x_1, x_2\}$, but the addition of $x_3$ confuses me.
Problem
Derive the demand function $x(p,w)$ from $u(x) = \min\{x_1, x_2\} + x_3$.
What I ...
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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 ...
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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 ...
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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 ...
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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 ...
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