Questions tagged [consumer-theory]
the study of consumer choice and its fundamental underpinnings in preferences and constraints.
464 questions
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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:
$$
p_t = E_t\left[\beta \frac{u'(c_{t+1})}{u'(c_t)}p_{t+1}\right]
$$
...
- 111
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43
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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 ...
- 69
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answer
38
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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), ...
- 13
2
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1
answer
148
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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 ...
- 69
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67
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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 ...
- 21
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1
answer
37
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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}...
- 11
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28
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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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16
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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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2
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447
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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
$$
U(x_1, y_1) + \beta U(x_2, y_2)\ .
...
- 297
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1
answer
67
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Infinite marginal utility for vanishing consumption: Is this always true?
I am considering a utility function over a single good for an intertemporal allocation problem. The class of power utility functions
$$
u(x) = \frac{x^\gamma}{\gamma}
$$
where $\gamma < 1$, $\gamma ...
- 297
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1
answer
74
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What is the point of Slutsky and Hicksian Compensation. And What to they have to to with WARP?
I am currently working through a Advanced Microeconomics textbook by Muñoz-Garcia for a upcoming class. I am very confused about the idea of compensation in which we take away wealth in price ...
- 3
2
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1
answer
123
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Shape of the contract "curve"
In the edgeworth box model, is the pareto set / contract curve necessarily shaped like a monotonically increasing function? This seems to be stated / implied in various places (such as Wikipedia), but ...
- 123
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0
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43
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To what extent are people's preferences quasilinear?
In many economic models (e.g. in auction theory, as well as fair division), it is common to assume that the agents' preferences are quasilinear, that is, their utility to a bundle of items and money ...
- 3,115
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50
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Implications of assuming quadratic utility; the search for an alternative
In this answer, I was pointed to the utility function
$$
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 ...
- 297
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votes
1
answer
86
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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 $...
- 129
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120
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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 ...
2
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1
answer
85
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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$.
...
- 223
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vote
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answer
37
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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 ...
- 2,084
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1
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89
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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$, ...
- 223
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vote
2
answers
74
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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 ...
- 53
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0
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38
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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{...
- 223
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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 ...
- 25
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votes
1
answer
426
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 ...
- 23
3
votes
1
answer
331
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 ...
3
votes
1
answer
80
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: (\...
- 191
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vote
1
answer
75
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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 ...
- 11
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0
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38
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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
...
- 1,633
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0
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50
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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 ...
- 11
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1
answer
57
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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 ...
- 834
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0
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28
views
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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1
answer
80
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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 ...
- 1
4
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1
answer
343
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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 ...
- 505
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1
answer
103
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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?
5
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1
answer
205
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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 ...
- 105
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0
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22
views
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 ...
- 288
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votes
1
answer
438
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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 ...
- 105
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votes
1
answer
276
views
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 ...
- 105
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votes
0
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121
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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 ...
- 223
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vote
1
answer
91
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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 ...
- 223
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2
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200
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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 ...
- 45
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61
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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 ...
- 11
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vote
0
answers
25
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 ...
- 11
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votes
0
answers
47
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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 ...
- 21
1
vote
1
answer
69
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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
...
- 11
1
vote
1
answer
128
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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 ...
- 297
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1
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187
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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 ...
- 297
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63
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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 ...
1
vote
2
answers
487
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 ...
- 13
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1
answer
81
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,
- 21
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1
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108
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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 ...
